M5 measurement contributions: running coupling, string tension, and boosted-clock force

[vantasnerdan]

Follow-up to the review of #437: I agree that the current scripts do not resolve the three M5 rows. They reproduce conditional algebra, do not consume M5 field data, use colliding task numbers, and cite a repository that is currently private and unlicensed. I will replace or retire that content rather than defend it.

I would like to take three independent measurement tasks, delivered as three separate PRs (one document/merge each). Please assign roadmap/task IDs and confirm whether #437 should be repurposed for the first task or closed in favor of clean PRs. I will not edit MODELS.md; the model owner and maintainers can adjudicate any status change after the evidence lands.

A. Running-coupling scale curve from the M5/Faber curvature field

Entry point: research/scripts/m5_6_4b_faber_curvature_em.py.

The first deliverable will densely sample the constructed field rather than five radii. It will publish the raw dimensionless shell observable

[
C(\rho)=\rho^2,\langle|R_{ij}|\rangle_{|x|=\rho r_0},
\qquad \mu/\mu_0=1/\rho,
]

and its logarithmic derivatives with grid, box, shell-width, and derivative-method refinement.

There is a convention question that must be settled by the field/action dictionary rather than by agreement with a target. Two preregistered interpretations are:

1. action/energy convention: g_R^2/g_ref^2 = C/C_ref;
2. field-amplitude convention: g_R/g_ref = C/C_ref.

Both curves will be reported until the M5 source and kinetic normalization selects one. A later one-loop b0 or effective-flavour conversion is only a conditional fit after the measured slope exists; it will not be presented as an M5-to-QCD derivation. If neither convention is licensed by the model, the result remains a curvature form-factor measurement, not a beta function.

Competing stronger estimator: a potential/force-scheme coupling from stationary two-core M fields. I propose the dense Faber scan first because it is the reviewer-named entry point and supplies a cheap exact/numerical instrument test; the two-core scheme remains the escalation path if the single-profile observable cannot identify a coupling.

Falsifiers: loss of the far-field plateau, derivative disagreement above propagated discretization error, slope instability under fixed-physical-domain refinement, or failure of normalization/load-bearing mutations to change the result.

B. Confinement/string-tension instrument

Entry points: research/scripts/m5_21_4_a_pair.py and research/findings/m5_21_4_note.md.

The present approximately linear seed curve is useful evidence, but it is not a continuum tension: the freely relaxed pair merges, the winding-2 line remains singular, changing the seed tube radius moves the slope, and the existing n=32/n=48 comparison keeps approximately the same lattice spacing.

Primary estimator: constrained smooth charge-2 stationary branches, fit before comparator inspection to

[
V(d)=C+A/d+\sigma d.
]

Independent estimator: the constraint reaction/virtual-work derivative, compared with dV/dd. A transverse excess-energy plateau will be a diagnostic rather than a substitute for either force estimator.

Required gates: fixed-box h refinement, separate box refinement, measured rather than seed separation, stationary residual convergence, multiple smooth initializations and constraint supports, fit-window/branch/error budget, singular-seed negative control, and an independently implemented audit.

The first honest result will be sigma in continuum code units. Comparison with the Cornell approximately 1 GeV/fm anchor requires energy and length scales from the same M5 functional, normalization, and state family. The existing M5.16 scale chain uses a different functional, so I will report the physical conversion as blocked unless a same-functional bridge is supplied and validated.

C. Boosted-clock two-body force and Newton exponent

Entry points: the boost-dressed 4x4 M construction in research/scripts/m5_8_2q_delta_scaling.py and the static 4D M functional in research/scripts/m5_21_3_a_4d.py (plus the fixed-clock/fixed-J machinery if the model owner confirms that as the canonical mass proxy).

The missing prerequisite is a canonical two-center boost-dressed fixed-J construction. For two local clock flows, the inertia is a matrix, not two independent scalar terms:

[
K_{ab}=4h^3\sum_i\langle[a_a,A_i]\eta,[a_b,A_i]\eta\rangle_\eta,
\qquad E_J=E_{stat}+\tfrac14 J^T K^{-1}J.
]

The overlap term K_12 is load-bearing and positive-definiteness/conditioning of K will be checked at every separation.

Two-center boost composition is also preregistered rather than chosen by its answer: (1) a single exponential of the summed local rapidity field, (2) a core-swap-symmetric/Strang product, and (3) either construction used only as a seed before constrained full-field relaxation. Selection criteria are Lorentz membership, exact core-swap symmetry, one-core and far-vacuum limits, parameter economy, and control closure. Composition-sensitive force results will not support a Newton claim.

Primary estimator: constrained stationary two-clock configurations at separation d, with interaction energy after separately measured self-energy subtraction, followed by a local derivative F_E(d)=-dE_int/dd.

