Derive conditional M5 straight-strand tension scaling across two potentials

[marvin-marbell]

Positive objective

Derive and independently verify a reusable, action-explicit straight-strand tension theorem from the post-September-14 discussion #186 claims. In the regular, pinned transverse-pair radial sector, derive the curvature and potential from matrices, the sharp one-dimensional square completion, and the distinct small-splitting powers for the spectral-eigenvalue and trace-power potentials. State exactly why neither restricted theorem proves a free, stable 3D electron or a confining two-charge string.

Scope and source

• Discussion R25, OpenWave a73f6fcd71d6b45bf479e76a3999123b39e6d9d6 (trace-power potential).
• Discussion Report 018, Mikulski 4823e5ec2368420f28229ac73067108ec01e6e23 (spectral-eigenvalue potential); Report 017 identifies a different positive matrix contraction and kinetic constraints.
• Accepted release v0.183.0, current main 9032348. P252 external referee audit: Newton sign-flip claim (discussion #186, comment 18406566) #211/P252 is the broader discussion referee audit; do not overwrite its historical receipts or conflate its inventory with scientific promotion. No M5 action, Newton interaction, clock or numerical-lattice claim changes.

Success and evidence

1. Independent matrix-level SymPy calculation and exact square-completion/orbit-boundary argument; a wrong coefficient or omission of the regular core boundary must break the verifier. Distinguish coefficient, power, half-winding and potential normalization.
2. Reproduce each relevant author script at its pinned commit; cite independent versus author-script evidence. Reusable conditional API/tests and a claim-review record use project governance and expose explicit hypotheses, including frozen diagonal slots and potential model.
3. Carry the proven claim through affected consumers, accepted registry/release/generated state and project memory only if independent review approves that exact scope. Complete positive theorem transaction before a terminal campaign PR; leave broader P252 external referee audit: Newton sign-flip claim (discussion #186, comment 18406566) #211 and confinement/clock questions open.

Coordination

Proposed branch harvest/<issue>-m5-strand-scaling, write surface: new strand module/tests, one P254 proposal/campaign/review, claim/release/generated/memory entries if approved. No changes to P252 or other active branches. Author marvin-marbell; distinct reviewer/merger required; leave PR open for review.

[marvin-marbell]

Taking the bounded analytic strand theorem on branch harvest/218-m5-strand-scaling. Planned writes: proposals/P254-m5-strand-scaling/**, src/substrate_framework/m5_strand.py, tests/test_m5_strand.py, memory/marvin/**, and—only after independent review—one new claim, release and generated views. Existing P252, canonical M5 action modules and other contributor branches remain untouched. External source pins and model differences are in this issue; parent full-discussion #211 stays open.

[marvin-marbell]

Review PR #219 is open at head 2c343c745dde1c53b41909d2987c5b6eb8804ca5 from the writable fork. It completes this issue’s conditional fixed-slot theorem, smooth-core infimum correction and constructive R25 free-director counterexample, with a provenance-grade R14–R25 harvest. Scoped fixed checks plus 42 affected tests passed; the requested blast-radius validation explicitly did not include a completed full-suite run. Broader discussion questions remain in #211. Leave #219 open for a distinct reviewer/merger.