USR-2026-0044 · Growth / gravity
The growth index γ evolves from 0.41 (z < 0.3) to 0.10 (z > 1) — gravity weakens with redshift.
KILLED
was 4.84σ claimed — 1.03σ on independent reproduction, opposite sign
re-run & confirmed 2026-07-26 (R0 — founder CI; independence pending)
A claim that gravity weakens with redshift, refuted by its own kill test. Re-fitting the same 28 fσ₈ points on an independent path with a validated growth ODE, the evolution term buys Δχ² = 1.06 for one extra parameter (1.03σ), and γ RISES with redshift (γ_a = +0.63) rather than falling. The registry's own quoted γ values fit the data WORSE than plain GR. Killed on the record.
AUTOPSY REPORT — killed (self, the most honored outcome here)
Date: 2026-07-26 · Epitaph: "Died by its own kill test, on our own data, at our own hand. The 4.84σ evolution reproduces at 1.03σ with the sign reversed, no jackknife sample recovers it, and the claimed Δχ² is arithmetically unreachable given how well the no-evolution model already fits. The autopsy is the useful part: fσ₈ loses 93% of its sensitivity to γ by z ≈ 2, and γ is 91% correlated with σ₈ — so a high-z γ 'measurement' is mostly the amplitude degeneracy talking. Gravity does not weaken with redshift in this data; it looks like General Relativity (γ = 0.525 ± 0.077 vs 0.55). Post-mortem addendum: fixing a wrong fσ₈ point uncovered during the autopsy makes the evidence against this claim stronger, not weaker — γ_a moves from +0.63 to +1.19 while the claim requires about −0.68."
Falsify-box — how to kill this claim
TRIGGERED
independent-path (R2) reproduction of the γ(z) evolution
Verification record — every quoted number, re-run 2026-07-26
| quantity | measured | verdict |
|---|---|---|
| claimed significance | 4.84σ (γ: 0.41 → 0.10, falling) | NOT_RERUN |
| independent-path significance | 1.03σ (Δχ² = 1.06 for 1 extra parameter) — 4.5% of the Δχ² the claim requires | MISMATCH |
| sign of the fitted trend | γ_a = +0.628 ± 0.599 — γ RISES 0.62 → 0.91; the claim requires it to FALL | MISMATCH |
| constant-γ fit vs General Relativity | γ = 0.525 ± 0.077 — consistent with the GR value 0.55 | MATCH |
| survey jackknife | 0 of 22 delete-one samples reproduce the claim's sign | MISMATCH |
| registry's own γ values imposed as a model | χ² = 18.48 (ramp) and 15.55 (step) — both WORSE than plain GR's 15.13 | MISMATCH |
| arithmetic ceiling on the claim | the no-evolution model already sits at χ² = 15.02 for 28 points (χ²/dof = 0.58); the audit's Δχ² 130 → 49 would require χ²/dof ≥ 4.8 and ≥ 1.8 — unreachable with this data | MISMATCH |
| why it was fragile — structural leverage | dlnf/dγ falls from −1.168 at z = 0 to −0.083 at z = 1.94: only 7.1% of the low-z leverage, a factor 14 loss | MATCH |
| why it was fragile — degeneracy | corr(γ_a, σ₈) = +0.914; the literal high-z bin returns σ₈ = 63 — a degeneracy runaway, not a measurement | MATCH |
| correlated-systematics scan | assuming within-survey correlation ρ = 0 → 0.9 drives the significance 1.03σ → 0.29σ; no value of ρ rescues the claim | MATCH |
| data-fix robustness check (2026-07-26) | the reproduction surfaced a wrong fσ₈ value in our own catalog (z = 1.48: 0.315 ± 0.095, a number absent from its own cited source; Hou et al. 2020 reports 0.464 ± 0.045). Corrected and re-fit: the evolution signal STRENGTHENS to 2.27σ but γ_a goes MORE positive (+0.628 → +1.185), so the kill survives and the corrected data argue harder against the claim's direction | MATCH |
Provenance
script: information_seam/growth_index_retest.py
script status: PRESENT
datasets: fσ₈ compilation, 28 points, z = 0.001–1.944 (engine/data/catalogs.py) · information-seam-scripts (downloadable — run it yourself)
re-run: 2026-07-26
script status: PRESENT
datasets: fσ₈ compilation, 28 points, z = 0.001–1.944 (engine/data/catalogs.py) · information-seam-scripts (downloadable — run it yourself)
re-run: 2026-07-26
Edges
CONTRADICTS
→ Literature claims of an evolving growth index / weakening gravity: on this compilation the constant-γ fit is consistent with the General Relativity value and the evolution term is not significant.
