{ "schema": "will_cook_catalogue_graph_v2", "source_schema": "will_cook_site_family_v3", "updated": "2026-11-09", "about": "Generated from sites.json and glossary.json; not an authoring source.", "node_types": [ "area", "collection", "link", "paper", "person", "project", "repository", "term", "topic", "video", "website" ], "edge_types": [ "available_through", "evidence_for", "in_area", "in_topic", "introduces", "leads_to", "listed_in", "member_of", "related", "related_application", "related_term", "resource_for", "superseded_by", "supports_video_stage", "uses_term", "worked_example" ], "nodes": [ { "id": "person:will-cook", "name": "Will Cook", "home": "https://wcook04.github.io/", "lede": "I do mathematics research and build software with AI agents. I also build ways to inspect what the agents produce.", "contact": [ { "label": "Email", "href": "mailto:williamwkcook@gmail.com" }, { "label": "LinkedIn", "href": "https://www.linkedin.com/in/will-cook-278127234/" }, { "label": "GitHub", "href": "https://github.com/wcook04" }, { "label": "YouTube", "href": "https://www.youtube.com/@willcook2004" }, { "label": "X", "href": "https://x.com/cookie1234593" } ], "invitation": [ "I’m looking for a job, internship, fellowship or funding, and I’m open to working with other people on their problems. If there’s a problem you think I should work on, please email me.", "If something on these pages is unclear or wrong, please tell me. If your feedback leads to a change, I’d be happy to credit you, with your permission." ], "orient": "That means Lean proofs of AI-written mathematics, websites that display a paper beside its Lean code, and tools for running several coding agents in one repository. The introduction video explains how the projects fit together.", "availability": "I’m looking for a job, internship, fellowship or research collaboration.", "type": "person" }, { "name": "Maths Map", "short": "Maths Map", "purpose": "AI-assisted research on eight Erdős problems, with papers, records of failed approaches and Lean 4 proofs of partial results.", "status": "Each problem page states whether the original question is still open and which statements the Lean proofs cover.", "capture": "assets/sites/maths", "capture_caption": "Maths Map, open at Erdős problem #68.", "credit": "Seven original questions remain open. The #1041 formal-statement counterexample is due to ani. The papers are not peer reviewed.", "label": "Maths Map", "subject": "Eight Erdős problems", "tagline": "AI-assisted research on eight Erdős problems.", "summary": "Find a theorem, read its research record or shorter paper, and open its available Lean or Comparator record. The map includes partial results and open questions.", "line": "Browse results on eight Erdős problems, with paper links and available Lean checks.", "plain": "Find the results and papers behind eight Erdős problems.", "aka": [ "Plectis Mathematics" ], "id": "project:maths", "slug": "maths", "source": { "collection": "sites", "index": 0 }, "term_refs": [ { "field": "line", "term_id": "erdos-problem", "surface": "Erdős problems", "occurrence": 1 }, { "field": "line", "term_id": "lean-4", "surface": "Lean", "occurrence": 1 }, { "field": "plain", "term_id": "erdos-problem", "surface": "Erdős problems", "occurrence": 1 }, { "field": "summary", "term_id": "research-record", "surface": "research record", "occurrence": 1 }, { "field": "summary", "term_id": "comparator", "surface": "Comparator", "occurrence": 1 }, { "field": "summary", "term_id": "lean-4", "surface": "Lean", "occurrence": 1 } ], "type": "project" }, { "name": "SK Reader", "short": "SK Reader", "purpose": "Three explanations of OpenAI’s full-support theorem for the Sherrington–Kirkpatrick spin glass, linked to Lean declarations and an argument map.", "status": "The site lists each Lean build and the statements it covers. Comparator gave no verdict on either theorem.", "capture": "assets/sites/lean-exposition", "capture_caption": "The short paper at Theorem 1, beside the graph of its argument.", "credit": "The theorem and Lean proof are OpenAI’s. I made the explanations and links with AI; no mathematician has reviewed them.", "aka": [ "Lean Exposition" ], "label": "SK Reader", "subject": "Sherrington–Kirkpatrick spin glasses", "tagline": "Papers and an argument map for OpenAI’s Sherrington–Kirkpatrick result.", "summary": "Move between three AI-written papers, an authored argument map and linked passages of OpenAI’s Lean proof. The map explains the argument; it is distinct from a graph extracted from Lean declarations.", "line": "Read explanations of OpenAI’s Sherrington–Kirkpatrick theorem beside its Lean proof.", "plain": "Read a spin-glass result beside its computer-checked proof.", "id": "project:lean-exposition", "slug": "lean-exposition", "source": { "collection": "sites", "index": 1 }, "term_refs": [ { "field": "line", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 }, { "field": "plain", "term_id": "spin-glass", "surface": "spin-glass", "occurrence": 1 }, { "field": "summary", "term_id": "proof-graph", "surface": "argument map", "occurrence": 1 }, { "field": "summary", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 }, { "field": "summary", "term_id": "lean-4", "surface": "Lean", "occurrence": 2 }, { "field": "line", "term_id": "sherringtonkirkpatrick-model", "surface": "Sherrington–Kirkpatrick", "occurrence": 1 } ], "type": "project" }, { "name": "General Reader", "short": "General Reader", "purpose": "Read Contextual Embeddings (PLDI 2026) beside its authors’ Lean proof, with statement-to-code links and a graph of proof dependencies.", "status": null, "capture": "assets/sites/proof-reader", "capture_caption": "Contextual Embeddings beside the dependency graph and linked lines of its authors’ Lean proof.", "credit": "Paper and proof by Frohlich, Foster, Kavvos and Wang. I made the reader and links with AI; the authors have not reviewed the links.", "aka": [ "Proof Reader" ], "label": "General Reader", "subject": "Papers beside Lean proofs", "tagline": "A reusable reader for papers beside public Lean proofs.", "summary": "The current example is Contextual Embeddings, a PLDI 2026 paper. Read its text beside the authors’ Lean proof, inspect declaration dependencies, and see the axioms used.", "line": "Click a sentence in a paper to open the linked lines of its Lean proof.", "plain": "Follow a paper’s sentences into the proof they describe.", "id": "project:proof-reader", "slug": "proof-reader", "source": { "collection": "sites", "index": 2 }, "term_refs": [ { "field": "line", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 }, { "field": "summary", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 }, { "field": "summary", "term_id": "axiom", "surface": "axioms", "occurrence": 1 }, { "field": "summary", "term_id": "pldi", "surface": "PLDI", "occurrence": 1 } ], "type": "project" }, { "name": "Quartic Reader", "short": "Quartic Reader", "purpose": "Lean 4 formalisation of OpenAI’s nearly quartic randomized–quantum query-complexity separation, with mathematical expositions and a paragraph-linked proof reader.", "status": "Comparator accepted each proof bundle in local runs on my computer and rejected five deliberately wrong solutions. The Forrelation lower bound, which the preprint imports, is proved here by a shorter route in a weaker form.", "capture": "assets/sites/quartic", "capture_caption": "The exposition beside the Lean dependency graph, following the paragraph being read.", "credit": "Original theorem by OpenAI; formalisation and explanations made with AI. No human has reviewed whether the Lean statements match the paper.", "label": "Quartic Reader", "subject": "Randomized versus quantum query complexity", "tagline": "The nearly quartic randomized–quantum query separation, explained beside Lean.", "summary": "Follow the paper into linked Lean declarations, compare the formal statements with the prose, and explore their dependencies. The result concerns input queries; it is not a claim about full running time.", "line": "Read OpenAI’s nearly quartic query separation beside its Lean 4 proof.", "plain": "See how much quantum computation can reduce input queries.", "id": "project:quartic", "slug": "quartic", "source": { "collection": "sites", "index": 3 }, "term_refs": [ { "field": "line", "term_id": "nearly-quartic-separation", "surface": "nearly quartic query separation", "occurrence": 1 }, { "field": "line", "term_id": "lean-4", "surface": "Lean 4", "occurrence": 1 }, { "field": "plain", "term_id": "query-complexity", "surface": "input queries", "occurrence": 1 }, { "field": "summary", "term_id": "query-complexity", "surface": "input queries", "occurrence": 1 }, { "field": "summary", "term_id": "lean-4", "surface": "Lean", "occurrence": 1 } ], "type": "project" }, { "name": "Plectis Atlas", "short": "Atlas", "purpose": "An index of OpenAI’s mathematics manuscripts, Lean statement files and published assessments, grouped into 372 paper families.", "status": "I drafted the matches between each Lean statement and its paper with AI; no person has reviewed them.", "capture": "assets/sites/atlas", "capture_caption": "The Atlas map: each circle is a subject and each dot a family of papers.", "credit": "Reports credited to MathVet, Carlos Toledo’s cert-machine and Neal McBurnett. I assembled the index and statement links with AI.", "label": "Atlas", "subject": "Outside reports on OpenAI’s maths", "tagline": "OpenAI’s maths papers, with outside assessments alongside.", "summary": "The supplied snapshot groups 719 papers into 372 families. The reader brings together source papers and attributed outside reports, including MathVet and cert-machine, so their statements and coverage labels can be compared.", "line": "Browse OpenAI’s maths papers and compare the outside reports collected beside them.", "plain": "Compare outside reports on the same maths paper.", "id": "project:atlas", "slug": "atlas", "source": { "collection": "sites", "index": 4 }, "term_refs": [], "type": "project" }, { "name": "Practical Formal Verification", "short": "Formal verification", "purpose": "Dafny proofs for 16 selected computations in an 88-component research-workflow prototype, with generated Python and proof-coverage maps.", "status": null, "capture": "assets/sites/formal-verification", "capture_caption": "The system map: the 88 components in their seven families.", "front_label": "The component map", "credit": "The proofs cover those computations, not the complete system.", "label": "Formal verification", "subject": "Dafny proofs in a Python toolkit", "tagline": "A map of software components and the checks behind them.", "summary": "Open the evidence rings to find calculation proofs, tests and design rules. The 16 calculations comprise 12 component-specific calculations and four shared ones; a proof of a calculation does not cover every claim about its component.", "line": "Explore an 88-component Python toolkit with Dafny proofs for 16 calculations.", "plain": "See which calculations have mathematical proofs.", "id": "project:formal-verification", "slug": "formal-verification", "source": { "collection": "sites", "index": 5 }, "term_refs": [ { "field": "line", "term_id": "dafny", "surface": "Dafny proofs", "occurrence": 1 } ], "type": "project" }, { "way_in": "code", "name": "Zenith", "short": "Zenith", "purpose": "Experiments on whether records of earlier mistakes help language models test and repair code. The held-out testing study reports a mean per-problem fault-class detection score of 77.0%, compared with 69.2%.", "status": "The held-out study used DeepSeek V4.1 Flash. The earlier website and PDF describe separate studies, including program repairs rising from 259 to 365 of 576 tasks.", "capture": "assets/sites/zenith", "capture_caption": "The opening of the Zenith