# n186 — The constants audit, third pass: every constant against the post-retraction theory

**Date:** 2026-07-11 · **Scope:** all fundamental constants re-examined against the state after n180–n185 (functional gate failed, noise gate executed, corrections adopted). **Script:** the sweep in this note's session log; floor table reproducible from PDG masses. Statuses: DERIVED (in-model) / LOCKED (relation, not value) / CALIBRATED / FAILED / REFUSED / UNTOUCHED.

## The ledger

| Constant | Status | Current state |
|---|---|---|
| **c** | unit anchor, ASSUMED | and the sector's wound: the raw computed bubble speed is c_g² = 0.46 — the knot's wall (excluded as-is by GW data) |
| **ħ** | ASSUMED | QM wholesale; the theory runs *on* it |
| **G** | NOT DERIVED | target of the unwritten knot (G, γ, ρ_G from g, Δ, κ — three equations still unwritten); the CODATA G-spread is bet to be systematics (prediction 13) |
| **α** | FAILED ×45 | 4πS∞ = 6206 vs 137.04; no beta function (matter sector absent); Cs/Rb 5σ discrepancy bet systematic (live) |
| **γ_knee = α·mc²/ħ** | the theory's ONE new constant | 5.665×10¹⁸ s⁻¹ = 3.729 keV (electron anchor) / 1.040×10²² s⁻¹ = 6.847 MeV (proton); window exactly m_p/m_e; no amplitude armed since n181 |
| **Q = α/α_G** | LOCKED (defined) | 4.166×10⁴² (e) / 1.236×10³⁶ (p) — four jobs: weakness, CPS filter, frame-blindness, knee location |
| **e (charge)** | quantization DERIVED in-model | compactness + Alice (n123, n158); the value = α, which failed above |
| **m_e, m_p** | UNTOUCHED | the mass-scale half of the hierarchy — no mechanism; μ = m_p/m_e enters only as the anchor window |
| **d ln μ/d ln α** | LOCKED = 0 | prediction 8; data pattern consistent: μ bounds (10⁻⁷, methanol z~0.9) sit tighter than any α-dipole claim (10⁻⁵) — the lock survives; a confirmed μ drift ≥ α drift kills |
| **m_γ** | = 0 by in-model THEOREM | exact Gauss zero mode at every regulator; "photon" remains a reading |
| **m_g** | = 0 structurally | blind-channel thermostat; the 10⁻³³ eV figure is a conditional cosmological reading |
| **Λ** | sign only | ΔP > 0, coefficient demoted (61–404, branch-independent); scale wound 10⁸⁹; no T_μν map |
| **ξ = 0.2312** | CALIBRATED (Mercury) | owes an independent quantitative prediction — still unpaid |
| **ζ = 0.4834** | single-model | family sweep pending (pre-registered ×3) |
| **H₀** | REFUSED (F10) | γ_e/(2Q_p) = 70.7 km/s/Mpc recorded as Dirac-class coincidence (n185) |
| **Σm_ν** | PREDICTED window | [0.059, ~0.09] eV, normal ordering (prediction 34, the corner) |
| **Ω_DM** | UNPREDICTED | 40 orders under the cooling debt (n151) |
| **k_B·T_CMB/ħ** | checked, no constraint | 3.6×10¹¹ s⁻¹ — the audit is stiffer than the CMB bath by 10⁷: thermal cosmology cannot blur the knee |

## New this pass — the charge–mass floor, swept across the particle table

The in-model theorem |q| ≤ m (consumption non-negativity) was never confronted with the full PDG table. Honesty first: **the electron's exact saturation (m/floor = 1.0000) is calibration, not discovery** — the electron *defines* the substrate charge unit as the extremal dressing. The non-trivial content is everything else:

- **14/14 non-calibrated species pass**, including fractional charges (confined, per Alice/[C]) and the doubly-charged Δ++.
- **The nearest margin in nature: the up quark at 6.34× its floor** (2.16 MeV vs 0.341 MeV). A world with an up quark ~6× lighter would have falsified the bound — the floor is not vacuously loose.
- The muon sits at 207×, the proton at exactly μ = 1836.15× (the anchor window number reappearing, as it must).
- Standing kill unchanged (prediction 7): any confirmed millicharged particle below its line (0.001e → 511 eV).

## The structural inversion, stated once

After this audit the theory's *fundamental* scales are atomic, not Planckian: the coherence cell is a₀ (named assumption ℓ_c = c/γ), the knee is keV, the dark quantum is keV-band. The Planck scale appears nowhere as an input — Q absorbs the entire hierarchy into a rate ratio. Either that is the framework's deepest feature or its most damning symptom; the knot decides which.

**Classes: the floor sweep [A-theorem confronted with data]; statuses as tagged; nothing here adds a free parameter.**