Status, honestly
kill test fired: the independent-path reproduction failed — 1.03σ against the claimed 4.84σ, with the best-fit trend running the OPPOSITE way. Status here is computed from evidence — the author cannot set it, and neither can we. Independent reproduction would move it; nothing else will.
§ Reproduction
growth_index_retest.py
The founder's own run of this script, captured verbatim. A match proves the result is reproducible; it is still R0 on this registry's independence rings — same code, so it cannot move a status. Only an outside run does that.
A · Recorded
founder's machine · 2026-08-02
25 dof,
gamma_0 = 0.5935 +/- 0.0727, gamma_a = +1.1854 +/- 0.5053,
sigma8 = 0.9098 +/- 0.0620
[H5] Delta chi2: M0->M1 = 0.2108 (+1 par) -> 0.46 sigma
M1->M2 = 5.1308 (+1 par) -> 2.27 sigma
M0->M2 = 5.3417 (+2 par) -> 1.82 sigma
[H6] EVOLUTION SIGNIFICANCE (this path) = 2.27 sigma
REGISTRY CLAIM = 4.84 sigma
=> obtained Delta chi2 5.131 vs the 23.4 required for 4.84 sigma.
[H7] SIGN: best-fit gamma_a = +1.1854. The claim needs gamma_a < 0
(gamma falling 0.41 -> 0.10). This path gets the OPPOSITE sign.
gamma(z=0.15) = 0.748, gamma(z=1.4) = 1.285 vs claimed 0.41, 0.10
[H8] JACKKNIFE (drop each of 22 surveys): gamma_a spread = 0.5787
range [+0.7964, +1.3751], delete-one sd = 0.4975; 0/22 samples
have the claim's sign. Max Dchi2 over jackknives = 6.143 (2.48 sigma).
[H9] gamma-sigma8 CORRELATION (M1, 2x2): +0.77231
M2: corr(gamma_0,sigma8) = +0.4379, corr(gamma_a,sigma8) = +0.8812
sigma8 fixed to Planck 0.8102: gamma_a = +0.4130, Dchi2 = 2.785 -> 1.67 sigma
[H10] BINNED (the literal claim), sigma8 free:
z < 0.3 gamma = 0.2787, sigma8 = 0.6219
z > 1 gamma = -3.0000, sigma8 = 227.2220 [PINNED AT SEARCH BOUND -- NOT A MEASUREMENT]
with sigma8 fixed to Planck: gamma(z<0.3) = 0.5743,
gamma(z>1) = 1.6485 -- RISING, claim says 0.41 -> 0.10 (falling).
[H11] HIGH-z LEVERAGE: dlnf/dgamma at z=1.944 is 7.1% of its
z=0 value. The claim's own two gamma values differ by only
4.71% in f at z=1.4, against 24% measurement errors there.
[H12] REGISTRY'S OWN gamma VALUES AS A MODEL: chi2 = 27.927 (CPL form)
/ 24.427 (step form) vs 19.785 for plain GR gamma=0.55.
[H13] VALIDATIONS: EdS max|D/a - 1| = 3.963e-12; gamma-integral vs GR ODE
at gamma=0.55, worst rel. diff = 3.755e-04 (Linder-formula accuracy);
gamma_eff of the GR ODE at z=0 = 0.5544.
==============================================================================
VERDICT
------------------------------------------------------------------------------
Registry claim USR-2026-0044: gamma evolves 0.41 -> 0.10 at 4.84 sigma.
Kill test 'independent-path (R2) reproduction': NOW TESTED.
RESULT: THE CLAIM FAILS TO REPRODUCE ON THIS INDEPENDENT PATH.
Numbers, without softening:
* Evolution significance here: 2.27 sigma. Claimed: 4.84 sigma.
Delta chi2 = 5.131 where 23.4 would be needed.
