Factorial Linear Forms and Denominators: Detailed Proofs and Rationality Criteria

Source links from the short paper

These links collect the declarations formerly listed in the short paper’s source appendix, at the same historical revisions and paths. They supplement the concordance above. No fresh compilation or independent review is asserted by a link, and a theorem about a conditional family leaves its hypotheses to be established.

• maximal prime power survival.

• the explicit vector $U_9$.

• its weighted sums.

• divisibility of $V_d(\lambda )-M(\lambda )$ by $d!-1$.

• the Lean file on the integer basis.

• an account of the integer basis.

• an account of the primitive vector.

• the finite formula for the gcd.

• the finite gcd verification script.

• a script.

• Generic gcd lemmas in the Lean sources.

• the liminf bound for the common denominator.

• the inequality for a terminal block.

• the vector $2e_3-e_4$.

• the exact floor correction for the companion series.

• the prime-power noncancellation criterion.

The remaining links from the short paper use revision 99f4bf47422a; the links in the preceding concordance use this record’s own revision. The following numbers link to source lines within each named module, retaining both revisions where they differ.

AdjacentUnitCarryWindow.lean

• 148
• 215
• 243
• 337

ChannelBreakpointRigidity.lean

• 71
• 91
• 101
• 130

ChannelIntegralCongruence.lean

• 868
• 885
• 905
• 1084
• 1103

DivisorFactorialCentre.lean

• 34
• 39
• 44
• 49
• 80
• 88
• 102
• 129
• 146
• 170
• 179
• 188

EndpointWeightedPrivateSupport.lean

4766.

FactorialChannelCertificate.lean

• 25
• 39
• 43
• 51
• 55
• 59
• 65
• 105
• 109
• 112
• 119
• 126
• 133
• 140
• 151
• 156

FactorialZeroPlateau.lean

• 876
• 940

PrimeUnitTranslator.lean

1559.

PrimeZeroBranch.lean

6099.

The hypotheses about short intervals, least prime factors, and the nonzero real remainders are stated in the mathematical sections above. They remain hypotheses when a declaration link is followed.