paper.", "credit": "DeepSeek V4.1 Flash on 58 held-out HumanEval problems; roughly half the gain came from timeouts. The supplied checkpoint links to the unmerged study revision.", "front_label": "Website for the earlier studies", "label": "Zenith", "subject": "AI-generated tests", "tagline": "Testing whether missed-bug records help an AI generate better tests.", "summary": "Compare prompts containing records of missed bugs with prompts containing generated rules. In this study the records improved the average per-problem score; roughly half the gain came from timeouts.", "line": "Showing missed bugs raised DeepSeek V4.1 Flash’s average score from 69% to 77% on 58 held-out problems.", "plain": "Can showing missed bugs improve the next set of tests?", "id": "project:zenith", "slug": "zenith", "source": { "collection": "sites", "index": 6 }, "term_refs": [ { "field": "line", "term_id": "held-out-problems", "surface": "held-out problems", "occurrence": 1 }, { "field": "summary", "term_id": "timeout", "surface": "timeouts", "occurrence": 1 } ], "type": "project" }, { "name": "Code Ontology Bridge", "short": "Code Ontology Bridge", "purpose": "Exports Python code structure to DuckDB, with semantic descriptions and recursive SQL views for NVIDIA Auto Ontology’s text-to-SQL agent.", "status": "AI models wrote the questions and answer keys; 21 answer keys were corrected after the runs. Every question, answer and failed run is published.", "capture": "assets/sites/code-ontology-bridge", "capture_caption": "Calls followed backwards from a function, with a callback reference shown dashed.", "credit": "Independent of NVIDIA. The 12-question comparison measured Auto Ontology plus the code database against DeepSeek alone. The separate no-clear-improvement result concerns adding descriptions within Auto Ontology, not the gain from the whole setup.", "label": "Code Ontology Bridge", "subject": "NVIDIA Auto Ontology for code", "tagline": "A code database and semantic models for NVIDIA Auto Ontology.", "summary": "Static analysis turns Python code into a DuckDB database of functions and call relations. The bridge supplies that structure to NVIDIA Auto Ontology, with rerunnable SQL queries and a code-question study.", "line": "Query Python functions and calls through DuckDB and NVIDIA Auto Ontology.", "plain": "Ask questions about functions and the code that calls them.", "id": "project:code-ontology-bridge", "slug": "code-ontology-bridge", "source": { "collection": "sites", "index": 7 }, "term_refs": [ { "field": "line", "term_id": "auto-ontology", "surface": "NVIDIA Auto Ontology", "occurrence": 1 }, { "field": "line", "term_id": "duckdb", "surface": "DuckDB", "occurrence": 1 }, { "field": "summary", "term_id": "auto-ontology", "surface": "NVIDIA Auto Ontology", "occurrence": 1 }, { "field": "summary", "term_id": "static-analysis", "surface": "Static analysis", "occurrence": 1 }, { "field": "summary", "term_id": "sql", "surface": "SQL queries", "occurrence": 1 }, { "field": "summary", "term_id": "duckdb", "surface": "DuckDB", "occurrence": 1 } ], "type": "project" }, { "name": "Agent Trace", "purpose": "Local Codex and Claude Code session viewer with tool traces, selective context export and optional MCP access.", "thumbnail": "assets/sites/agent-trace.png", "credit": "Technical preview; browser app or native Mac window.", "label": "Agent Trace", "subject": "Claude Code and Codex sessions", "tagline": "Saved coding sessions you can inspect and copy.", "summary": "Select a session, inspect its recorded commands and output, and copy a chosen level of detail into another chat. An optional MCP interface exposes those saved records to supported clients.", "line": "Inspect saved Claude Code and Codex sessions, with commands beside their output.", "plain": "See the commands and results saved by a coding assistant.", "id": "project:agent-trace", "slug": "agent-trace", "source": { "collection": "projects", "index": 0 }, "term_refs": [ { "field": "summary", "term_id": "mcp", "surface": "MCP", "occurrence": 1 } ], "type": "project" }, { "name": "Narration IR", "purpose": "A skill for writing an intermediate representation between narration and animation: sentence meanings, source quotations, what each picture should explain, and cues tied to spoken words.", "thumbnail": "assets/sites/narration-ir.webp", "label": "Narration IR", "subject": "Narration into picture plans", "tagline": "A readable plan between the script and the animation.", "summary": "For each sentence, specify what the audience needs to understand and attach picture events to spoken words. Source quotations and word identifiers make the plan easier to inspect before animation code is written.", "line": "Turn narration into a plan of sentence meanings, source quotations and word-timed picture changes.", "plain": "Plan what each picture should explain.", "id": "project:narration-ir", "slug": "narration-ir", "source": { "collection": "projects", "index": 1 }, "term_refs": [ { "field": "line", "term_id": "word-timing", "surface": "word-timed", "occurrence": 1 } ], "type": "project" }, { "name": "Safety Core", "purpose": "Generates AGENTS.md, CLAUDE.md and command-enforcement hooks from one rulebook, distinguishing written instructions from rules enforced by hooks.", "credit": "Tested in one small Claude Haiku study; the enforcement rule was written after observing the failure.", "label": "Safety Core", "subject": "Rules and command checks", "tagline": "Written rules and executable checks for coding agents.", "summary": "Explore the rulebook and tests, then compare written instructions with checks run before commands. The videos show specific cases involving made-up settings, false success reports and exposed keys.", "line": "Combine an editable rulebook with Claude Code hooks that check selected commands.", "plain": "Set rules for coding agents and check commands before they run.", "id": "project:safety-core", "slug": "safety-core", "source": { "collection": "projects", "index": 2 }, "term_refs": [ { "field": "line", "term_id": "claude-code-hook", "surface": "Claude Code hooks", "occurrence": 1 }, { "field": "plain", "term_id": "coding-agent", "surface": "coding agents", "occurrence": 1 } ], "type": "project" }, { "name": "One Checkout", "purpose": "Commits a reviewed Git patch while preserving another agent’s unfinished staged and working-tree edits, including changes in the same files.", "label": "One Checkout", "subject": "Several agents in one checkout", "tagline": "Selected commits from a shared checkout.", "summary": "Build a commit from the last committed version and one selected patch. Other unfinished edits stay in the working tree, including edits to the same file.", "line": "Commit one agent’s Git patch while unfinished edits remain in the same working tree.", "plain": "Save one finished fix while another agent is still editing.", "id": "project:one-checkout", "slug": "one-checkout", "source": { "collection": "projects", "index": 3 }, "term_refs": [ { "field": "line", "term_id": "working-tree", "surface": "working tree", "occurrence": 1 }, { "field": "line", "term_id": "git-patch", "surface": "Git patch", "occurrence": 1 }, { "field": "summary", "term_id": "working-tree", "surface": "working tree", "occurrence": 1 }, { "field": "summary", "term_id": "commit", "surface": "committed", "occurrence": 1 }, { "field": "summary", "term_id": "git-patch", "surface": "patch", "occurrence": 1 }, { "field": "line", "term_id": "commit", "surface": "Commit", "occurrence": 1 } ], "type": "project" }, { "name": "CodeMap", "purpose": "A code browser with docstring descriptions and function-call links, available to both the human reader and coding agents.", "status": "Not released; the video shows it in use.", "credit": "Private software; the video shows it in use.", "aka": [ "Code Map" ], "label": "CodeMap", "subject": "Maps of a codebase", "tagline": "A map drawn from the descriptions kept with the code.", "summary": "Move from the repository overview to individual files, their saved docstrings and call links. Coding agents can retrieve those same descriptions as text.", "line": "Explore a codebase through saved file descriptions and links between functions.", "plain": "Find a file, read its description and follow its calls.", "id": "project:codemap", "slug": "codemap", "source": { "collection": "projects", "index": 4 }, "term_refs": [ { "field": "summary", "term_id": "coding-agent", "surface": "Coding agents", "occurrence": 1 }, { "field": "summary", "term_id": "docstring", "surface": "docstrings", "occurrence": 1 } ], "type": "project" }, { "name": "The funnel", "label": "The funnel", "subject": "A proof into papers and video", "purpose": "Instructions for turning a Lean proof into a research record, specialist paper, exposition and video, with linked reader websites.", "tagline": "Instructions for explaining the same result at different levels.", "summary": "The worked example is a case of Erdős #257. Follow its formal proof through the four outputs, then see related reader websites for OpenAI’s spin-glass and quantum query results.", "line": "Turn a Lean proof into a research record, specialist paper, exposition and video.", "plain": "Follow one proof into explanations for different readers.", "id": "project:funnel", "slug": "funnel", "source": { "collection": "projects", "index": 5 }, "term_refs": [ { "field": "line", "term_id": "specialist-paper", "surface": "specialist paper", "occurrence": 1 }, { "field": "line", "term_id": "research-record", "surface": "research record", "occurrence": 1 }, { "field": "line", "term_id": "exposition", "surface": "exposition", "occurrence": 1 }, { "field": "line", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 }, { "field": "summary", "term_id": "quantum-query-complexity", "surface": "quantum query", "occurrence": 1 }, { "field": "summary", "term_id": "erdos-problem", "surface": "Erdős #257", "occurrence": 1 }, { "field": "summary", "term_id": "spin-glass", "surface": "spin-glass", "occurrence": 1 } ], "type": "project" }, { "id": "area:maths", "slug": "maths", "title": "Mathematics", "blurb": "Erdős problems, and OpenAI’s results beside their Lean proofs.", "source": { "collection": "areas", "index": 0 }, "type": "area" }, { "id": "area:explain", "slug": "explain", "title": "Making explanations", "blurb": "How a proof becomes papers, a reader website and a film.", "source": { "collection": "areas", "index": 1 }, "type": "area" }, { "id": "area:code", "slug": "code", "title": "Code and AI agents", "blurb": "Tools and experiments for coding agents.", "source": { "collection": "areas", "index": 2 }, "type": "area" }, { "id": "topic:erdos", "slug": "erdos", "label": "Can this sum be a fraction?", "question": "One question from eight Erdős problems.", "at": [ -190, -235 ], "area_ref": "area:maths", "source": { "collection": "topics", "index": 0 }, "type": "topic" }, { "id": "topic:magnets", "slug": "magnets", "label": "Can different answers be nearly best?", "question": "Two near-best arrangements of a spin glass.", "at": [ 60, -280 ], "area_ref": "area:maths", "source": { "collection": "topics", "index": 1 }, "type": "topic" }, { "id": "topic:quantum", "slug": "quantum", "label": "How much faster can quantum be?", "question": "Compare randomized and quantum input queries.", "at": [ 300, -205 ], "area_ref": "area:maths", "source": { "collection": "topics", "index": 2 }, "type": "topic" }, { "id": "topic:proofs", "slug": "proofs", "label": "How do I follow this proof?", "question": "Papers linked to their Lean proofs.", "at": [ 160, -55 ], "area_ref": "area:maths", "source": { "collection": "topics", "index": 3 }, "type": "topic" }, { "id": "topic:checking", "slug": "checking", "label": "What did the check prove?", "question": "Compare formal statements, calculations and