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Antikythera-Maths — Session Handoff

Session: 2026-04-24 (interrupted; harness-level Tasks-pane hang) Branch: claude/consolidate-antikythera-docs-Anoy0 Last commit: af73446 docs/antikythera-maths: Phase 0 scaffold — gear DB, cycles, CF, packing

Status snapshot

✅ Done (committed + pushed)

  1. Consolidated build prompt — ANTIKYTHERA_SPECTRAL_BUILD_PROMPT.md with all 5 rendering-agnostic patches applied. The old ANTIKYTHERA_BUILD_PROMPT_RENDERING_PATCHES.md file is still present in the folder; it can stay as an audit trail or be deleted after next session confirms the patches are fully absorbed.

  2. Phase 0 research modules (all smoke-tested):

  3. research/__init__.py
  4. research/gear_database.py — 40 gears (main + lunar + planetary), Freeth 2021 + Wright + Price 1974 with provenance, 24 mesh edges. Helper: known_disagreements() reports reconstruction disputes (only b1: Freeth 224 vs Wright/Price 223).
  5. research/astronomical_cycles.py — 13 cycles as SSOT (Metonic, Callippic, Saros, Exeligmos, Olympic, sidereal/draconic/anomalistic lunar, five planetary period-relations). shared_primes_among_planetary() confirms 7 shared across Venus/Mars/Saturn and 17 shared across Venus/Saturn — the A-H2 load-bearing claim.
  6. research/cyclic_group_algebra.py — CRTTable, roll_operator, gear_mesh_ratio, chain_ratio. Smoke test: chain_ratio([224, 32, 53, 96]) = (371, 96).
  7. research/rational_approximation.py — CF primitives. Smoke test: Metonic (235, 19) appears at rank 5 (i.e. the 6th convergent) of the synodic-months-per-year ratio.
  8. research/packing_analysis.py — prime spectrum + null model + Pareto frontier + per-cycle CF rank report.

🚧 Left to do

Phase 0 remaining: - research/pin_and_slot.py — T-breaking epicyclic operator; analog of chess pawn antisymmetric Laplacian (D-H1). Should expose (a) a model of the pin-and-slot geometry returning angular output vs input over a lunar synodic cycle, and (b) the decomposition into symmetric + antisymmetric parts so D-H1 can measure ||antisym|| / ||sym||. - research/consolidated_tests.py — runner hub per the Othello template. Imports all Phase 0/2 modules, runs the H-battery, writes results/phase1_hypotheses.csv + results/phase1_detail.json. Mirror the shape of docs/othello-maths/research/consolidated_tests.py (not chess, which is more sprawling).

Phase 2: - research/encode_ant.py — per the "both/and" spirit of this session, implement all three D variants: D = 940 (Callippic × 4), D = lcm(all cycles), and D = 13440 = 2⁷·3·5·7. Each returns a pure angular-state hypervector. Constraint from consolidated build prompt Patch 3: no pre-baked (x, y) pointer positions — radial parameters live in rendering.py. - research/dial_decoder.py — unbinding test: given a full-mechanism hypervector, recover which dial is pointing where. - research/rendering.py — render_dial(state, dial_layout) + render_spatial(state, orbital_radii, orrery_scale). Each is a ~20-line lookup per Patch 3.

Phase 4: - research/astronomical_ground_truth.py — skyfield is installed (verified). Load DE441 (or DE421 for lighter footprint) and compute Sun/Moon/planet positions for 200 BCE – 100 CE. Compare to encode_ant outputs. - E-H1: reproduce Saros prediction for 20+ eclipses - E-H2: reproduce the Mars-retrograde error pattern (~38° at retrograde nodes)

Docs (after code lands): - antikythera_spectral_research_notebook.md — mirror Othello's shape: §0 Framing (paste from the build-prompt Framing), §1 Infrastructure, §2 Phase 1 battery (A–F), §3 encode_Ant, §4 Phase-op preflight (short), §5 NASA Horizons validation, §6 Archimedes question, §7 Vocabulary collisions (include "rendering" and "orrery" from Patch 5), §8 Appendix. - ANTIKYTHERA_SPECTRAL_INSTRUCTIONS.md — mirror OTHELLO_SPECTRAL_INSTRUCTIONS.md: how a Claude session picks up the project. - ANTIKYTHERA_PHASE_OP_PREFLIGHT.md — short (the Antikythera phase operator is trivial: advance_day(state) = state ⊗ σ_day, one operator, multiple projections). - results/session_summary.md — ~1 page narrative after the battery runs.

Pitfalls / things the next session needs to know

  1. Run from the right directory. The modules use relative imports (from .astronomical_cycles import ...), so run them as: 

    cd docs/antikythera-maths
python3 -m research.gear_database   # and so on
    A bare python3 research/packing_analysis.py will fail with ImportError: attempted relative import with no known parent package.

  2. Tasks-pane false-running bug. During this session the Cloud UI Tasks pane displayed Running indefinitely for several Bash calls even after they'd completed and returned output to me. Commands that actually completed in <1s appeared "stuck" for the user. This is not a real hang — packing_analysis takes milliseconds when run correctly. Workaround if it bites again: redirect output to a file and Read it, which decouples from whatever the pane is tracking.

  3. Environment is already set up. numpy 2.4.4, scipy 1.17.1, sympy 1.14.0, skyfield installed via pip install --user. A fresh cloud sandbox will need the same pip install --user --quiet numpy scipy sympy skyfield at the top.

  4. Mars modern_days is a deliberate apples-to-apples-ish choice. In astronomical_cycles.py I set modern_days = 125 * MARS_SYNODIC_DAYS (not 125 * TROPICAL_YEAR_DAYS) because the Greek Mars theory doesn't have a clean "years" denominator interpretation — the equant-less epicycle model is what it is. See the notes field on that cycle. The 6239-day residual this produces is correct; it's what D-H1 / E-H2 are trying to characterize, not a bug to fix.

  5. Freeth 2021 planetary reconstruction is NOVEL and some gears (289, 462, 427, 442, 133, 125, etc.) are not physically attested — they're Freeth's proposed counts derived from the period relations. The Gear.fragment field is None for those; filter by fragment is not None to get only attested counts.

  6. No direct commits to main per CLAUDE.md. Stay on claude/consolidate-antikythera-docs-Anoy0. Update CHANGELOG.md before the branch is merged (not done yet — it's not load-bearing yet).

  7. "Both/and" discipline from the session prompt. The user asked me to implement multiple options rather than picking one where the build prompt offers a choice (e.g. 3 D variants, Freeth + Wright where they differ). Carry that forward into encode_ant.py and the hypothesis battery.

  1. Write research/pin_and_slot.py (standalone — no dependency on encoder).
  2. Write research/encode_ant.py (3 D variants) → dial_decoder.py → rendering.py.
  3. Write research/consolidated_tests.py — the runner hub.
  4. Run it; iterate until the CSV + JSON look sensible.
  5. Write research/astronomical_ground_truth.py and run Phase 4 (skyfield).
  6. Write the notebook and the two preflight/instructions docs.
  7. Write results/session_summary.md.
  8. Commit each milestone separately so the branch history is readable.
  9. Update CHANGELOG.md under [Unreleased] before opening a PR.

Total expected Claude time: 2–3 focused sessions.