(git-record date, not publication date)
partly settled
ordinary mathematical derivation
primary investigation
verified
The perfect-power cap saving for old fixed-seed square-root-support lifts is at most order N^{1/4} log N, and an explicit balanced Mobius-prefix family at N=36864 lowers full excess over N from 877.252193 to 220.982190 by excluding composites witnessed by 2, 3, 5, 7, with coefficients unchanged; the uniform N+O(sqrt(N) log(N)^2) target remains unproved.
hunts/paid_shortfall_scaling (Record 97 of 98 in chronological sequence)
Guiding Question
Can scale-dependent balanced coefficients lower the complete paid excess, and how much can perfect-power caps contribute?
Method & Verification
An exact signed factorial-sum identity prices the perfect-power cap, a Mobius-prefix family is given with mass at most 2y-1, and five fixed cutoffs were checked with two interval implementations at two precisions.
Lineage & Relationships
paid_shortfall ↗, paid_shortfall_saturation ↗, paid_surplus_obstruction ↗
Primary Sources (at pin 8fa46e134)
Editorial Notes
Disposition is partly settled because the finite identities and the N=36864 improvement are recorded, while the uniform complete-cost target is explicitly unproved. No extrapolated exponent, RH claim, or novelty claim.
Date Provenance
commit fd04f1fac9d48a4d769048817e678acdea3b4bdb, hunts/paid_shortfall_scaling/RESULTS.md, author 2026-09-13T19:31:01-05:00