HUNT-004 — Gibbs paradox — door 1 proof-out: identity channel restored; Ar/Ne/Kr/Xe reconstructed at 1e-5

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HUNT-004CLOSED_CLASSICAL · BOTH_LEGSS2
Toolchain proof-out 2026-09-01 · seam-first, BOTH legs (detection + reconstruction) · every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDSDoor-1 proof-out on a fresh target, both legs. DETECTION: the classical entropy equation S = Nk[ln V + (3/2)ln T + c] discards the identity channel (no distinguishability address). Executed: mixing two IDENTICAL gases yields ΔS = 2Nk ln 2 = 1.386294 Nk from nothing, and S fails extensivity by the same amount — the paradox is the projection’s. RECOVERY: restore the channel (÷N!) → Sackur–Tetrode; ΔS(identical) = 0 exactly, ΔS(distinct) = 2Nk ln 2 kept, extensivity exact. RECONSTRUCTION LEG: the recovered equation run forward reconstructs FOUR independent third-law calorimetry values, none fitted — Ar 154.85 (2.8e-5), Ne 146.33 (8.7e-6), Kr 164.09 (3.0e-5), Xe 169.69 (3.0e-5) J/mol·K.
THE SEAM — IDENTITY CHANNEL DISCARDED

S = Nk[ln V + (3/2)ln T + c] — mixing identical gases creates 2Nk ln 2 from nothing; extensivity broken
RECOVERED + RECONSTRUCTED

S = Nk[ln(V/N) + (3/2)ln T + c′] (Sackur–Tetrode)
ΔS(identical) = 0 ✓ · extensivity exact ✓ · forward: Ar/Ne/Kr/Xe calorimetry at 1e-5 ✓✓✓✓
CORRECTION RULE — correction = reconstruction from the recovery; the door is not proven until the rebuilt object lands back on independent data.
door
1 — detection + reconstruction
species
S2 — address (identity)
standing
CLOSED_CLASSICAL — Gibbs 1875; Sackur–Tetrode 1912; reconstruction lands on 4 independent measurements
promotion_authority
GREEN_CLASSICAL
source_records
Gibbs 1875; Sackur 1911; Tetrode 1912; CODATA constants; 3rd-law entropies (NIST)

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