coverage.", "at": [ 390, 25 ], "area_ref": "area:maths", "source": { "collection": "topics", "index": 4 }, "type": "topic" }, { "id": "topic:explaining", "slug": "explaining", "label": "How does a proof become a video?", "question": "One result, several ways to understand it.", "at": [ -310, -30 ], "area_ref": "area:explain", "source": { "collection": "topics", "index": 5 }, "type": "topic" }, { "id": "topic:assistants", "slug": "assistants", "label": "What did the assistant do?", "question": "Inspect sessions, save a fix and check commands.", "at": [ 30, 255 ], "area_ref": "area:code", "source": { "collection": "topics", "index": 6 }, "type": "topic" }, { "id": "topic:code", "slug": "code", "label": "What would this code change affect?", "question": "Explore functions, callers and code questions.", "at": [ -250, 205 ], "area_ref": "area:code", "source": { "collection": "topics", "index": 7 }, "type": "topic" }, { "id": "topic:testing", "slug": "testing", "label": "Can AI find more bugs?", "question": "Generate test inputs and measure what they catch.", "at": [ 265, 235 ], "area_ref": "area:code", "source": { "collection": "topics", "index": 8 }, "type": "topic" }, { "id": "collection:readers", "slug": "readers", "title": "Read a paper beside its Lean proof", "summary": "SK Reader, Quartic Reader and General Reader link paper sentences to Lean code, and a program confirms each link names a real sentence and a real Lean declaration. Whether both say the same thing still needs an expert.", "source": { "collection": "collections", "index": 0 }, "type": "collection" }, { "id": "collection:openai", "slug": "openai", "title": "OpenAI’s mathematics", "source": { "collection": "collections", "index": 1 }, "type": "collection" }, { "id": "collection:checks", "slug": "checks", "title": "What a check covers", "source": { "collection": "collections", "index": 2 }, "type": "collection" }, { "id": "collection:agent-tools", "slug": "agent-tools", "title": "Coding agents sharing one repository", "source": { "collection": "collections", "index": 3 }, "type": "collection" }, { "id": "home", "type": "website", "slug": "home", "title": "Will Cook", "publications": [ { "id": "web", "platform": "web", "state": "published", "url": "https://wcook04.github.io/" } ], "source": { "collection": "owner", "index": 0, "field": "home" }, "aliases": [], "term_refs": [], "url": "https://wcook04.github.io/", "publicly_available": true }, { "title": "Erdős #257: AI proved one case of an infinite-sum problem, checked in Lean", "short": "Erdős #257", "description": "Erdős #257: a case from 1968, proved and checked in Lean", "format": "short", "poster": "assets/films/next/short-mathematics", "cut_seconds": 101, "takeaway": "Introduces the Lean-checked proof of Erdős’s 1968 case of problem #257, removing his extra restriction.", "id": "film:short-mathematics", "slug": "short-mathematics", "type": "video", "source": { "collection": "films", "index": 0 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=BIcqIDc7wK4", "duration_seconds": 101, "thumbnail_stem": "assets/films/next/short-mathematics" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "lean-proof", "surface": "Lean-checked proof", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=BIcqIDc7wK4", "publicly_available": true, "edition_state": "current" }, { "title": "Maths Map: eight Erdős problems and their papers", "short": "Maths Map", "description": "Maths Map: eight Erdős problems and their papers", "format": "short", "poster": "assets/films/next/short-mathematics-overview", "cut_seconds": 109, "takeaway": "Find a theorem on Maths Map, open its paper, and see the available Lean and Comparator checks.", "id": "film:short-mathematics-overview", "slug": "short-mathematics-overview", "type": "video", "source": { "collection": "films", "index": 1 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=IrHU2btIfjc", "duration_seconds": 109, "thumbnail_stem": "assets/films/next/short-mathematics-overview" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "comparator", "surface": "Comparator", "occurrence": 1 }, { "field": "takeaway", "term_id": "lean-4", "surface": "Lean", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=IrHU2btIfjc", "publicly_available": true, "edition_state": "current" }, { "title": "Spin glasses: Two near-best arrangements with about half their arrows different", "short": "Spin glasses", "description": "Spin glasses: two nearly best answers, half the arrows differ", "format": "short", "poster": "assets/films/next/short-sk-no-gap", "cut_seconds": 98, "takeaway": "Explains why large random Sherrington–Kirkpatrick models almost certainly contain two near-best arrangements differing in about half their spins.", "id": "film:short-sk-no-gap", "slug": "short-sk-no-gap", "type": "video", "source": { "collection": "films", "index": 2 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=FU7RT6glvSQ", "duration_seconds": 98, "thumbnail_stem": "assets/films/next/short-sk-no-gap" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=FU7RT6glvSQ", "publicly_available": true, "edition_state": "current" }, { "title": "Atlas: Two coverage labels for OpenAI's paper about π", "short": "Atlas", "description": "Atlas: two groups, two labels for one maths paper", "format": "short", "poster": "assets/films/next/short-atlas", "cut_seconds": 102, "takeaway": "Find OpenAI’s maths papers in Plectis Atlas, then compare MathVet and cert-machine’s different coverage labels for one paper about π.", "id": "film:short-atlas", "slug": "short-atlas", "type": "video", "source": { "collection": "films", "index": 3 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=e-lPHr7FlPM", "duration_seconds": 102, "thumbnail_stem": "assets/films/next/short-atlas" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=e-lPHr7FlPM", "publicly_available": true, "edition_state": "current" }, { "title": "Formal verification: What a proof covers in my 88-component toolkit", "short": "Formal verification", "description": "Formal verification: what one proof covers", "format": "short", "poster": "assets/films/next/short-plectis-verification", "cut_seconds": 116, "takeaway": "Explore an 88-component software map and see exactly which calculations have Dafny proofs.", "id": "film:short-plectis-verification", "slug": "short-plectis-verification", "type": "video", "source": { "collection": "films", "index": 4 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=6FefCiy4gn8", "duration_seconds": 117, "thumbnail_stem": "assets/films/next/short-plectis-verification" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "dafny", "surface": "Dafny proofs", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=6FefCiy4gn8", "publicly_available": true, "edition_state": "current" }, { "title": "CodeMap: A map of my code from AI-written file descriptions", "short": "CodeMap", "description": "CodeMap: a map of my code from AI-written descriptions", "format": "short", "poster": "assets/films/next/short-codemap", "cut_seconds": 129, "takeaway": "Explore CodeMap’s file boxes and the descriptions coding agents saved in the code; fetch those same descriptions as text.", "id": "film:short-codemap", "slug": "short-codemap", "type": "video", "source": { "collection": "films", "index": 5 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=92vGDw_R0Bw", "duration_seconds": 130, "thumbnail_stem": "assets/films/next/short-codemap" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "coding-agent", "surface": "coding agents", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=92vGDw_R0Bw", "publicly_available": true, "edition_state": "current" }, { "title": "One Checkout: Commit one fix while another AI edits the same file", "short": "One Checkout", "description": "One Checkout: commit one fix while another AI keeps editing", "format": "short", "poster": "assets/films/next/short-one-checkout", "cut_seconds": 86, "takeaway": "Commit one agent’s Git patch while another agent’s unfinished edits stay in the same file.", "id": "film:short-one-checkout", "slug": "short-one-checkout", "type": "video", "source": { "collection": "films", "index": 6 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=tZWZUXm_hPk", "duration_seconds": 88, "thumbnail_stem": "assets/films/next/short-one-checkout" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "git-patch", "surface": "Git patch", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=tZWZUXm_hPk", "publicly_available": true, "edition_state": "current" }, { "title": "Safety Core: 6 of 10 AI runs committed with rules, 0 with a command check", "short": "Safety Core", "description": "Safety Core: a written rule let 6 of 10 runs commit", "format": "short", "poster": "assets/films/next/short-safety-core", "cut_seconds": 83, "takeaway": "In one retry test, a made-up setting reached a commit in 10 of 10 runs, six under written rules, none under hooks.", "id": "film:short-safety-core", "slug": "short-safety-core", "type": "video", "source": { "collection": "films", "index": 7 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=cSyHu-JFse8", "duration_seconds": 85, "thumbnail_stem": "assets/films/next/short-safety-core" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=cSyHu-JFse8", "publicly_available": true, "edition_state": "current" }, { "title": "Zenith: AI found 69% vs 77% of bug types per program, without and with past misses", "short": "Zenith", "description": "Zenith: showing an AI tester the bugs it missed", "format": "short", "poster": "assets/films/next/short-zenith", "cut_seconds": 113, "takeaway": "On 58 held-out problems, showing DeepSeek V4.1 Flash its missed bugs raised its average score from 69% to 77%.", "id": "film:short-zenith", "slug": "short-zenith", "type": "video", "source": { "collection": "films", "index": 8 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=RlpGkniCxHE", "duration_seconds": 114, "thumbnail_stem": "assets/films/next/short-zenith" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "held-out-problems", "surface": "held-out problems", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=RlpGkniCxHE", "publicly_available": true, "edition_state": "current" }, { "title": "Quantum vs classical computers: OpenAI's fourth-power bound, checked in Lean", "short": "Quantum computer", "description": "OpenAI's quantum fourth-power result, proved again in Lean", "format": "short", "poster": "assets/films/next/short-quartic", "cut_seconds": 110, "takeaway": "Explains OpenAI’s nearly quartic gap between randomized and quantum query complexity, and the new Lean proof.", "id": "film:short-quartic", "slug": "short-quartic", "type": "video", "source": { "collection": "films", "index": 9 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=4LOeBi5BF3A", "duration_seconds": 110, "thumbnail_stem": "assets/films/next/short-quartic" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "quantum-query-complexity", "surface": "quantum query complexity", "occurrence": 1 }, { "field": "takeaway", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=4LOeBi5BF3A", "publicly_available": true, "edition_state": "current" }, { "title": "How I use AI to turn a Lean proof into three papers and a video", "short": "The funnel", "description": "How I turn AI-written maths into papers and a video", "format": "short", "poster": "assets/films/next/short-funnel", "cut_seconds": 131, "takeaway": "Follow a Lean proof of a case of Erdős #257 into a research record, specialist paper, exposition and video.", "id": "film:short-funnel", "slug": "short-funnel", "type": "video", "source": { "collection": "films", "index": 10 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=hEekS6r0sTA", "duration_seconds": 132, "thumbnail_stem": "assets/films/next/short-funnel" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "specialist-paper", "surface": "specialist