Independent estimator: constraint reaction or localized virtual work, F_R(d). The preregistered model comparison is Coulomb/Newton K/d^2 versus a free power K/d^p, screened/Yukawa, and nonzero-offset alternatives. The Newton row moves only if the two force estimators agree, p=2 survives refinement and fit-window changes, and the effect is absent in zero-boost/zero-clock controls.

Required gates: an explicit mass/clock observable, fixed-separation constraints, stationary residuals, self-energy and boundary subtraction, zero-boost and Euclidean-signature controls, b-to-minus-b and J-to-minus-J evenness, h/box/tolerance refinement, covariance-aware exponent fit, load-bearing mutations, and an independent implementation. Total, eta-time-mixing, and matched boosted-minus-undressed energies will be reported separately because an inverse-square shape alone cannot distinguish gravity from the existing electric/topological channel. If the current boost channel does not admit a stable two-body branch, that is recorded as attempt evidence and not renamed a Newton result.

Shared contribution boundary

• Each PR will contain equations first, an equation-to-code map, a small physics module, tracked JSON/plot summaries, exact reproduction commands, and a claim-by-claim adversarial audit.
• Raw large fields will remain outside git with a dataset manifest and hashes.
• No private Substrate URL or code will be cited/copied. Small answer-neutral numerical and dimensional checks will be independently derived in OpenWave. If Substrate is later published and compatibly licensed, reusable primitives can be proposed separately without claiming that they supply M5's missing field dictionary.
• No comparison value will select an estimator or normalization; structural criteria and failure thresholds are frozen first.

Model-owner input requested from @JarekDuda: (1) which C(r)-to-g_R convention follows from the intended Faber/M5 action, and (2) which boosted-clock/fixed-J construction is the canonical inertial-mass proxy for the two-body test.

[vantasnerdan]

Implementation update — all three preregistered pilots now have signed, independently audited handoffs.

1. Running-coupling boundary: PR M5/Faber: measure the curvature scale curve with an audited coupling boundary #437 is rewritten at d5f36bd as an M5.6.4b field-derived classical curvature form factor with a no-import audit. The scale curve and logarithmic slope are measured; the audit explicitly REFUTES calling it a renormalized coupling or beta coefficient without the missing source/action dictionary. Ready for maintainer re-review and task allocation.

2. Confinement/string tension candidate: signed branch commit 08b4015: vantasnerdan@08b4015 . The constrained reaction arithmetic works, but the physical interpretation is falsified: a neutral no-core field passes the original gates with sigma=0.161575; no post-relax core separation is measured; the finite-tanh target retains an axis obstruction; kappa/support shifts are 26.97%/38.01%. The note carries the exact repair list. This is a useful failed-instrument/method record, not a tension or Cornell-unit result.

3. Newton/GEM candidate: signed branch commit bc38193: vantasnerdan@bc38193 . It implements three Lorentz-valid two-center boost compositions, the full two-flow K_ab including K12, fixed-J energy, self-subtracted U(d), and null/sign/composition controls. K12 changes clock energy by 39–46%, so it is load-bearing. All tested curves change force sign; N16→N24 shifts 31.9%; independent fits reject inverse-square support. This is an ansatz-level negative diagnostic pending a model-owner-approved two-center mass state.

Per CONTRIBUTING.md I have not opened the latter two PRs or invented task IDs. Please allocate the appropriate roadmap IDs and advise whether you want each bounded method/failure record submitted as-is or only after the named next construction. MODELS.md remains untouched in every branch.

[xrodz]

Answers to the coordination questions, following the #437 re-review:

• M5/Faber: measure the curvature scale curve with an audited coupling boundary #437 is repurposed, not closed. The rewritten PR is the deliverable itself and is approved as task M5.31 (files renamed on the branch as maintainer edits, roadmap row and task record added; details in the review).
• Task B (string tension) and task C (boosted-clock force): proceed as separate PRs, as you proposed. Each gets its roadmap row and task ID when its PR materializes. For B, reporting the physical conversion as blocked is the honest outcome if no same-functional bridge to the M5.16 scale chain exists; a sigma in continuum code units is a real deliverable on its own.
• Preregistration size. The review standards now carry a process-weight budget (dev_docs/PR_REVIEW_STANDARDS.md § 12.2): keep any preregistration near or under ~8,000 words and land it with, not ahead of, the run it governs. Your per-task sketches above are the right size; no separate freeze documents are needed.
• The two model-owner questions (the C-to-g_R convention, and the canonical fixed-J two-body construction) stay open here for the author. Nothing in A, B, or C is blocked on them for the instrument-grade deliverables: both conventions reported side by side, as M5.31 does, is the acceptable form until the dictionary exists.