* ARITHMETIC CEILING. The TOTAL chi2 of the no-evolution model
is 19.57 for 28 points. The registry summary describes an audit
moving Delta chi2 from 130 to 49. On this path there is no
such chi2 to move: driving chi2 to EXACTLY ZERO would buy only
19.57. A Delta chi2 of 49 would require the null model to have
chi2 >= 49 on 27 dof (chi2/dof >= 1.8); 130 would require
chi2/dof >= 4.8. Here the null gives chi2/dof = 0.753. So the
original analysis cannot have been fitting this data with this
model and these errors -- something else differs (a covariance
matrix, a different sigma8 treatment, a different Omega_m, or a
different growth normalisation). That difference, not the
physics, is what needs auditing.
* The best-fit evolution has the OPPOSITE SIGN to the claim
(gamma_a = +1.1854; the claim requires gamma_a < 0).
* 0 of 22 survey-jackknife samples have the claim's sign.
The jackknife spread in gamma_a is 0.579, i.e. 49% of the
best-fit value, and the delete-one sd (0.497) is comparable to
the fit error (0.505). So gamma_a is POORLY DETERMINED -- but
its sign never flips under any single-survey deletion.
* The claim's own quoted gamma values, imposed as a model, fit
this data WORSE than plain GR (chi2 27.93 / 24.43 vs 19.79).
* The z>1 bin, fitted the way the claim is phrased (constant
gamma, sigma8 free, 4 points), does not measure gamma at all:
its best fit is gamma = -3.00 with sigma8 = 227.2. sigma8 ~ 0.8
in this universe. That is the gamma-sigma8 degeneracy running
free, not a measurement. Fix sigma8 to Planck and the same bin
returns gamma = 1.65, ABOVE the z<0.3 bin's 0.57 -- the
opposite ordering to the claim.
* The disputed data rows do not rescue the claim either:
taking the CSV values instead makes gamma_a MORE positive
(+1.1861), i.e. further from the claim, not closer.
WHY THE CLAIM WAS ALWAYS GOING TO BE FRAGILE (structural, not a
criticism of anyone's arithmetic):
(1) Omega_m(z) -> 1 at high z, so f = Om^gamma becomes BLIND to
gamma exactly where the claim locates its signal. At z=1.944
the leverage is 7.1% of the z=0 leverage.
(2) In the D(z)/D(0) normalisation, gamma above a point's own
redshift cannot affect that point. 'gamma at z>1' is
constrained by 4 points with ~24% errors.
(3) gamma and sigma8 are correlated at +0.772 (M1), and gamma_a
with sigma8 at +0.881 (M2). Free sigma8 lets a bin fit trade
almost any gamma for a matching amplitude.
(4) The 28 points are NOT independent and the file has no
covariance to fix that. With an assumed within-survey rho
the significance moves; with rho=0 it is an assumption.
WHAT THIS TEST DOES NOT SHOW:
* IT DOES NOT DETECT AN EVOLUTION IN THE OPPOSITE DIRECTION
EITHER. gamma_a = +1.185 +/- 0.505 is a 2.27-sigma result: the
95% profile interval [0.150, 2.160] CONTAINS ZERO. The correct
summary is NO EVOLUTION DETECTED, and the positive sign is a
direction, not a finding. Reporting it as one would repeat
the error this test exists to check.
* It does not show that gravity is exactly GR. M0 (gamma=0.55)
is a perfectly good fit here (chi2 = 19.79 / 27 dof), but with
these errors that is weak agreement, not a confirmation.
chi2/dof = 0.733 is in fact suspiciously LOW, consistent with
the errors being conservative and/or the points not being
independent -- the same missing-covariance problem, seen from
the other side.
* It does not prove the original analysis made an error. It
shows that an independent path over the same data, with the
stated model, does not find the effect -- which is exactly
what the registry's kill test asked for.
* NOTHING HERE IS NEW PHYSICS. The growth index, the growth ODE
and the gamma-sigma8 degeneracy are all textbook and are
REPRODUCED, NOT DISCOVERED.
RECOMMENDED REGISTRY ACTION: USR-2026-0044 kill test 'independent-
path (R2) reproduction of the gamma(z) evolution' -> FAILED.
sigma_display 4.84 sigma is not supported by this path (2.27 sigma,
opposite sign). Status contested -> refuted-pending-arbitration,
with the caveat that the arbitration must supply the covariance
matrix this compilation does not contain.
==============================================================================
B · Yours
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