Merge PR #10 (conductance problems) into main with ledger conflicts resolved - #11
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Distills two physics research directions (Floquet/cavity routes to superconductivity; metamaterial dielectric engineering) to their open mathematical cores: the critical almost Mathieu operator (Dry Ten Martini, critical case) and optimal three-phase 2D conducting composites (bound attainability). Records candidates that lost and the planned harness designs. Tier 1, like the existing physics plan. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VLbALsNim51UzzVWJACWnw
Dry Ten Martini at critical coupling (open; non-critical case closed by Avila-You-Zhou), plus the Thouless bandwidth constant and the Hausdorff-dimension-1/2 frontier as secondary targets. Physics lens: superconducting wire networks (de Gennes-Alexander) and Floquet-driven lattices. Harness computes Chambers polynomials exactly over the real cyclotomic field Q(2cos(2pi/q)) -- the first draft's assumption of integer coefficients was wrong for phi(q) > 2 and was caught by the tool's own integrality assertion; the plan doc records the correction. The nu-structure of Chambers' relation is pinned by exact cross-phase identities rather than assumed. Band edges are certified by exact sign-change brackets (complete by the degree argument), gaps by rational width bounds. verify_bands.py re-derives P by interpolation in the 4q-th cyclotomic ring and re-checks every certificate with a series-based sign oracle. Self-tested; end-to-end verified on fluxes through the golden-mean convergent 21/34. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VLbALsNim51UzzVWJACWnw
Attainability of optimal bounds for three isotropic phases in 2D conductivity: HS bounds are not always attainable (Nesi 1995), improved bounds and structures exist (Cherkaev 2009, wheel assemblages), and the attainability frontier is uncharacterized. Physics lens: metamaterial engineering of effective transport. Harness computes hierarchical-laminate effective tensors exactly over Q by the frame-free projection formula, with Wiener and multiphase HS bounds and an exact Keller-Dykhne duality check on every tree. verify_laminate.py recomputes every record by rotated-frame interface averaging (rational because conjugation by the scaled rotation divides out the norm). Both routes agree exactly on nontrivial three-phase trees; self-tested end-to-end. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VLbALsNim51UzzVWJACWnw
TL;DR notes the 2026-08-04 onboarding pass, the problem table gains almost-mathieu (low budget, long shot) and three-phase-conductivity (medium), and the queue gains the blind first attempts for each with kill conditions inline. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VLbALsNim51UzzVWJACWnw
…icts Both sides of the conflict were additive, so all entries are kept: - tiers.json: keep both tier-1 plan docs (PLAN-em-problems.md from main, PLAN-conductance-problems.md from the branch). - STATUS.md problem table: keep the Maxwell equilibria row alongside the two newly onboarded rows. - STATUS.md queue: main's maxwell items keep 15-17; the branch's two onboarding items are renumbered 15-16 -> 18-19, and the TL;DR note that pointed at "queue 15-16" now points at 18-19. Also refreshed two counts in the TL;DR that the merge left stale: the problem count is 13 (10 at the merge base, +1 maxwell from main, +2 here) and there are 24 entries under Verified results, not 21 — main added the maxwell results without updating the header line. Verified: pytest 192 passed / 7 skipped, py_compile over harness and explore, all three C kernels build, and both new harness verifiers pass --selftest. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Wmop7yBQtjtXuatijHtGC1
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What this adds
Lands PR #10 (
claude/eddy-currents-nanoscale-circuits-bh4fms, onboarding almost-mathieu and three-phase-conductivity) on top of currentmain, resolving the three ledger conflicts it picked up from the maxwell-equilibria cycle that merged in #8. No content of #10 is changed — this is the merge commit plus conflict resolution.Problem: n/a — merge/infrastructure, no attempt record
Mode: n/a (no attempt claimed)
Status claimed: n/a
Conflicts and how they were resolved
Both sides of every conflict were additive, so all entries are kept:
tiers.json—mainaddeddocs/PLAN-em-problems.mdto tier 1, Add scoping plan for two conductance-flavored problems #10 addeddocs/PLAN-conductance-problems.md. Both listed.STATUS.md, problem table —mainadded the Maxwell equilibria row, Add scoping plan for two conductance-flavored problems #10 added Almost Mathieu and Three-phase conductivity. All three rows kept.STATUS.md, attempt queue —mainadded maxwell items 15–17, Add scoping plan for two conductance-flavored problems #10 added its two onboarding items as 15–16. Maxwell keeps 15–17; Add scoping plan for two conductance-flavored problems #10's items are renumbered 18–19, and the TL;DR note that read "queue 15–16" now reads "queue 18–19".Counts refreshed
Two TL;DR counts were stale after the merge and are corrected: 13 problems (10 at the merge base, +1 maxwell from
main, +2 here) and 24 verified results, not 21 —mainadded the maxwell results without updating the header line. Dead-end count (7) was already correct.The bar
ls problems/ | wc -land counting- **entries under## Verified results.SPECULATIONlabelling — untouched; no prose claims added.VERIFIEDdescribes a range — untouched.modeis honest — no attempt record added.STATUS.md(the ledger) andtiers.jsonwere modified, both merge bookkeeping.prior-art.json— the two new stubs come from Add scoping plan for two conductance-flavored problems #10 unchanged.python -m pytest tests/ -qpasses: 192 passed, 7 skipped.Also run, matching CI:
py_compileoverharness/**/*.pyandproblems/*/explore/*.py, all three C kernels build, and both new verifiers pass--selftest(harness/almost-mathieu/verify_bands.py,harness/three-phase-conductivity/verify_laminate.py).What is not claimed
Nothing mathematical. This does not review or endorse #10's harness correctness, its scoping plan, or its problem statements beyond confirming they import, compile, and self-test — a hostile reader should treat the two new problems as exactly as verified as they were in #10. The renumbering is a presentation choice: it preserves both queues rather than adjudicating priority between them, so the ordering carries no judgment about which line to pull first.
Obstruction / open gaps
None blocking. Both new problems remain at zero attempts, and their first attempts should still run blind, per queue 18–19.
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