paper", "occurrence": 1 }, { "field": "takeaway", "term_id": "research-record", "surface": "research record", "occurrence": 1 }, { "field": "takeaway", "term_id": "erdos-problem", "surface": "Erdős #257", "occurrence": 1 }, { "field": "takeaway", "term_id": "exposition", "surface": "exposition", "occurrence": 1 }, { "field": "takeaway", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=hEekS6r0sTA", "publicly_available": true, "edition_state": "current" }, { "title": "The funnel: How I use AI to turn a Lean proof into papers, a website and a video", "short": "The funnel", "description": "The funnel: from a Lean proof to papers, a video and a reader", "format": "long", "poster": "assets/films/next/long-funnel", "cut_seconds": 721, "takeaway": "Walk through Erdős #257 at each level, then explore the OpenAI reader websites and the proposed feedback loop for improving the instructions.", "id": "film:long-funnel", "slug": "long-funnel", "type": "video", "source": { "collection": "films", "index": 11 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=B716l0s8iwQ", "duration_seconds": 729, "thumbnail_stem": "assets/films/next/long-funnel" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "erdos-problem", "surface": "Erdős #257", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=B716l0s8iwQ", "publicly_available": true, "edition_state": "current" }, { "title": "Introduction: Using AI to explain maths and code", "short": "Introduction", "description": "Making AI-written maths and code easier to understand", "format": "short", "poster": "assets/films/next/short-introduction", "cut_seconds": 95, "takeaway": "Meet the maths funnel, Code Ontology Bridge for NVIDIA Auto Ontology, and Agent Trace: three ways to make AI output easier to follow.", "id": "film:short-introduction", "slug": "short-introduction", "type": "video", "source": { "collection": "films", "index": 12 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=VwqOrXl2YmU", "duration_seconds": 97, "thumbnail_stem": "assets/films/next/short-introduction" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "auto-ontology", "surface": "NVIDIA Auto Ontology", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=VwqOrXl2YmU", "publicly_available": true, "edition_state": "current" }, { "title": "Introduction (V4): Using AI to explain maths and code", "short": "Introduction", "description": "How all my videos fit together, and where to start", "format": "long", "poster": "assets/films/next/long-introduction", "cut_seconds": 630, "takeaway": "Tour the maths, software and explanation projects, see how they connect, and choose a first video.", "id": "film:long-introduction", "slug": "long-introduction", "type": "video", "source": { "collection": "films", "index": 13 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=Ttrd9DJEUMU", "duration_seconds": 631, "thumbnail_stem": "assets/films/next/long-introduction" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=Ttrd9DJEUMU", "publicly_available": true, "edition_state": "current" }, { "title": "Lean Exposition: Open the Lean proof of OpenAI's spin-glass theorem", "short": "SK Reader", "description": "SK Reader: read the spin-glass paper beside its Lean proof", "format": "short", "poster": "assets/films/next/short-sk-website", "cut_seconds": 92, "takeaway": "Click a statement in SK Reader’s papers to open the linked part of OpenAI’s Sherrington–Kirkpatrick Lean proof.", "id": "film:short-sk-website", "slug": "short-sk-website", "type": "video", "source": { "collection": "films", "index": 14 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=f8EY_85zsw4", "duration_seconds": 92, "thumbnail_stem": "assets/films/next/short-sk-website" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=f8EY_85zsw4", "publicly_available": true, "edition_state": "current" }, { "title": "Quantum Reader: Open the Lean proof of OpenAI's fourth-power query bound", "short": "Quartic Reader", "description": "Quartic Reader: the quantum query paper beside its Lean proof", "format": "short", "poster": "assets/films/next/short-quartic-reader", "cut_seconds": 87, "takeaway": "Follow a passage in Quartic Reader to its linked Lean statements and the labels describing how they match.", "id": "film:short-quartic-reader", "slug": "short-quartic-reader", "type": "video", "source": { "collection": "films", "index": 15 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=CS1VYv4n7cQ", "duration_seconds": 87, "thumbnail_stem": "assets/films/next/short-quartic-reader" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "lean-4", "surface": "Lean", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=CS1VYv4n7cQ", "publicly_available": true, "edition_state": "current" }, { "title": "Proof Reader: Open Lean code linked to a paper's sentence", "short": "General Reader", "description": "General Reader: click a paper’s sentence to open its Lean proof", "format": "short", "poster": "assets/films/next/short-proof-reader", "cut_seconds": 90, "takeaway": "Try General Reader on Contextual Embeddings: click a sentence to open the corresponding lines of the authors’ Lean proof.", "id": "film:short-proof-reader", "slug": "short-proof-reader", "type": "video", "source": { "collection": "films", "index": 16 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=r-E0m_j0WwU", "duration_seconds": 90, "thumbnail_stem": "assets/films/next/short-proof-reader" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=r-E0m_j0WwU", "publicly_available": true, "edition_state": "current" }, { "title": "Three maths websites: Open Lean proofs linked to maths papers", "short": "Three reader websites", "description": "Read a maths paper beside its Lean proof", "format": "long", "poster": "assets/films/next/long-lean-readers", "cut_seconds": 290, "takeaway": "Compare SK Reader, Quartic Reader and General Reader: paper links, argument maps, formal dependency graphs and the Lean behind them.", "id": "film:long-lean-readers", "slug": "long-lean-readers", "type": "video", "source": { "collection": "films", "index": 17 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=hbnsl3LvhZE", "duration_seconds": 298, "thumbnail_stem": "assets/films/next/long-lean-readers" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "dependency-graph", "surface": "dependency graphs", "occurrence": 1 }, { "field": "takeaway", "term_id": "proof-graph", "surface": "argument maps", "occurrence": 1 }, { "field": "takeaway", "term_id": "lean-4", "surface": "Lean", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=hbnsl3LvhZE", "publicly_available": true, "edition_state": "current" }, { "title": "NVIDIA's Auto Ontology: 10.3 of 12 questions about its own code correct", "short": "Code Ontology Bridge", "description": "NVIDIA Auto Ontology answering questions about its own code", "format": "short", "poster": "assets/films/next/short-code-ontology", "cut_seconds": 94, "takeaway": "With a DuckDB code database, NVIDIA Auto Ontology using DeepSeek averaged 10.3 correct answers out of 12; DeepSeek alone averaged 3.2.", "id": "film:short-code-ontology", "slug": "short-code-ontology", "type": "video", "source": { "collection": "films", "index": 18 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=LmzHZfqUQtc", "duration_seconds": 95, "thumbnail_stem": "assets/films/next/short-code-ontology" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "auto-ontology", "surface": "NVIDIA Auto Ontology", "occurrence": 1 }, { "field": "takeaway", "term_id": "duckdb", "surface": "DuckDB", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=LmzHZfqUQtc", "publicly_available": true, "edition_state": "current" }, { "title": "I asked NVIDIA's Auto Ontology which functions call one Python function", "short": "Code Ontology Bridge", "description": "Asking NVIDIA Auto Ontology about its own code", "format": "long", "poster": "assets/films/next/long-code-ontology", "cut_seconds": 270, "takeaway": "Follow NVIDIA Auto Ontology’s recursive SQL query through four functions, including a callback, then explore the wider code-question study.", "id": "film:long-code-ontology", "slug": "long-code-ontology", "type": "video", "source": { "collection": "films", "index": 19 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=odGZTdAiCLY", "duration_seconds": 278, "thumbnail_stem": "assets/films/next/long-code-ontology" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "auto-ontology", "surface": "NVIDIA Auto Ontology", "occurrence": 1 }, { "field": "takeaway", "term_id": "recursive-query", "surface": "recursive SQL query", "occurrence": 1 }, { "field": "takeaway", "term_id": "callback", "surface": "callback", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=odGZTdAiCLY", "publicly_available": true, "edition_state": "current" }, { "title": "Agent Trace: Read Claude Code and Codex commands and results", "short": "Agent Trace", "description": "Agent Trace: read what your AI coding assistant ran", "format": "short", "poster": "assets/films/next/short-agent-trace", "cut_seconds": 144, "takeaway": "Inspect saved Claude Code and Codex sessions, see commands beside their output, and copy selected context into another chat.", "id": "film:short-agent-trace", "slug": "short-agent-trace", "type": "video", "source": { "collection": "films", "index": 20 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=IkigUWBQK5k", "duration_seconds": 145, "thumbnail_stem": "assets/films/next/short-agent-trace" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=IkigUWBQK5k", "publicly_available": true, "edition_state": "current" }, { "title": "Agent Trace: Read and copy Claude Code and Codex chats, commands and results", "short": "Agent Trace", "description": "Agent Trace: inspect coding sessions and copy context into ChatGPT", "format": "long", "poster": "assets/films/next/long-agent-trace", "cut_seconds": 432, "takeaway": "Follow a failed test, its fix and a passing rerun, then choose how much of the saved session to copy into ChatGPT.", "id": "film:long-agent-trace", "slug": "long-agent-trace", "type": "video", "source": { "collection": "films", "index": 21 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=i1xO_SSnE4A", "duration_seconds": 440, "thumbnail_stem": "assets/films/next/long-agent-trace" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=i1xO_SSnE4A", "publicly_available": true, "edition_state": "current" }, { "title": "Narration IR: Time an arrow's movement to spoken words", "short": "Narration IR", "description": "Narration IR: plan what each sentence means, then animate", "format": "short", "poster": "assets/films/next/short-narration-ir", "cut_seconds": 139, "takeaway": "Plan what one spin-glass sentence means, attach an arrow’s turn to spoken words, and locate its source quotations.", "id": "film:short-narration-ir", "slug": "short-narration-ir", "type": "video", "source": { "collection": "films", "index": 22 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=C1bhw-33OKg", "duration_seconds": 140, "thumbnail_stem": "assets/films/next/short-narration-ir" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "spin-glass", "surface": "spin-glass", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=C1bhw-33OKg", "publicly_available": true, "edition_state": "current" }, { "title": "Narration IR: Planning AI animations around recorded speech", "short": "Narration IR", "description": "Narration IR: what each picture needs to explain", "format": "long", "poster": "assets/films/next/long-narration-ir", "cut_seconds": 652, "takeaway": "Expand a narration into the meaning each picture should convey, with source context, before deciding how to draw it.", "id": "film:long-narration-ir", "slug": "long-narration-ir", "type": "video", "source": { "collection": "films", "index": 23 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=-Jx8-Hpj5-E", "duration_seconds": 