antikythera-spectral 0.2.0

Hyperdimensional-computing encoder + Pyodide bridge for the Antikythera mechanism

antikythera-spectral

A hyperdimensional-computing model of the Antikythera mechanism, packaged for Python and the browser.

Encode any date as a state vector that any of the mechanism's dials can be read from. Decode, compare against modern ephemeris truth, simulate the Hellenistic operator's seasonal-recalibration workflow, and run the project's 31-row hypothesis battery — all from one pip install. Pyodide-compatible: the same package runs in a browser via micropip so a web app can drive a digital Antikythera with no Python server.

What is the Antikythera mechanism?

A bronze hand-cranked astronomical calculator built in Hellenistic Greece around 150–60 BCE, recovered in 1901 from a shipwreck off the island of Antikythera. Its surviving 30+ gears predict solar / lunar / planetary positions, eclipses (via the 18-year Saros cycle), and the four-year Olympiad calendar. Freeth et al. 2021 (Sci. Rep. 11:5821) is the current authoritative reconstruction; the device's planetary front face has not survived intact and remains the subject of active research.

The HDC framing this package implements: every gear is a faithful representation of ℤ/nℤ; every mesh is a rational map between cyclic groups; every dial pointer is a hypervector whose components are the phase angles on the various dials. The Greeks built a resonant HDC object before Plate wrote HRR.

Install

pip install antikythera-spectral

The base install pulls only numpy and is fully self-contained as of v0.2.0 — every bridge method works out of the box, including visibility windows, heliacal-rising prediction, eclipse search, and solar-elongation queries (using algebraic synodic-cycle propagation; ~±1 day Antikythera-grade precision). No JPL ephemeris kernel required.

Optional extras for sub-arcsec-precision validation against modern ephemerides:

pip install "antikythera-spectral[ephemeris]"    # adds skyfield + jplephem; pass precise=True
pip install "antikythera-spectral[hypotheses]"   # adds scipy (for chi-square in H-H1)
pip install "antikythera-spectral[plot]"         # adds matplotlib
pip install "antikythera-spectral[all]"          # everything above

In algebraic mode (the default), the four sky-truth bridge methods accept precise=False (the default) and use frozen per-planet anchors + closed-form propagation. With precise=True they switch to skyfield + a JPL DE-kernel for sub-arcsec accuracy. See ADR 0011 for the discipline.

Pyodide / micropip (in-browser)

import micropip
await micropip.install("antikythera-spectral[ephemeris]")

The full Bridge API is available from a Pyodide REPL with no server-side Python.

Quick start (Python)

>>> from antikythera_spectral import bridge
>>> result = bridge.get_dial_state(jd_tdb=1684500.0)   # ~205 BCE
>>> result['ok']
True
>>> result['dials']['mars']['angle_deg']
247.3

Quick start (CLI)

antikythera-spectral encode --jd 1684500.0
antikythera-spectral visibility --planet mars --from-jd 1684500 --to-jd 1685000
antikythera-spectral compare ephemerides --jd 1684500 --body mars \
                                          --kernel-a de421 --kernel-b de441_part1
antikythera-spectral hypotheses --csv-out -

What can you do with it?

• Encode any Julian date as a state vector across all of the mechanism's dials.
• Decode any state vector back to per-dial residues (round-trip is exact for the LCM variant).
• Convert dates between Gregorian, Julian, Athenian archonship + Attic months, and Olympiad year — the four calendar systems an ancient Greek astronomer or modern reader might use.
• Compute visibility windows for each planet (heliacal rising / setting + solar elongation), the astronomical reality that gates the operator's recalibration workflow.
• Search for eclipses in any date band via sky-driven ephemeris enumeration.
• Simulate the operator workflow (§11.6.16 of the research notebook): start at a date, advance, observe at heliacal rising, re-anchor, repeat.
• Compare reconstructions — Freeth 2021 vs Wright vs Price 1974 dial readings simultaneously at any date.
• Compare ephemeris kernels — DE421 vs DE441 vs DE441_part1 deltas at a chosen JD/body in arc-seconds, kilometers, AU.
• Run the 31-row hypothesis battery that drives the research notebook, get JSON / CSV output.
• Override gear ratios (what-if mode) — re-encode with arbitrary p/q to explore alternative period relations like the canonical Venus 5/8.
• Inventory by fragment (archaeological mode) — list which gears are attested in fragments A/B/C/D vs reconstructed by Freeth.
• Babylonian Goal-Year overlay — given a planet+date, return what an astronomer using the 47-year Mars cycle (or 59-year Saturn, etc.) would have predicted.
• Animation export — emit a time-series of states over a date range for a viewer / animation frontend.

Bridge API

docs/bridge_api.md is the consumer-facing contract. 28 methods grouped by purpose; each returns a Pyodide-JSON-serializable {"ok": True, ...} dict. Numpy arrays in return values are real-valued (Float32 for amplitude payloads) so JS consumers can use new Float32Array(...) directly.

Hypothesis battery

The package ships the same 31-row H-battery the research scaffold runs. Headlines:

• 22 PASS — encoder round-trips perfectly for all D variants; pin-and-slot encodes T-symmetry breaking; manufacturing tolerance is fine for one Metonic cycle; etc.
• 3 PARTIAL — the proxy-metric Pareto for {7, 17}; the prime spectrum vs null model; H-H1 chi-square against Almagest periods.
• 3 FAIL — including E-H2: uniform Mars encoder peak ≥ 150° (this is expected; the failure mode is the rationale for the §11.6.16 operator-recalibration framing).
• 3 UNDETERMINED — open exploration F-series rows, plus skyfield-gated rows when no ephemeris kernel is on disk.

See the research notebook for the full row-by-row narrative.

Documentation

Topic	Link
Research notebook (the project narrative)	antikythera_spectral_research_notebook.md
Bridge API contract	bridge_api.md
Calendar systems reference	CALENDAR_SYSTEMS.md
Ephemeris kernels (DE421 / DE441 / etc.)	EPHEMERIS_KERNELS.md
ΔT discussion (Earth-rotation drift at -200 BCE)	DELTA_T_MODEL.md
Operator workflow simulation (§11.6.16)	OPERATOR_WORKFLOW.md
Roadmap	ROADMAP.md
Changelog	CHANGELOG.md

Citing

If antikythera-spectral contributes to a paper or write-up, please cite both the package and the research notebook:

@software{antikythera_spectral,
  author = {Kirkland, Steven},
  title = {antikythera-spectral: Hyperdimensional-computing model of the Antikythera mechanism},
  year = {2026},
  url = {https://github.com/lemonforest/mlehaptics/tree/main/docs/antikythera-maths/antikythera-spectral},
  version = {0.1.0}
}

License

GPL-3.0-or-later. Matches the license of the parent monorepo.

See also

Sibling packages in the same monorepo:

• chess-spectral — the same HDC + cyclic-group-algebra framing applied to chess, with native C accelerator.