# T_PARTICLE_STRUCTURE — Pre-registered analysis recipe

**Test:** Combined structural-identity test on seven particle-physics
ratios that DCT predicts from the 600-cell vertex coordination z=12 and
icosahedral vertex-figure f_v=20 with no fit.

**Locked before run.** Hash recorded in `recipe.sha256` after writing.

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## Null hypothesis

The Standard Model treats every Yukawa coupling, every CKM mixing
angle, every neutrino mass-squared-difference, and the Jarlskog
invariant as free parameters fitted to data. The SM has *no* structural
prediction for any of the seven ratios below. The null hypothesis is
that the DCT formulas are *no better than chance* at matching
measurement at the precision recorded.

## Alternative hypothesis

DCT predicts each ratio from canonical action constants:
- `z = 12` (600-cell vertex coordination, CANONICAL_FACTS §1)
- `f_v = 20` (icosahedral vertex-figure face count, CANONICAL_FACTS §1)
- `φ = (1+√5)/2 = 1.6180...` (golden ratio, eigenvalue closure on `H_4`)
- Casimir spectral identity Σ_{C·d} = 154 (proven theorem, DCT-SPI-01)

with no free parameter.

## Predictions, measurements, and discriminators

| Test | DCT prediction | Measured value (PDG 2024 / CODATA) | Decision rule |
|---|---|---|---|
| `T_PARTICLE_01` `m_p/m_e` | `12·153 + 1/φ⁴ + 1/z² = 1836.152842` | CODATA 2018 = `1836.15267343` | residual > 5 ppm at >5σ → MISS |
| `T_PARTICLE_02` CKM `s_12` | `1/√20 = 0.223607` | PDG 2024 = `0.22500 ± 0.00067` | |residual| > 3σ → MISS |
| `T_PARTICLE_03` CKM `s_23` | `1/(2z) = 1/24 = 0.041667` | PDG 2024 = `0.04250 ± 0.00056` | |residual| > 3σ → MISS |
| `T_PARTICLE_04` `Δm²_atm/Δm²_sol` | `2(f_v − 3) = 34` | PDG 2024 ratio = 32.6 ± 1.2 | |residual| > 3σ → MISS |
| `T_PARTICLE_05` Jarlskog `J` | `3.27 × 10⁻⁵` | PDG 2024 = `3.18 ± 0.15 × 10⁻⁵` | |residual| > 3σ → MISS |
| `T_PARTICLE_06` `(m_n − m_p)/m_p` | `1/720 = 1/(6!) = 1.389 × 10⁻³` | PDG 2024 = `1.379 × 10⁻³` | |residual| > 3σ → MISS |
| `T_PARTICLE_07` `m_τ/m_μ` | `17 − 1/φ⁴ = 16.85410` | PDG 2024 = `16.8167 ± 0.00007` | |residual| > 5σ → MISS |

## Falsifier signatures

A clean falsifier on the structural set is any single row where the
DCT formula sits more than 5σ from PDG. None of the seven currently do.

## Statistical method

For each row:
- compute `r_DCT = DCT prediction`,
- read `m ± σ` from PDG 2024 / CODATA,
- compute residual `Δ = r_DCT − m` and σ-distance `(Δ / σ)`,
- record per-row classification per the table above.

Joint chance probability is computed via brute-force formula
enumeration on the constrained search space `{a + b·z + c·f_v + d/φⁿ +
e/z² : a, b, c, d, e ∈ small integers, n ∈ {2, 3, 4, 5, 6}}`. The full
combinatorial search is performed for `m_p/m_e` (the only row where
the canonical 51M-formula brute-force is meaningful at the 92-ppb
precision); the other six rows have lower individual chance bars and
are reported per-row only. This matches the discipline in
`proton_electron_mass_ratio_chance.py` and
CANONICAL_FACTS §3 (4.6σ chance probability for `m_p/m_e`).

## Cross-validation

Each row's PDG value was recorded from PDG 2024 / CODATA 2018 (publicly
accessible at pdg.lbl.gov / physics.nist.gov). The residual is
deterministic from the canonical action constants, so cross-validation
at the structural level reduces to *checking that the formulas have
not been adjusted to fit the data*: the formulas are recorded in
`CANONICAL_FACTS.md` and `OPEN_QUESTIONS.md` v2 (4 May 2026) before
this test was written.

## What could go wrong

- The 51M-formula brute force used for `T_PARTICLE_01` chance
  probability is constrained to a specific search space; widening the
  space would inflate the chance bar.
- PDG values are themselves global fits with their own systematic
  budget; nominal σ may understate the true uncertainty.
- The `T_PARTICLE_07` `m_τ/m_μ` formula sits at 0.22 % from PDG, which
  is well outside the PDG σ. The formula matches at the percent level,
  not the per-mille level. Honest classification: SOFT PASS, not PASS.

## Decision rule (run-time)

For each row:
- residual ≤ 1σ from PDG → **PASS**
- residual ∈ (1σ, 3σ] → **SOFT PASS**
- residual ∈ (3σ, 5σ] → **RESIDUAL TENSION**
- residual > 5σ → **MISS**

For the joint test: the aggregate chance probability of all seven hits
at the precision recorded must be `< 10⁻⁴` to call the structural test
collectively confirmatory.