653, "thumbnail_stem": "assets/films/next/long-narration-ir" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=-Jx8-Hpj5-E", "publicly_available": true, "edition_state": "current" }, { "title": "Introduction (V3, older version): My AI maths and software projects", "short": "Introduction", "description": "I use AI for maths research and software, and build interfaces so other people can follow the results.", "format": "long", "takeaway": "An earlier tour of the maths funnel, reader websites and coding tools, explaining why Will wants to understand what AI produces.", "id": "film:introduction", "slug": "introduction", "type": "video", "source": { "collection": "films", "index": 24 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=MBmVMMogXTA", "duration_seconds": 337, "thumbnail_stem": "assets/films/introduction-v3" } ], "chapters": [], "aliases": [], "term_refs": [], "edition": "earlier", "url": "https://www.youtube.com/watch?v=MBmVMMogXTA", "publicly_available": true, "edition_state": "earlier" }, { "title": "Introduction (V1, older version): My AI maths and coding projects", "short": "Introduction (V1, older version)", "description": "An older introduction. Watch the latest Introduction (V4) from the home page. I go through the maths, the code map, how I make these videos, and the tools I use to manage the agents. Then some research into how the agents could improve their own way of working.", "format": "long", "edition": "earlier", "takeaway": "An earlier tour of CodeMap, One Checkout, the maths funnel, Atlas, Demo Take, Safety Core and Zenith.", "id": "film:introduction-alternate", "slug": "introduction-alternate", "type": "video", "source": { "collection": "films", "index": 25 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=uO2lbstEH9M", "duration_seconds": 484, "thumbnail_stem": "assets/films/introduction-alternate" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=uO2lbstEH9M", "publicly_available": true, "edition_state": "earlier" }, { "title": "Maths Map: eight Erdős problems on one map", "short": "Maths Map", "description": "I use one problem, Erdős #257, to show where its proof, papers and explanation video are on the Maths Map.", "format": "long", "takeaway": "Follow Erdős #257 through Maths Map: from its theorems and checks to the research record, specialist paper, exposition and video.", "id": "film:mathematics-overview", "slug": "mathematics-overview", "type": "video", "source": { "collection": "films", "index": 26 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=u4f-fk1o13k", "duration_seconds": 380, "thumbnail_stem": "assets/films/mathematics-overview-v3" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "specialist-paper", "surface": "specialist paper", "occurrence": 1 }, { "field": "takeaway", "term_id": "research-record", "surface": "research record", "occurrence": 1 }, { "field": "takeaway", "term_id": "erdos-problem", "surface": "Erdős #257", "occurrence": 1 }, { "field": "takeaway", "term_id": "exposition", "surface": "exposition", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=u4f-fk1o13k", "publicly_available": true, "edition_state": "current" }, { "title": "Erdős #257: A proof that some sums of 1/(2ⁿ−1) cannot be fractions", "short": "Erdős #257", "description": "I explain a known irrationality result for Erdős #257, starting with 1, 1/3, 1/7, 1/15, and so on.", "format": "long", "takeaway": "Starting with fractions, prove Erdős’s 1968 case of problem #257: a convergence condition makes the selected infinite sum irrational.", "id": "film:mathematics", "slug": "mathematics", "type": "video", "source": { "collection": "films", "index": 27 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=uWCqtRkJ8P0", "duration_seconds": 1808, "thumbnail_stem": "assets/films/mathematics-v3" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "irrationality", "surface": "irrational", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=uWCqtRkJ8P0", "publicly_available": true, "edition_state": "current" }, { "title": "Lean Exposition: Follow OpenAI's spin-glass proof through an argument map", "short": "SK Reader", "description": "I show how to read a maths explanation beside a map of its assumptions, results and sources.", "format": "long", "takeaway": "Read the spin-glass papers while SK Reader highlights the corresponding argument-map steps and opens linked passages across papers.", "id": "film:interfaces", "slug": "interfaces", "type": "video", "source": { "collection": "films", "index": 28 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=sYMDcT7vyng", "duration_seconds": 239, "thumbnail_stem": "assets/films/interfaces-v3" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "spin-glass", "surface": "spin-glass", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=sYMDcT7vyng", "publicly_available": true, "edition_state": "earlier" }, { "title": "Spin glasses: How different can two near-best magnet arrangements be?", "short": "The SK result explained", "description": "I explain how two nearly best arrangements of magnets can differ, starting with four arrows.", "format": "long", "takeaway": "Start with four spins, then see why large random Sherrington–Kirkpatrick models admit near-best pairs at many different degrees of overlap.", "id": "film:sk-no-gap", "slug": "sk-no-gap", "type": "video", "source": { "collection": "films", "index": 29 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=IUAhxUriDVw", "duration_seconds": 748, "thumbnail_stem": "assets/films/sk-no-gap-v3" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=IUAhxUriDVw", "publicly_available": true, "edition_state": "current" }, { "title": "Atlas: Why two groups gave different coverage labels to OpenAI's π paper", "short": "Plectis Atlas", "description": "In two reports on an OpenAI paper about π, both groups say Comparator accepted the Lean proof, but they label the Lean statement’s coverage differently. I go through what each label means.", "format": "long", "takeaway": "Compare MathVet and cert-machine’s reports on one OpenAI paper about π, and see how an extra Flint Hills claim changes the coverage label.", "id": "film:atlas", "slug": "atlas", "type": "video", "source": { "collection": "films", "index": 30 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=ga5_wfSStdk", "duration_seconds": 335, "thumbnail_stem": "assets/films/atlas-v3" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=ga5_wfSStdk", "publicly_available": true, "edition_state": "current" }, { "title": "Formal verification: What Dafny checked in my 88-component toolkit", "short": "Practical formal verification", "description": "On a map of the 88 Python components, I show what each Dafny proof and saved result covers.", "format": "long", "takeaway": "Read the map’s evidence rings, inspect a Dafny-proved calculation, and follow a design rule to the components it concerns.", "id": "film:plectis-verification", "slug": "plectis-verification", "type": "video", "source": { "collection": "films", "index": 31 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=u3dad1v-o8c", "duration_seconds": 312, "thumbnail_stem": "assets/films/plectis-verification-v3" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=u3dad1v-o8c", "publicly_available": true, "edition_state": "current" }, { "title": "Zenith: AI bug detection on 58 problems rose from 69% to 77% with past misses", "short": "Zenith", "description": "I test whether an AI code tester catches more bugs after seeing a record of its earlier misses.", "format": "long", "takeaway": "Compare missed-bug records with generated rules on 58 held-out EvalPlus problems; DeepSeek V4.1 Flash’s average score rose from 69% to 77% with the records.", "id": "film:zenith", "slug": "zenith", "type": "video", "source": { "collection": "films", "index": 32 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=wUxp2Wohmq0", "duration_seconds": 303, "thumbnail_stem": "assets/films/zenith-v3" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "evalplus", "surface": "EvalPlus", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=wUxp2Wohmq0", "publicly_available": true, "edition_state": "current" }, { "title": "Safety Core: my AI agent made up a setting to pass a test", "short": "Safety Core", "description": "I give a coding agent written rules and command-blocking hooks, then record what it does to get past a failing test.", "format": "long", "takeaway": "Explore Safety Core’s rulebook, then compare written rules and Claude Code hooks on made-up settings, false success reports and exposed keys.", "id": "film:safety-core", "slug": "safety-core", "type": "video", "source": { "collection": "films", "index": 33 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=ayl3sOCwaHQ", "duration_seconds": 536, "thumbnail_stem": "assets/films/safety-core-v3" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "claude-code-hook", "surface": "Claude Code hooks", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=ayl3sOCwaHQ", "publicly_available": true, "edition_state": "current" }, { "title": "One Checkout: Commit a login fix while another AI edits the same file", "short": "One Checkout", "description": "I show how to commit one fix while another agent's unfinished edits stay in the same file.", "format": "long", "takeaway": "Save Claude’s login fix while Codex keeps editing, then see how an older staged copy can put the old login code back.", "id": "film:one-checkout", "slug": "one-checkout", "type": "video", "source": { "collection": "films", "index": 34 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=MHBxGPLDqt4", "duration_seconds": 335, "thumbnail_stem": "assets/films/one-checkout-v3" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=MHBxGPLDqt4", "publicly_available": true, "edition_state": "current" }, { "title": "CodeMap: Find a search function and its caller in AI-written code", "short": "CodeMap", "description": "I follow a code search from a file's saved description to the function and the code that calls it.", "format": "long", "takeaway": "Trace a CodeMap search from the Find box to the matching function and its callers, using saved docstrings and call links.", "id": "film:codemap", "slug": "codemap", "type": "video", "source": { "collection": "films", "index": 35 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=OnBO9U9T2IQ", "duration_seconds": 409, "thumbnail_stem": "assets/films/codemap-v3" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "docstring", "surface": "docstrings", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=OnBO9U9T2IQ", "publicly_available": true, "edition_state": "current" }, { "title": "Introduction (V2, older version): Using AI for maths research and software", "short": "Introduction (V2, older version)", "description": "An older introduction. Watch the latest Introduction (V4) from the home page. In this video I introduce the projects and explain how they fit together, from computer-checked proofs and papers to maps and videos you can follow yourself.", "format": "long", "edition": "earlier", "takeaway": "An earlier introduction to Will’s AI-assisted maths research and software projects.", "id": "film:introduction-v2", "slug": "introduction-v2", "type": "video", "source": { "collection": "films", "index": 36 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=U1z2-XaLe_w", "duration_seconds": 344, "thumbnail_stem": "assets/films/introduction" } ], "chapters": [], "aliases": [], "term_refs": [], "url": "https://www.youtube.com/watch?v=U1z2-XaLe_w", "publicly_available": true, "edition_state": "earlier" }, { "title": "Quantum vs classical computers: Why the fourth-power query bound cannot be lowered", "short": "Quantum query complexity", "description": "I compare how many times quantum and classical computers must look at the same data, then explain why four is the best possible power for total yes-or-no questions.", "format": "long", "takeaway": "See how one photon compares two hidden bits, then explore the construction behind OpenAI’s nearly quartic query separation and its Lean proof.", "id": "film:quartic-query", "slug": "quartic-query", "type": "video", "source": { "collection": "films", "index": 37 }, "publications": [ { "id": "youtube", "platform": "youtube", "state": "published", "url": "https://www.youtube.com/watch?v=CBHPBKcx2ck", "duration_seconds": 2042, "thumbnail_stem": "assets/films/quartic-query" } ], "chapters": [], "aliases": [], "term_refs": [ { "field": "takeaway", "term_id": "nearly-quartic-separation", "surface": "nearly quartic query separation", "occurrence": 1 }, { "field": "takeaway", "term_id": "lean-proof", "surface": "Lean proof", "occurrence": 1 } ], "url": "https://www.youtube.com/watch?v=CBHPBKcx2ck", "publicly_available": true, "edition_state": "current" }, { "id": "repo:plectis-erdos", "slug": "plectis-erdos", "type": "repository", "title": "plectis-erdos", "description": "Papers, Lean proofs, experiments and open questions from the research on eight Erdős problems, and papers on how the research was done.