# Element Projection Lab 0.6.0: ATLAS publication-level dimension-evidence audit

## Result

The published ATLAS periodic dielectron/diphoton search does **not** pass the
project's necessary cross-channel evidence screen for a physical extra
dimension.

At the preselected periodicity-focused `R<50%` threshold, ATLAS reports signed
model-independent significances of:

- dielectron: **+1.5 standard deviations**;
- diphoton: **-0.2 standard deviations**.

Across all four reported threshold variants, the largest positive significance
is +1.5 in dielectrons and -0.2 in diphotons. One-sided standard-normal tails
with a Bonferroni correction over four variants give:

- dielectron: local p = **0.0668072013**, adjusted p = **0.2672288051**;
- diphoton: local p = **0.5792597094**, adjusted p = **1.0**.

The primary cross-channel rule fails, the conservative familywise rule fails,
and ATLAS's model-dependent analysis separately reports no significant
deviation from the background-only hypothesis. These are externally measured
collision-data summaries from ATLAS, not measurements made by this project.

Primary source: ATLAS Collaboration, arXiv:2305.10894v2 / JHEP 10 (2023) 079,
https://arxiv.org/html/2305.10894v2. The associated data record is HEPData DOI
10.17182/hepdata.140955.v1.

## Assumptions and correction

The protocol fixes the `R<50%` row as primary, uses one-sided positive tests,
applies Bonferroni within each channel without assuming the four variants are
independent, and requires positive evidence in both channels plus a positive
model-specific conclusion. Passing would remain necessary, not sufficient:
spin, widths, couplings, branching fractions, calibrated detector response,
matched conventional explanations, and independent experimental replication
would still be required.

This audit is explicitly **retrospective**. The publication and its null
conclusion were known before the protocol. It therefore cannot become blind or
preregistered by being frozen now. The release also does not reproduce the
event-level or binned-spectrum likelihood; it lacks the complete nuisance
model, covariance, trained networks, and event data used by ATLAS.

## Counterexamples

- A constructed +4.0/+4.2 standard-deviation primary pair with a positive
  model-specific conclusion passes the necessary software screen.
- A constructed +3.1/+3.1 pair passes the uncorrected primary 3-sigma rule but
  fails after four-variant correction: adjusted p = **0.00387041285** in both
  channels, above the frozen 0.00135 threshold.
- A constructed +6.0/0.0 pair fails because one strong channel is not
  cross-channel support and is certainly not independent replication.

These counterexamples test the logic; they are not physical evidence.

## Verification and classification

- **Written mathematics:** standard-normal survival probabilities and
  Bonferroni familywise control.
- **Finite computation:** deterministic replay of eight published signed
  significances and three constructed controls.
- **Measured evidence:** the ATLAS publication's collision-data summary and
  model-dependent null conclusion.
- **Hypothesis:** a locked dimensional tower could produce correlated excesses
  with predicted masses, widths, spins, couplings, and channel ratios.
- **Theological interpretation:** not tested or identified.

All **53** package tests pass. The independent implementation imports no
production module and passes **12/12** checks of the protocol digest, exact
source matrix, tail calculations, gate decisions, retrospective status, and
likelihood boundary.

## Next test

Obtain the official machine-readable spectra and statistical model and use
them only for a retrospective calibration/reproduction study. Then freeze one
complete tower model before genuinely independent future collision data are
opened. A failed fit may indicate a wrong model, omitted conventional physics,
miscalibration, or fluctuation; it is not automatic evidence for hidden
variables or extra dimensions.