Plan: E&M problem onboarding round (maxwell-equilibria first) - #7
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Companion to PLAN-physics-problems.md. Recommends onboarding Maxwell's 1873 equilibrium-count conjecture (open even for N=3) with the Thomson problem second; records the watch list (Sendov/Smale MVC, almost Mathieu) and the rejected candidates with reasons. Plan only — nothing implemented. Registered as tier 1 in tiers.json. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn
Maxwell's 1873 problem on equilibrium points of point-charge fields. PROBLEM.md records the published frontier including the July 2026 preprints (arXiv:2607.27197 refuting the general (n-1)^2 conjecture at n=5 with no explicit certified witness; arXiv:2607.28785 taking the three-positive-charge bound to 6, leaving 4-vs-6 open) and a verification contract built on certificates decidable over Q. Harness: equilibria.py produces complete certified equilibrium counts (dyadic-rational interval arithmetic, Krawczyk isolation, exclusion tiling with split paths, localization + domination lemmas, index-sum identity); verify_equilibria.py independently re-verifies certificates (directed-rounding decimal intervals, preconditioned interval Newton via interval Gaussian elimination, re-derived lemmas, exact Kraft tiling check). Both validate against classical knowns: 1 equilibrium for two charges, n-1 for collinear, 4 for the equilateral triangle, with end-to-end cross-verification passing. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn
STATUS gains the problem row (budget high), three queue items (blind self-test census; explicit certified witness for the arXiv:2607.27197 refutation; the 4-vs-6 three-charge hunt) with kill/win conditions inline, and an insights note recording that the general conjecture was refuted by preprint six days before onboarding, plus the split-path certificate pattern and the decimal-sqrt rounding trap. Plan doc gains an execution addendum: maxwell onboarded reframed, thomson-sphere deferred with reasons. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn
Float exploration (explore/abk_witness_scan.py) maps the 24-count window of the rational ABK embedding: it exists only for t <= 0.085 (eps <= 0.18), width ~0.5% in q. Chosen witness t=17/200, q=4367/1000000 (matches the ABK charge law to 2e-8): 24 float zeros, minsep 1.5e-3, index sum -4. Certified census of the config is running; attempt record 001 follows with its results. equilibria.py gains --progress-every for long runs. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn
Complete census certificate (gzipped, 235993 leaves) and a compact summary: 24 isolated equilibria, 0 unresolved, index sum -4, all 24 det-signs certified. Independent re-verification is running; the attempt record interpreting this lands with its verdict. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn
The rational five-charge configuration (units at e1,e2,e3; charges 4367/1000000 at (1/3,1/3,1/3) +- (17/200)(1,1,1)) is certified to have exactly 24 isolated nondegenerate equilibria: complete census over the localization ball (472k boxes, 0 unresolved, index sum -4), re-established leaf-by-leaf by the independent checker (PASS, 924s). 24 > (5-1)^2 = 16 - an explicit machine-checkable instance of the arXiv:2607.27197 refutation of Maxwell's conjecture, at a concrete witness the asymptotic preprint does not supply. Ledger: route VERIFIED with escalation open - queue 16 is now the contract-mandated skeptic review of the shared subdivision driver; float side-finding (24-window needs eps <= 0.18, ~0.5% wide in q) recorded as EVIDENCE with certified brackets as leads. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn
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Companion to PLAN-physics-problems.md. Recommends onboarding Maxwell's
1873 equilibrium-count conjecture (open even for N=3) with the Thomson
problem second; records the watch list (Sendov/Smale MVC, almost
Mathieu) and the rejected candidates with reasons. Plan only — nothing
implemented. Registered as tier 1 in tiers.json.
Co-Authored-By: Claude Fable 5 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_015Pi8N8wWXhAiaMHVWj1kPn