Validating the spectrum: scores, null tests, audits

A spectrum is only worth how it is judged: medians over the whole set, never hand-picked cases; quantified chance windows; failures on record. This chapter unrolls the validation apparatus of the canonical spectrum — and keeps the former PDG scan as a protocol archive.

1. The canonical engine and its scores

The canonical spectrum is produced by a single machinery ($m = \sqrt{\sigma_\chi}\,\mathcal{S}$, chapter 4) and judged on medians, never on hand-picked cases:

• 89 states at 0.13 % median (91 % below 5 %) — the core of the spectrum;
• 226 states (extension, bands included) at 1.43 %, with 31 of the 32 spins read by inverse Regge;
• heavy sector: 57 states at ~0.3 %, including 15 heavy baryons at 0.23 % with no parameter or anchor per state;
• threshold states (metaxions): X(3872), T$_{cc}$, P$_c$… below 1 % once counted with their half-turns.

2. The null-test rule

A numerical agreement obtained by assignment (this knot ↔ that particle) counts as evidence only if it beats chance. The framework's rule: before presenting an agreement as load-bearing, count how many random assignments would do as well — the null window.

The most instructive example is electroweak: the W/Z/H/top quadruplet at 0.74 % RMS fails the null test (~$8\times10^5$ equivalent quadruplets at free calibration). The agreement is therefore classed a compatibility, not evidence — what carries the weight is the structure (the $8_3$ knot shared by the four asthenions). In all, about 25 results pass the null and carry the case; the rest is declared compatibility.

3. Anchors, cross-constraints and free controls

• Double constraint: the leptons (Koide) and the octet base demand the same scale to $7\times10^{-5}$ — the $\sqrt{\sigma_\chi}$ recalibration is over-determined.
• Free controls: a new assignment must improve (or leave stable) the rest of the spectrum with no readjustment — the elimination test (e.g. pinning the strange knot to $5_2$).
• Methodological inheritance: the K-fold cross-validation of the former scan (annex, §6) remains the protocol reference — calibrate on one part, evaluate on the other.

4. The honest audits and the falsifications

The framework keeps a public record of its failures and requalifications: falsifications F1 (pure inflation) and F2 (reheating) are closed by later computations, F3 (Class-E γ lines) is lifted under the canonical masses; twelve internal refutations are on record with a “never reintroduce” tag. Conversely, announced successes have been withdrawn after audit (JWST, NICER, NANOGrav: not discriminating). The rule: a withdrawn result is recorded, never erased.

5. Dated predictions

The current falsifiable tests are quantified and dated: $\Xi_{cc}^* = 3659$ MeV, $\Omega_b^* = 6067$ MeV, the $B_0^*/B_1'$ centroid at 5665 MeV, the fifth $\Omega_b(1P)$ at 6297–6304 MeV — with the $\Omega_{cc}$ antecedent (~3727 MeV observed, predicted window 3715–3788). See chapter 4, §8 and the Predictions page.

6. Annex: the former exhaustive scan (archive)

The former engine ($\Omega_{ts}$, chapter 4 §9) had been confronted through an exhaustive scan: 1539 candidate links enumerated (single knots ≤ 10 crossings, 2–4-component links), matched to the PDG particles — 118/122 masses at 0.68 % median, validated by K-fold (calibrating $\alpha_0$ and $f(3)$ on 4 folds, evaluating on the 5th), with a “P23 plasticity” refinement now archived as well (its constant $C_{\rm plast}$ has no object under the canonical law).

That scan is superseded: its catalogue curves were topologically wrong (14/19) and its assignment freedom too large — but its methodology (enumeration, K-fold, comparison to naive fits) remains the protocol model, and its residual predictions have been requalified (the “4th-generation lepton” became an inverted prediction: $Z_3$ saturation is derived — any 4th family would refute). The full chapters are in the monograph's docs/Archives_recherches/ and the V5 catalogue in docs/TQNT_catalog_V5_diffusion.xlsx.

7. Reproduction

The canonical spectrum and its scores are reproducible from the open repository:

# spectre canonique : 89 états (médiane 0,13 %) + extension 226 (1,43 %)
python3 -m simulation.experiments.spectrum_sigmachi_full
# test nul d'assignation (exemple électrofaible)
python3 -m simulation.experiments.null_assignation_ew
# confrontation LHCb 2026 (Omega_cc, discriminants dates)
python3 -m simulation.experiments.confrontation_lhcb_2026