# Trials-Factor Audit (2026-07) — Supporting Computations for Appendix CE

This directory contains the complete, reproducible computation behind the
combined-evidence (no-coincidence) analysis of Appendix CE in the main paper.
The question it answers is the hostile one: *if the theory's numerical
agreements were numerology, how many numbers could the construction have
scanned, and how surprising are the observed hits once every scan is charged?*
All look-elsewhere charges are set conservatively (the charged choice space is
always taken as large as defensible), and every number is computed by the
scripts below — none is hand-set.

## Pipeline (run in order; each stage writes the JSON the next stage reads)

| Stage | Script | Output | What it computes |
|---|---|---|---|
| E1 | `E1_address_space.py` | `E1_address_space.json` | Defines the discrete "address space": every discrete choice (bundle, flux, exponent, prefactor, convention) the construction could in principle have made, with corpus citations for each dimension. |
| E2 | `E2_enumeration.py` | `E2_enumeration.json` | Enumerates each address-space dimension and grades the completeness of each enumeration (proven / cited / honest-hole), yielding the total charged choice count. |
| E3 | `E3_hit_list_dependency_matrix.py` | `E3_output.txt` | Builds the raw hit list (predicted vs. measured values with fractional agreements), then collapses it through a dependency matrix so correlated agreements are counted once. Exclusion rules (selectors, inherited SM decimals, untested predictions) are applied and printed row by row. |
| E4 | `E4_probability.py` | `E4_results.json` | Converts the collapsed hit table and the E2 choice count into tail probabilities and one-sided sigmas under several null conventions (floor / central / maximal hit counts). |
| E5 | `E5_skeptic_attacks.py`, `E5_skeptic_recount.py` | `E5_skeptic_attacks.json`, `E5_results.json` | Stress-tests the enumeration and the null: enlarges the charged space where any enumeration could be incomplete, reprices double-counted rows, and constructs the fairest hostile null including the across-observable selection charge that E3/E4 do not levy. |
| E5b | `E5b_moderate_tier.py` | `E5b_results.json` | A moderate (still conservative) tier with per-hit windows not resolution-capped, plus a Poisson expected-hits cross-check, so the verdict does not rest on a single maximally-stacked corner. `E5c_preregistered.json` freezes the pre-registered menu definitions. |
| E6 | `E6_synthesis.py` | `E6_synthesis.json` | Folds the enlarged space (E5) and the selection-null recount into the final conditional bound quoted in Appendix CE, worst case first. |

## Independent re-verification (`verify3x/`)

Every decisive number above was recomputed from scratch, with fresh
implementations and fresh random seeds, before being quoted in the paper:

- `partI_verify.py`, `partI_alpha_ladder_verify.py` — independent re-derivation
  of the finiteness count and the alpha-ladder infeasibility theorem, followed
  by explicit break attempts (window semantics, step heterogeneity, missed
  families, target rescalings).
- `lens2_null_ladder_verify.py` — independent Monte Carlo of the null ladder,
  cross-checked against exact closed-form product-of-uniforms analytics.
- `lens3_verify.py` — a third, fully fresh implementation, including the
  specific per-row objections (window vs. target uncertainty, dependency
  chains, rational menus) and an independent "middle path" repricing.
- `verify_recount.py` — an end-to-end recount of row prices, products, and the
  corrected hit set with the selection-null order statistics.
- `synth_check.py` / `synth_check.json` — recomputes every number cited from
  the five audit reports; the figures quoted in Appendix CE are read from this
  file.

## Reading the result

The headline conclusion, exactly as stated in Appendix CE: under a full
across-observable selection charge (the most hostile admissible null) the
combined evidence is not statistically significant; under hostile menu
accounting with no selection charge the four surviving independent hits give
roughly 3.7–5.0 sigma; the conditional bounds and the alpha-ladder
infeasibility theorem are quoted with their exact JSON sources. Discrepancies
between a rerun and the shipped JSON are wanted — please report them.