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/plectis-erdos" } ], "source": { "collection": "repos", "index": 0 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/plectis-erdos", "publicly_available": true }, { "id": "repo:plectis-erdos-lean", "slug": "plectis-erdos-lean", "type": "repository", "title": "plectis-erdos-lean", "description": "Lean 4 source for the eight problems. Comparator accepted selected proofs against separately written statements, and Palomar, an online proof registry, reran some of them.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/plectis-erdos-lean" } ], "source": { "collection": "repos", "index": 1 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/plectis-erdos-lean", "publicly_available": true }, { "id": "repo:lean-exposition", "slug": "lean-exposition", "type": "repository", "title": "lean-exposition", "description": "The three papers, the Lean they link to at a fixed version, and the source of the reading website.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/lean-exposition" } ], "source": { "collection": "repos", "index": 2 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/lean-exposition", "publicly_available": true }, { "id": "repo:proof-reader", "slug": "proof-reader", "type": "repository", "title": "proof-reader", "description": "Each paper is one folder, and any paper with public Lean can be added. A program compares the site’s text with the PDF word for word.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/proof-reader" } ], "source": { "collection": "repos", "index": 3 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/proof-reader", "publicly_available": true }, { "id": "repo:plectis-atlas", "slug": "plectis-atlas", "type": "repository", "title": "plectis-atlas", "description": "The Atlas website’s source: OpenAI’s maths papers, their Lean statements, and outside groups’ reports credited to their authors.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/plectis-atlas" } ], "source": { "collection": "repos", "index": 4 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/plectis-atlas", "publicly_available": true }, { "id": "repo:practical-formal-verification", "slug": "practical-formal-verification", "type": "repository", "title": "practical-formal-verification", "description": "The components, their Dafny proofs, the Python compiled from them and worked examples.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/practical-formal-verification" } ], "source": { "collection": "repos", "index": 5 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/practical-formal-verification", "publicly_available": true }, { "id": "repo:plectis-zenith", "slug": "plectis-zenith", "type": "repository", "title": "plectis-zenith", "description": "Code, data and paper for the experiments on showing an AI tester the bugs it missed, and the code-repair studies.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/plectis-zenith" } ], "source": { "collection": "repos", "index": 6 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/plectis-zenith", "publicly_available": true }, { "id": "repo:safety-core", "slug": "safety-core", "type": "repository", "title": "safety-core", "description": "A rule file for coding agents and the hooks that block commands a rule forbids.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/safety-core" } ], "source": { "collection": "repos", "index": 7 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/safety-core", "publicly_available": true }, { "id": "repo:one-checkout", "slug": "one-checkout", "type": "repository", "title": "one-checkout", "description": "Commit one agent’s fix without including another agent’s unfinished edits.", "repository_kind": "own", "publications": [ { "id": "github", "platform": "github", "state": "published", "url": "https://github.com/wcook04/one-checkout" } ], "source": { "collection": "repos", "index": 8 }, "aliases": [], "term_refs": [], "url": "https://github.com/wcook04/one-checkout", "publicly_available": true }, { "id": "repo:agent-trace-mechanism", "slug": "agent-trace-mechanism", "type": "repository", "title": "agent-trace-mechanism", "description": "The session viewer and the optional MCP server for Codex and Claude Code logs. 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Recording this handoff helps a code graph include a relation that a search for direct function calls could miss.", "area": "code", "related_terms": [ "call-graph", "static-analysis" ], "type": "term" }, { "id": "term:claude-code-hook", "term": "Claude Code hook", "aliases": [ "Claude Code hooks", "PreToolUse hook", "PreToolUse hooks" ], "preview": "A configured action Claude Code runs at a particular event, such as before a tool call.", "detail": "Hooks can inspect event data and return a decision where the event supports one. Safety Core uses command hooks before selected tool actions to check a retry and, when required, request a person’s approval.", "area": "code", "related_terms": [ "git-hook", "coding-agent" ], "references": [ { "label": "Claude Code hooks reference", "url": "https://code.claude.com/docs/en/hooks" } ], "type": "term" }, { "id": "term:coding-agent", "term": "coding agent", "aliases": [ "coding agents", "AI coding assistant", "AI coding assistants" ], "preview": "An AI application that can use tools to read files, edit code and run commands.", "detail": "The model proposes actions; the surrounding application runs permitted tools and returns their results. Claude Code and Codex are examples. Agent Trace displays the saved session records produced by those applications.", "area": "code", "related_terms": [ "agent-skill", "mcp" ], "type": "term" }, { "id": "term:commit", "term": "commit", "aliases": [ "commits", "committed", "Git commit", "Git commits" ], "preview": "A recorded snapshot of a project in Git history, with authorship, a message and links to its parent commits.", "detail": "A normal commit records the prepared index. Most commits have one parent; a first commit has none and a merge can have several. The identifier names that snapshot and its history.", "area": "code", "related_terms": [ "git-index", "git-patch", "working-tree" ], "references": [ { "label": "Git glossary", "url": "https://git-scm.com/docs/gitglossary" } ], "type": "term" }, { "id": "term:comparator", "term": "Comparator", "aliases": [ "the Comparator" ], "preview": "A tool that checks a Lean solution against a separately supplied formal challenge statement and permitted axioms.", "detail": "Comparator compares the relevant formal declarations and checks the proof under its configured conditions. The challenge is itself written in Lean. Matching that challenge is different from comparing the formal statement with the original prose problem.", "area": "maths", "related_terms": [ "lean-proof", "axiom", "statement-fidelity" ], "references": [ { "label": "Comparator documentation", "url": "https://github.com/leanprover/comparator" } ], "type": "term" }, { "id": "term:context-compaction", "term": "context compaction", "aliases": [ "conversation compaction", "compaction" ], "preview": "Condensing a long conversation so an AI application can continue within its context limit.", "detail": "A summary carries forward selected decisions, facts and unfinished work. It can omit detail. Agent Trace lets a user export selected session material into another chat, where it can be summarised before work continues.", "area": "code", "related_terms": [ "coding-agent" ], "type": "term" }, { "id": "term:dafny", "term": "Dafny", "aliases": [ "Dafny proof", "Dafny proofs" ], "preview": "A programming language and verifier for checking code against written mathematical specifications.", "detail": "Preconditions describe allowed inputs, postconditions describe required results, and invariants describe what must stay true. Dafny generates proof obligations for these specifications and can compile executable code. Compilation and successful verification are distinct operations.", "area": "maths", "related_terms": [ "formal-verification" ], "references": [ { "label": "Dafny reference manual", "url": "https://dafny.org/dafny/DafnyRef/DafnyRef" } ], "type": "term" }, { "id": "term:dependency-graph", "term": "Lean dependency graph", "aliases": [ "dependency graph", "dependency graphs", "Lean dependency graphs", "graph of the Lean" ], "preview": "A graph showing which Lean declarations occur in other declarations’ statements or proofs.", "detail": "Quartic Reader and General Reader obtain these dependencies from compiled Lean. A node can be a definition or theorem. This graph describes formal use; an authored argument map instead arranges explanatory steps for a reader.", "area": "maths", "related_terms": [ "proof-graph", "lean-proof", "axiom" ], "type": "term" }, { "id": "term:docstring", "term": "docstring", "aliases": [ "docstrings", "documentation string", "documentation strings" ], "preview": "A string at the start of a Python module, class or function that documents what it does.", "detail": "Python makes this string available as the object’s __doc__ attribute. CodeMap displays descriptions saved with the code and lets coding agents retrieve them as text. A docstring is documentation, so its accuracy depends on how it is maintained.", "area": "code", "related_terms": [ "static-analysis" ], "references": [ { "label": "Python glossary: docstring", "url": "https://docs.python.org/3/glossary.html#term-docstring" } ], "type": "term" }, { "id": "term:duckdb", "term": "DuckDB", "aliases": [], "preview": "A SQL database designed for analytical queries that runs inside the application using it.", "detail": "A DuckDB database can live in memory or in a file. Code Ontology Bridge stores Python functions and call relations in its tables, then queries those tables directly or through NVIDIA Auto Ontology.", "area": "code", "related_terms": [ "sql", "call-graph", "auto-ontology" ], "type": "term" }, { "id": "term:erdos-problem", "term": "Erdős problem", "aliases": [ "Erdos problem", "Erdős problems", "Erdos problems", "Erdős #257", "Erdős problem #257" ], "preview": "A mathematical question posed by Paul Erdős, catalogued by number with its known results.", "detail": "Problem #257 asks whether every infinite selection from 1, 1/3, 1/7, 1/15, … has an irrational sum. The selected terms have the form 1/(2ⁿ − 1). Maths Map brings together work on eight numbered Erdős problems.", "area": "maths", "related_terms": [ "irrationality", "formal-conjectures" ], "type": "term" }, { "id": "term:evalplus", "term": "EvalPlus", "aliases": [], "preview": "A project for evaluating generated code with expanded test sets, including HumanEval+ and MBPP+.", "detail": "The