Continue the factorial-certificate investigation from main d393e1a. The previous LP imposes positivity at every integer cell through N, although its prime sum evaluates the certificate only at floor(N/d). Test the smaller constraint set of all attainable integer quotients, without using prime locations to choose the constraints. Audit the claimed asymptotic barriers separately from these finite measurements.
Scope: this directory, its regression test, its hunts/README.md case-log entry, regenerated CONTEXT.md, and a dated correction pointer at the top of the earlier LP results. Earlier recorded text remains intact. No core-package changes. Every numerical optimization is a measured finite result. No claim about RH or novelty follows from a successful finite optimization.
id: quotient_certificate
question: How much excess does positivity on unattainable cells force in the finite factorial-certificate LP?
frontier: The all-cell LP has measured excess 62.923 at N=1000,y=31 and 323.65 at N=10000,y=100; its proposed N/sqrt(y) lower bound is unproved
proposed_attack: Impose positivity at every attainable quotient floor(N/d), derive validity without prime locations, and compare with the all-cell and prime-cell LPs
dead_routes:
- treating three fitted cutoff values or a Gaussian heuristic as an asymptotic obstruction
- treating exact evaluation through prime-counting data as an independent estimate
required_oracles:
- direct enumeration of all integer quotients
- exact rational evaluation of candidate floor-sum inequalities
- independently factored von Mangoldt sums and high-precision logarithms
- primary literature for statements about RH and approximation rates
kill_conditions:
- any attained quotient violates the proposed ceiling
- direct weighted excess disagrees with the factorial objective
- a claimed improvement disappears after exact feasibility repair
agents_may:
- derive
- measure
- search
- attack
agents_may_not:
- declare novelty
- promote an asymptotic conclusion from finite fits
- modify earlier research records