Written 2026-10-24, corrected 2026-10-27. Grade: measured, one route, float/mpmath values, no enclosure. It is a kill, so the usual ladder does not apply: a negative result does not need a certificate to be worth recording, only a reproduction.
This is not the missing outcome of the hunt.
hunts/README.mdHunt #2 already withdraws the recorded correlation, on three defects checked in tree: the completeness gate was never called, a lesion shows an incomplete on-line list forges the off-line signal at zero factorization defect, and the test set is the rival set. This file is an additional, independent defect in the same scanner. It does not replace that withdrawal.
What was claimed
run_experiment.py sweeps a one-parameter family F_kappa, kappa from 0 to 1, and records a factorization_defect together with a max_position_residue. The saved rows rise together: defect 1.58 to 105.95, residue 3.66 to 4.99. Read straight, that is a quantitative relation between failure to factor and failure to sit on the line, which is the MISSION's hypothesis.
What is actually there
Re-run on 2026-10-24 with the hunt's own modules (detector.py, family.py), same parameters, c grid 20, 40, 60, 80, 86, 90, 95, t_max 110, n_max 2000. The script that prints these numbers is hunts/factorization_vs_position/diagnose_kappa_scan.py. It imports detector.py and family.py unchanged.
kappa = 0.0 defect = 1.5823 online zeros = 59
c arith zeroside residue
20 2.9587 2.7761 0.1826
40 4.0783 4.3832 -0.3049
60 4.3375 4.3640 -0.0265
80 4.5441 4.5661 -0.0220
86 5.0705 1.4059 3.6645
90 4.9870 4.7697 0.2173
95 5.0495 5.1623 -0.1128
kappa = 1.0 defect = 105.9511 online zeros = 59
c arith zeroside residue
20 2.2710 2.7761 -0.5051
40 5.2349 4.3832 0.8516
60 4.4007 4.3640 0.0367
80 4.5666 4.5661 0.0004
86 6.3965 1.4059 4.9906
90 4.4010 4.7697 -0.3687
95 5.4911 5.1623 0.3289Three defects, in order of severity. Defect 1 is the one this file adds. Defects of completeness, the lesion, and the rival set are Hunt #2's, already withdrawn there.
1. The scanner's output does not depend on kappa
zeroside is identical at every c for the two ends of the family: 2.7761, 4.3832, 4.3640, 4.5661, 1.4059, 4.7697, 5.1623 in both runs, and online_zero_count is 59 in every one of the nine saved rows. The on-line zero side is a functional of one list of zeros, so an unchanged zero side means the same zeros were found for every member.
The mechanism is exact proportionality, not a shared sample. family.Z_kappa returns the real part of one fixed rotation, expjpi(dh_theta(t)/pi), times f_kappa. That real part is (1 + 0.284079*kappa) times one fixed function of t. 0.284079 is the leading digits of zeta.epstein.KAPPA_REF. The ratio Z_kappa(t, 1) / Z_kappa(t, 0) tracks 1 + KAPPA_REF at t = 4, 12.3, 30.3, 50 and 77.7. The values are float64: family.Z_kappa returns float(mp.re(val)). Proportionality is confirmed numerically at roughly 1e-16 relative residual in float64, not to 20 digits (test_kappa_proportionality.py pins the identity at rel=1e-12). The factor is positive for kappa in [0, 1], so sign changes of the scanner's output cannot depend on kappa. The sweep is reading one fixed zero set, not nine.
The rotation is the Davenport-Heilbronn root number for every kappa, so the quantity is real only at the DH parameter. At kappa = 0 and kappa = 1, float(mp.re(val)) takes the real part of a complex value. Those sign changes are not zeros of F_kappa. Proportionality is why the list cannot move even before that point is reached: a positive scalar does not move a sign change.
2. The extremum is therefore fixed by construction
argmax_c = 86.0 in all nine rows because the residue at c = 86 is dominated by zeroside collapsing to 1.4059 there, in both runs above. That collapse is a property of the shared zero list, not of the family. Any sweep over this c grid will return 86 regardless of the defect, which is what an artifact looks like: an extremum location invariant under a 67x change in the independent variable.
3. kappa = 0 is not zeta, and is not an Euler product
Coefficients from f_kappa_coefficients, n = 1..12, kappa = 0:
n 1 2 3 4 5 6 7 8 9 10 11 12
f_0(n) +1 0 0 -1 0 +1 0 0 -1 0 +1 0Nonzero at 1, 4, 6, 9, 11 with signs +, -, +, -, +. This is not a Dirichlet character and not zeta. f_0 = (L(chi) + L(chibar))/2 is a linear combination of L(chi) and L(chibar) without a scalar Euler product. Its factorization_defect of 1.58 is therefore not a deviation from an Euler product it was supposed to have. The family never interpolates zeta to DH; both ends lack the property the x-axis is supposed to be measuring.
The independent control in results2.json supports this reading rather than contradicting it: zeta there has defect 0.0 and residue 0.0037, roughly a thousandth of the family's smallest residue. Whatever results.json is measuring, it is not a smooth departure from the zeta point, because zeta is not on that axis.
Verdict
The saved correlation is withdrawn. Hunt #2 already withdrew it on completeness, the lesion, and the rival set. This file adds an independent defect: the scanner's output is a positive multiple of one fixed function, so the zero list cannot depend on kappa. Nothing about factorization defect versus zero position is established here, in either direction.
Reproduce with the repository interpreter (backend python-flint) and:
python hunts/factorization_vs_position/diagnose_kappa_scan.py
python -m pytest hunts/factorization_vs_position/test_kappa_proportionality.py -q