(git-record date, not publication date)
completed
ordinary mathematical derivation
primary investigation
verified
An early-truncated finite balanced lift has a complete paid-tail bound of order sqrt(N) log N at square-root support, but the leading constant stays above one so excess over N is still linear, while at N=14 with support at most three, perfect-power caps remove the optimal raw excess log(2)/2.
hunts/paid_shortfall (Record 95 of 98 in chronological sequence)
Guiding Question
Can an early-truncated explicit factorial lift have a proved full paid-shortfall budget at square-root support?
Method & Verification
An explicit early-truncation lemma charges every remainder, and the durable run passed 768 truncation cases and 3072 inequalities on both interval backends at 35 and 70 digits, including the exact N=14 primal and dual identities.
Lineage & Relationships
paid_shortfall_scaling ↗, quotient_certificate ↗, prime_pair_error ↗
Primary Sources (at pin 8fa46e134)
Editorial Notes
No Lean proof or external review. The all-N bound rests on the displayed derivation, not on the size of the finite domain. The base-6 seed has leading constant (4 log 2 + 3 log 3)/5 > 1. No RH or novelty claim.
Date Provenance
commit 4efa72ad70a1e535709c33d0eded886d29c19274, hunts/paid_shortfall/RESULTS.md, author 2026-09-13T18:47:57-05:00