Technical record · Result 04 · Row 29 · matter scale

isoQCD Nucleon Mass / Matter-Scale Closure

Row 29 tests whether the nucleon mass scale can be reconstructed without using a proton or neutron mass as a forward solve target. The hardened model-averaged result is 941.223 ± 35.184 MeV.

Result Mathematical construction Claim boundary

Forward result

The quantity that was actually calculated.

Model-averaged forward value941.223 ± 35.184 MeV

Isospin-symmetric N_f=2+1 QCD nucleon mass: m_u=m_d=m_ud, no QED.

AICc-preferred model939.101 MeV

The closest single model is reported, but the final central value remains the predeclared AICc model average rather than selecting the numerically closest branch.

Production surface24 ensembles

Five lattice spacings: β = 3.40, 3.46, 3.55, 3.70, 3.85.

Row 29 verdict: PASS_TARGET_ISOLATED_ISOQCD_NUCLEON_MASS_CLOSURE. The proton/neutron mass is not used to choose the production data, fit model, scale, physical quark point, or stopping rule.

Mathematical construction

Dimensionless lattice coordinates first.

Each selected CLS ensemble is converted into renormalization-group-invariant quark coordinates, a dimensionless nucleon observable, and a cutoff coordinate. The fit is performed in this dimensionless space before the continuum physical point is evaluated.

x_ℓ = Z_M(a m_ℓ^AWI) √(t₀/a²)

x_s = Z_M(a m_s^AWI) √(t₀/a²)

Y_N = (a M_N) √(t₀/a²)

c = 1 / [8(t₀/a²)]

The β=3.34 ensemble A654 is excluded because the published nonperturbative Z_M table used by the gate begins at β=3.40; no extrapolated renormalization factor is introduced.

Continuum/chiral candidate family

The central reconstruction tests five declared polynomial/cutoff structures. Writing the generic linear core as

Y_N = b₀ + b_ℓx_ℓ + b_sx_s + b_cc + …

Model	Additional terms	χ²/dof	AICc	Weight	M_N (MeV)
L	none	2.240	54.898	0.0114	953.200
Qℓ	x_ℓ²	1.735	46.307	0.8348	939.101
Qmix	x_ℓ² + x_s² + x_ℓx_s	1.719	50.226	0.1176	951.534
LcutM	c x_ℓ + c x_s	2.120	55.109	0.0102	964.025
QℓCutM	x_ℓ² + c x_ℓ + c x_s	1.897	53.248	0.0260	948.523

Weighted least squares and AICc averaging

χ²_i = Σ_k [(Y_N,k − Y_N,k⁽ⁱ⁾)/σ_k]²

AICc_i = χ²_i + 2k_i + 2k_i(k_i+1)/(n−k_i−1)

w_i = exp(−ΔAICc_i/2) / Σ_j exp(−ΔAICc_j/2)

M̄_N = Σ_i w_iM_N,i = 941.223 MeV

The recorded model weights sum to exactly 1. The Row 29 verifier independently recomputes the weighted mean from the frozen model table before issuing PASS.

Physical point and QCD scale

The scale bridge is fixed upstream.

The physical quark point uses independent RGI Standard-Model/QCD inputs; the proton or neutron mass does not set the point.

M_ud^RGI = 4.70 MeV, M_s^RGI = 127.0 MeV

α_s(M_Z) = 0.1184

Λ_MS̄⁽³⁾ = 339.796 ± 4.2 MeV

√t₀ Λ_MS̄⁽³⁾ = 0.250228868

√t₀ = 0.736408948 GeV⁻¹

Continuum evaluation

Set c → 0, then evaluate the physical RGI coordinates.

x_ℓ^phys = √t₀M_ud^RGI = 0.003461122

x_s^phys = √t₀M_s^RGI = 0.093523936

M_N = Y_N(x_ℓ^phys,x_s^phys,0) / √t₀

Uncertainty propagation samples the RGI quark inputs, scale anchors, Λ₃, model choice, and fit covariance. The resulting Monte-Carlo σ is 35.184 MeV.

Hardening

The result survives the declared perturbations.

Leave one ensemble out

936.734–947.436 MeV

The preferred-model prediction remains in this interval when each production ensemble is removed in turn.

1% mass-coordinate stress

930.494–947.415 MeV

β-correlated 1% perturbations stress the omitted small mass-dependent O(a) improvement.

Integrity

Weights = 1.000000

The verifier checks the model-weight sum, forward hash, closeout hash, no-retuning flag, and protected publication-source hash.

Post-freeze diagnostics

Comparison is kept downstream of the forward result.

Diagnostic	Reference	Difference	Interpretation
Published CLS continuum nucleon	941.7 MeV	−0.477 MeV	Analysis consistency check using the same CLS ecosystem; not independent ensemble validation.
Historical physical proton	938.27208943 MeV	+2.951 MeV / +0.315%	Diagnostic only. The forward quantity is isoQCD; the physical proton includes m_u≠m_d and QED, and the holdout had been seen earlier.

No post-freeze correction or retuning is allowed.

The physical-proton comparison is deliberately not used to redefine the scale, select a model, or append an electromagnetic self-energy. The QCD/QED split for an absolute proton correction is scheme dependent and remains a separate sub-gate.

Claim boundary

What Result 04 does—and does not—claim.

Claimed

Target-isolated matter-scale closure

Given independently determined upstream SM quark masses and UTFANSWF’s frozen α_s/QCD-scale input, production multi-spacing N_f=2+1 lattice-QCD data close on the isoQCD nucleon mass without using a proton/neutron mass to choose the data, model, scale, physical quark point, or stopping rule.

Not claimed

The remaining boundaries stay explicit.

Not a pristine first-ever blind prediction; the historical proton value had been seen earlier.
Not a derivation of m_u, m_d, or m_s from frozen v22.
Not internally generated CLS gauge ensembles.
Not a full physical charged-proton QCD+QED calculation.
Flavor origin remains separate future research.

Source and provenance chain

The technical record points back to primary inputs.

Record	Role in Result 04
arXiv:2211.03744	CLS N_f=2+1 light-baryon production context and published 941.7 MeV continuum nucleon cross-check.
arXiv:1911.08025	ALPHA RGI quark masses M_ud=4.70(15)(12) MeV and M_s=127.0(3.1)(3.2) MeV.
arXiv:2412.10215	Dimensionless potential-scale anchor r₀Λ_MS̄⁽³⁾=0.820(28) and flow-scale relation.
hep-ph/9706430; hep-ph/0512060	High-order α_s running and heavy-quark threshold matching used in the Λ₃ bridge.
arXiv:1303.4896	Supports keeping the absolute QCD/QED proton-specific separation as a distinct convention-dependent sub-gate.

Frozen forward record: SHA-256 3d3058e25117f4b8fe7c97dd124bcdc35e6b7ce1a644a8c568d40b0ac15fb921.
Canonical executable: python -m harness.run_all_gates → Row 29 PASS.

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