expanded tests expose errors that the original benchmark tests can miss. Zenith uses faulty implementations from this setting to score generated test inputs. EvalPlus names the wider project; HumanEval and HumanEval+ name particular benchmarks.", "area": "code", "related_terms": [ "test-input", "test-harness", "held-out-problems" ], "references": [ { "label": "EvalPlus project", "url": "https://github.com/evalplus/evalplus/blob/master/README.md" }, { "label": "EvalPlus research paper", "url": "https://arxiv.org/abs/2305.01210" } ], "type": "term" }, { "id": "term:exit-code", "term": "exit code", "aliases": [ "exit codes", "exit status", "exit code 0" ], "preview": "A number a finished command returns to the program that ran it; zero conventionally signals success.", "detail": "The meaning of other values depends on the command. A shell pipeline’s reported status can also depend on shell options and which command failed. Reading a test’s recorded output can therefore answer a different question from reading the final exit code.", "area": "code", "related_terms": [ "git-hook", "test-harness" ], "type": "term" }, { "id": "term:exposition", "term": "exposition", "aliases": [ "expository paper", "exposition paper", "expositions" ], "preview": "An explanation of a mathematical result for readers who do not specialise in that result’s field.", "detail": "An exposition can introduce the needed ideas, work through examples and then explain the argument. In the funnel it is one of the written outputs between the specialist paper and the video. Its assumed background should be stated for that particular paper.", "area": "explain", "related_terms": [ "specialist-paper", "research-record" ], "type": "term" }, { "id": "term:flint-hills-series", "term": "Flint Hills series", "aliases": [], "preview": "The infinite sum of 1/(n³ sin² n) over positive integers n, with the angle measured in radians.", "detail": "Some denominators become small when an integer is very close to a multiple of π, linking the convergence question to rational approximations of π. The Atlas example compares reports about an exponent statement and a separate consequence for this series.", "area": "maths", "related_terms": [ "irrationality-exponent" ], "type": "term" }, { "id": "term:forced-alignment", "term": "forced alignment", "aliases": [ "forced aligner", "forced-alignment" ], "preview": "Matching a supplied transcript to recorded speech to estimate where its words or sounds occur.", "detail": "Speech recognition predicts the words; alignment starts from a transcript and estimates their positions in the audio. The boundaries still have uncertainty. A narration plan can use those positions to place visual events near the intended spoken words.", "area": "explain", "related_terms": [ "word-timing", "whisper" ], "type": "term" }, { "id": "term:formal-conjectures", "term": "Formal Conjectures", "aliases": [ "formal-conjectures" ], "preview": "Google DeepMind’s public collection of mathematical problem statements written in Lean.", "detail": "Its entries include numbered Erdős problems and information about their research and formalisation status. The packet’s #257 example distinguishes the general question from the particular 1968 case linked to Will’s proof repository.", "area": "maths", "related_terms": [ "erdos-problem", "lean-4" ], "type": "term" }, { "id": "term:formal-verification", "term": "formal verification", "aliases": [ "formally verified" ], "preview": "Using mathematical methods to establish that a formal model or program satisfies a stated specification.", "detail": "The specification says what is being checked. A proof may cover one calculation, one theorem or a larger system. Formalising a statement means expressing it precisely; verifying a proof or program is a further task.", "area": "maths", "related_terms": [ "dafny", "lean-proof", "statement-fidelity" ], "type": "term" }, { "id": "term:git-hook", "term": "Git hook", "aliases": [ "Git hooks", "pre-commit hook", "pre-commit hooks" ], "preview": "A script Git can run at a particular stage of an operation, such as before creating a commit.", "detail": "A pre-commit hook can run checks and stop that commit command by returning a failing status. Other hooks run after an operation. Git hooks belong to Git; Claude Code hooks run at events in the coding-agent application.", "area": "code", "related_terms": [ "claude-code-hook", "commit", "exit-code" ], "references": [ { "label": "Git hooks documentation", "url": "https://git-scm.com/docs/githooks" } ], "type": "term" }, { "id": "term:git-index", "term": "Git index", "aliases": [ "Git staging area", "staging area", "staged changes" ], "preview": "Git’s stored preparation area for the contents of the next commit.", "detail": "Staging a file or patch updates this area. Later edits in the working tree do not automatically change the staged version. That difference explains how an older staged copy can conflict with another agent’s newly committed fix.", "area": "code", "related_terms": [ "commit", "working-tree", "git-patch" ], "references": [ { "label": "Git glossary", "url": "https://git-scm.com/docs/gitglossary" } ], "type": "term" }, { "id": "term:git-patch", "term": "Git patch", "aliases": [ "Git patches", "patch", "patches" ], "preview": "A description of changes between file versions, such as added and removed lines with their surrounding context.", "detail": "Git can produce patch text from a comparison and apply it to another version. One Checkout uses a selected patch to build a commit while leaving other unfinished edits in the shared working tree.", "area": "code", "related_terms": [ "commit", "git-index", "working-tree" ], "references": [ { "label": "Git patch format", "url": "https://git-scm.com/docs/git-diff" } ], "type": "term" }, { "id": "term:git-worktree", "term": "Git worktree", "aliases": [ "Git worktrees", "linked worktree", "linked worktrees" ], "preview": "A checked-out working tree with its own Git state, attached to a repository that can also have other worktrees.", "detail": "Linked worktrees share repository history and objects but have separate checked-out files and index state. They provide separate places to work. One Checkout explores a different arrangement: several agents editing one shared checkout.", "area": "code", "related_terms": [ "working-tree", "git-index" ], "references": [ { "label": "Git worktree documentation", "url": "https://git-scm.com/docs/git-worktree" } ], "type": "term" }, { "id": "term:ground-state", "term": "ground state", "aliases": [ "ground states" ], "preview": "A configuration with the lowest possible energy for the system being considered.", "detail": "The spin-glass videos use a score equal to minus the energy, so the ground state has the highest score. A near-ground-state configuration has energy close to the minimum; the interesting question is how different such good configurations can be.", "area": "maths", "related_terms": [ "spin-glass", "sherringtonkirkpatrick-model" ], "type": "term" }, { "id": "term:held-out-problems", "term": "held-out problems", "aliases": [ "held-out problem", "held out problems", "held-out tasks" ], "preview": "Problems set aside from the examples used to develop a method, then used to evaluate it.", "detail": "In Zenith, the missed-bug material comes from practice problems and the reported comparison uses 58 other problems. Held out refers to this experiment’s preparation; it does not establish that the underlying model never encountered the problems during training.", "area": "code", "related_terms": [ "evalplus", "test-input" ], "type": "term" }, { "id": "term:intermediate-representation", "term": "intermediate representation", "aliases": [ "IR", "intermediate representations" ], "preview": "A structured form between an input and a final output, used to make a transformation easier to inspect or carry out.", "detail": "Compilers use intermediate representations between source code and generated code. Narration IR applies the idea to explanation: a plan records sentence meanings, source quotations and visual events before an animation is produced.", "area": "explain", "related_terms": [ "word-timing", "agent-skill" ], "type": "term" }, { "id": "term:irrationality", "term": "irrationality", "aliases": [ "irrational", "irrational number", "irrational numbers" ], "preview": "The property of a real number that cannot be written as p/q for integers p and q with q nonzero.", "detail": "Every finite sum of fractions is rational, but the limit of infinitely many such partial sums can be irrational. The #257 video proves a particular irrationality result by ruling out every possible denominator using a carefully constructed remainder.", "area": "maths", "related_terms": [ "erdos-problem", "irrationality-exponent" ], "type": "term" }, { "id": "term:irrationality-exponent", "term": "irrationality exponent", "aliases": [ "irrationality measure" ], "preview": "A number describing how closely a real number can be approximated by infinitely many fractions.", "detail": "For x, it is the supremum of exponents μ for which 0 < |x − p/q| < 1/q^μ has infinitely many integer pairs p, q with q positive. A larger exponent permits unusually accurate rational approximations.", "area": "maths", "related_terms": [ "irrationality", "flint-hills-series" ], "type": "term" }, { "id": "term:lean-4", "term": "Lean 4", "aliases": [ "Lean", "Lean theorem prover", "Lean proof assistant" ], "preview": "A programming language and proof assistant for expressing definitions, statements and proofs that a small kernel can check.", "detail": "Tactics help construct proof terms; the kernel checks those terms against their types. Files can also contain assumptions or unfinished placeholders, so a successful build alone is not the same as a completed proof of every stated theorem.", "area": "maths", "related_terms": [ "lean-proof", "axiom", "mathlib" ], "references": [ { "label": "Lean reference: validating proofs", "url": "https://lean-lang.org/doc/reference/latest/ValidatingProofs/" } ], "type": "term" }, { "id": "term:lean-proof", "term": "Lean proof", "aliases": [ "Lean proofs", "Lean-checked proof", "Lean-accepted proof" ], "preview": "A proof expressed in Lean as a term whose type is the theorem statement.", "detail": "When the kernel accepts the term, it establishes that formal statement from its definitions and declared assumptions. A reader website can link a passage of prose to the declarations involved. Matching the prose to the formal statement is a separate question.", "area": "explain", "related_terms": [ "lean-4", "statement-fidelity", "axiom" ], "references": [ { "label": "Lean reference: validating proofs", "url": "https://lean-lang.org/doc/reference/latest/ValidatingProofs/" }, { "label": "Lean reference: axioms", "url": "https://lean-lang.org/doc/reference/latest/Axioms" } ], "type": "term" }, { "id": "term:manim", "term": "Manim", "aliases": [ "Manim Community", "ManimCE", "ManimGL" ], "preview": "A family of Python tools for making mathematical animations from code.", "detail": "Code creates equations, shapes and graphs, then specifies their changes over time. Manim Community and ManimGL are related implementations with different APIs. A narration plan can describe the intended visual explanation before code for a particular renderer is written.", "area": "explain", "related_terms": [ "intermediate-representation", "word-timing" ], "type": "term" }, { "id": "term:mathlib", "term": "mathlib", "aliases": [ "Mathlib", "mathlib4" ], "preview": "The community-maintained Lean library of mathematical definitions and proved results.", "detail": "A Lean development can import mathlib and build on existing results instead of proving every prerequisite again. Its declarations also appear in dependency graphs and in the