{"collections":{"members":{"count":719,"page_size":256,"pages":["numbers/members/cf35cb2b6cd7cec332579c56.json","numbers/members/51169c4241f3ab3bf0024ea4.json","numbers/members/c092234b30453b7c8f96af57.json"]},"observations":{"count":719,"page_size":256,"pages":["numbers/members/74b05cfa6e53c6f3c6c6213e.json","numbers/members/6da60aa027b2c2f29351e239.json","numbers/members/f86b2424180f79e28b58260d.json"]},"universe":{"count":719,"page_size":256,"pages":["numbers/members/126feaac060cf07c4fcab484.json","numbers/members/1830e47fc1abbeb6ccfee61e.json","numbers/members/ede835a5c06fcc4af21e77ec.json"]}},"generation_id":"sha256:e44fe048bf34d4e55b76af0e42f931ce1121c5c189edf0e8cd6061a5902b3e47","kind":"number-receipt","number":{"aggregation":"sum","credit":{"boundary":"Inventory or textual extraction; no proof execution, scope review or exhaustive discovery is implied.","inputs":[{"credit":"Will Cook, OpenAI Math Atlas; source manuscripts and Lean quotations credited to OpenAI.","kind":"attributed-extraction","license":"Apache-2.0","pin":"8056826bbd00caea871ad036bd295182e2bef3e2","sha256":"sha256:cc051f78a9def390c8504bc276449e72b9b289623643e23d55b1034007f99d6c","source":"data/manuscripts.json"}],"kind":"computed-from-captured-ledger","pin":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","repository":"https://github.com/openai/math","source_fields":[{"path":"../ledger.json","pointer":"/manuscripts"}]},"hash_scope":"complete-receipt-except-sha256","issues":[],"key":"paper_environments_hypothesis","rule":"Sum of source per-manuscript counts for environment kind hypothesis over current manuscripts; these samples are not the separate canonical statement-row inventory.","sha256":"sha256:b46589f77c0c62d8c8cb3732ba37ead2eb832f1c38f852077549fb34a8ed1c32","state":"computed","unit":"source environment occurrences","value":21},"pin":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","reconstruction":"Concatenate each named collection in page order and restore it on number. The logical receipt digest binds the complete record; page hashes alone do not establish the aggregate.","release_id":"openai-math","schema":"statement-map-web/2"}