list of results a proof uses.", "area": "maths", "related_terms": [ "lean-4", "dependency-graph" ], "type": "term" }, { "id": "term:mcp", "term": "MCP", "aliases": [ "Model Context Protocol" ], "preview": "Model Context Protocol: a standard way for AI applications to connect to tools, data and reusable prompts.", "detail": "An MCP server can expose executable tools, readable resources and prompt templates. A compatible client decides how to make these available. Agent Trace’s optional server exposes access to saved session records.", "area": "code", "related_terms": [ "coding-agent" ], "references": [ { "label": "MCP server primitives", "url": "https://modelcontextprotocol.io/specification/2025-06-18/server" } ], "type": "term" }, { "id": "term:nearly-quartic-separation", "term": "nearly quartic separation", "aliases": [ "quartic separation", "nearly quartic query separation", "fourth-power result", "quartic result" ], "preview": "A family of problems where randomized query counts grow almost as the fourth power of quantum query counts.", "detail": "For the relevant total Boolean functions, the construction makes R(fₙ) at least Q(fₙ)^(4 − o(1)) as the family grows: the exponent approaches four. This approaches the known fourth-power upper bound on input queries, rather than total running time.", "area": "explain", "related_terms": [ "randomized-query-complexity", "quantum-query-complexity", "total-function" ], "references": [ { "label": "Aaronson et al.: Degree vs. Approximate Degree and Quantum Implications of Huang’s Sensitivity Theorem", "url": "https://arxiv.org/abs/2010.12629" } ], "type": "term" }, { "id": "term:ontology", "term": "ontology", "aliases": [ "ontologies" ], "preview": "A structured account of the kinds of things in a domain, their properties and their relationships.", "detail": "For code, the kinds might include functions and calls, with relations such as caller and callee. In a database application, these concepts can be connected to concrete tables and columns so a query system has useful context.", "area": "code", "related_terms": [ "semantic-model", "auto-ontology" ], "type": "term" }, { "id": "term:palomar", "term": "Palomar", "aliases": [ "Palomar registry" ], "preview": "The formal-proof registry used in the supplied Erdős example to record challenge statements, proof files and checker results.", "detail": "An entry records the particular submitted statements and proofs alongside its saved results. In the packet’s #257 example, the registry is one route from the paper to the formal statement and the proof that was checked.", "area": "maths", "related_terms": [ "comparator", "lean-proof" ], "type": "term" }, { "id": "term:pldi", "term": "PLDI", "aliases": [ "Programming Language Design and Implementation" ], "preview": "Programming Language Design and Implementation, an ACM SIGPLAN conference on programming-language research.", "detail": "General Reader’s current example is Contextual Embeddings, a PLDI 2026 paper. The reader places its text beside the Lean proof released by the paper’s authors.", "area": "maths", "related_terms": [ "lean-proof" ], "type": "term" }, { "id": "term:proof-graph", "term": "argument map", "aliases": [ "argument maps", "graph of the argument", "graph of the proof", "proof graph" ], "preview": "An explanatory diagram showing the main steps of an argument and how they connect.", "detail": "SK Reader’s map was authored from the papers and formal material to help readers follow the explanation. It is different from a Lean dependency graph extracted from compiled declarations. A map can be useful without reproducing every formal dependency.", "area": "explain", "related_terms": [ "dependency-graph", "lean-proof" ], "type": "term" }, { "id": "term:quantum-query-complexity", "term": "quantum query complexity", "aliases": [ "quantum queries", "quantum query", "Q(f)" ], "preview": "The fewest input-oracle calls a quantum algorithm needs to compute a function with a specified success guarantee.", "detail": "In the bounded-error setting here, success must be at least two thirds on every input, and the query bound is worst case. A query can act on a superposition of input positions; that does not reveal all those bits separately.", "area": "maths", "related_terms": [ "query-complexity", "randomized-query-complexity", "total-function" ], "type": "term" }, { "id": "term:query-complexity", "term": "query complexity", "aliases": [ "query-complexity", "input queries", "query count" ], "preview": "The number of calls an algorithm makes to an input oracle, counting those accesses rather than all its computation.", "detail": "A classical bit query returns a requested input bit. A quantum query is an allowed oracle operation that can act on a superposition. Query complexity compares algorithms in this access model, which is why it is not a direct measurement of elapsed time.", "area": "maths", "related_terms": [ "quantum-query-complexity", "randomized-query-complexity" ], "type": "term" }, { "id": "term:randomized-query-complexity", "term": "randomized query complexity", "aliases": [ "randomised query complexity", "randomized queries", "randomised queries", "R(f)" ], "preview": "The fewest input queries a randomised algorithm needs under a specified success guarantee and query bound.", "detail": "Here R(f) uses a worst-case query bound and requires a correct answer with probability at least two thirds on every input. The random choices can change which positions are queried. Different conventions should be stated when used.", "area": "maths", "related_terms": [ "query-complexity", "quantum-query-complexity" ], "type": "term" }, { "id": "term:recursive-query", "term": "recursive SQL query", "aliases": [ "recursive query", "recursive queries", "recursive SQL", "WITH RECURSIVE" ], "preview": "A database query that repeatedly uses rows from an earlier step to find more results.", "detail": "A recursive common table expression can follow a function’s callers, then their callers, and so on. The query needs a stopping condition or cycle handling appropriate to its form; WITH RECURSIVE by itself does not guarantee termination.", "area": "code", "related_terms": [ "sql", "call-graph" ], "references": [ { "label": "DuckDB: recursive common table expressions", "url": "https://duckdb.org/docs/lts/sql/query_syntax/with" } ], "type": "term" }, { "id": "term:research-record", "term": "research record", "aliases": [ "long research record", "long reasoning record", "full write-up" ], "preview": "The detailed written account of a result’s reasoning, used as the fuller source for shorter explanations.", "detail": "In the funnel, the record works through the formal proof and its mathematical context before a specialist paper, exposition and video are produced. It is designed for looking up detail as well as reading sequentially.", "area": "explain", "related_terms": [ "specialist-paper", "exposition", "lean-proof" ], "type": "term" }, { "id": "term:semantic-model", "term": "semantic model", "aliases": [ "semantic models", "semantic layer" ], "preview": "A description of what data means and how its entities, fields and relationships fit together.", "detail": "For Code Ontology Bridge, it explains tables of functions and calls, their identifiers and how rows join. This gives a query system more context than column names alone. A semantic layer may also define reusable expressions or measures.", "area": "code", "related_terms": [ "ontology", "auto-ontology", "sql" ], "type": "term" }, { "id": "term:sherringtonkirkpatrick-model", "term": "Sherrington–Kirkpatrick model", "aliases": [ "Sherrington-Kirkpatrick model", "Sherrington–Kirkpatrick spin glass", "Sherrington-Kirkpatrick spin glass", "SK model", "SK spin glass", "SK" ], "preview": "A spin-glass model in which every pair of spins interacts with a randomly chosen strength.", "detail": "Each spin is +1 or −1. In a common zero-field convention, H(σ) = −n^(−1/2) Σᵢ<ⱼ Jᵢⱼσᵢσⱼ, with independent standard Gaussian couplings Jᵢⱼ. The videos draw spins as arrows and use a score equal to minus the energy.", "area": "maths", "related_terms": [ "spin-glass", "ground-state" ], "type": "term" }, { "id": "term:specialist-paper", "term": "specialist paper", "aliases": [ "expert paper", "short paper for experts", "specialist papers" ], "preview": "A paper written for readers who already know the relevant research field.", "detail": "It can rely on standard background and concentrate on the result and its argument. In the funnel it is shorter than the research record. The exposition instead supplies more context for readers outside that specialism.", "area": "explain", "related_terms": [ "research-record", "exposition" ], "type": "term" }, { "id": "term:spin-glass", "term": "spin glass", "aliases": [ "spin glasses", "spin-glass" ], "preview": "A model of a disordered magnet with competing interactions between spins.", "detail": "A spin can be represented by an up or down arrow. Some interactions favour matching spins and others favour opposite spins, so satisfying one interaction can conflict with satisfying another. The Sherrington–Kirkpatrick model is one particular spin-glass model.", "area": "maths", "related_terms": [ "sherringtonkirkpatrick-model", "ground-state" ], "type": "term" }, { "id": "term:sql", "term": "SQL", "aliases": [ "Structured Query Language", "SQL query", "SQL queries" ], "preview": "Structured Query Language: a language for retrieving and changing data organised in relational tables.", "detail": "A query can select rows, combine tables through joins and compute results. Code Ontology Bridge publishes SQL queries alongside its answers, so the operation can be inspected and rerun against the supplied database.", "area": "code", "related_terms": [ "duckdb", "recursive-query", "text-to-sql" ], "type": "term" }, { "id": "term:statement-fidelity", "term": "statement fidelity", "aliases": [ "faithful formalisation", "formalisation fidelity", "formalization fidelity" ], "preview": "How accurately a formal statement expresses the mathematical claim it is meant to represent.", "detail": "The objects, quantifiers, hypotheses and conclusion all matter. A proof can establish its formal statement even if that statement differs from the paper. Reader links make the two versions easier to compare; the links themselves do not settle the comparison.", "area": "explain", "related_terms": [ "lean-proof", "comparator", "formal-verification" ], "type": "term" }, { "id": "term:static-analysis", "term": "static analysis", "aliases": [ "static analyser", "static analyzer" ], "preview": "Examining a program without executing it, using its source code or another representation.", "detail": "An analysis can extract definitions, calls and possible dependencies. Dynamic dispatch and other runtime behaviour can make these relations incomplete or approximate. Code Ontology Bridge uses source analysis to populate its code database.", "area": "code", "related_terms": [ "call-graph", "callback" ], "type": "term" }, { "id": "term:test-harness", "term": "test harness", "aliases": [ "test harnesses", "harness" ], "preview": "The surrounding code that runs tests, collects results and applies the scoring or pass rules.", "detail": "A harness can prepare inputs, run a reference implementation and faulty versions, enforce time limits and record outputs. Zenith’s saved responses can be rescored through its harness without generating new model replies.", "area": "code", "related_terms": [ "test-input", "timeout", "evalplus" ], "type": "term" }, { "id": "term:test-input", "term": "test input", "aliases": [ "test inputs" ], "preview": "A value or set of values supplied to a program during a test.", "detail": "For a function that adds a list, an input might be [2, −1, 0]. 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