ephemerides-spectral 0.6.0

High-precision HDC reference instrument for the solar system based on JPL DE441 (native C backend, runtime kernel patching, 38 bodies including all major Jovian + Saturnian moons; SPICE-free runtime)

ephemerides-spectral

High-precision HDC reference instrument for the Sol Star System.

Overview

ephemerides-spectral is a hyperdimensional-computing instrument that encodes the barycentric state of our star system using high-precision ephemeris data (NASA JPL DE441 / DE442) as resonant phases over a graph Laplacian.

Three interchangeable backends ship with the package:

• bip (default) — bit-serialised integer ALU in pure Python. Phase composition lives in the cyclic group Z_{2^32}; binding is (φ_1 + φ_2) mod 2^32, which is implicit uint32 overflow — no FPU in the hot path. 305× faster than the FPU reference; 256 KB state at D=65536. Always available.
• c (v0.3.1+) — native C library (libephemerides_spectral.{so,dll,dylib}) bundled in the platform wheel under _native/, loaded via ctypes. Byte-for-byte identical phase residues to bip; ~1000× speedup on the chunk loop (encode at +20 yr: 46 ms Python → 0.04 ms C). Falls back transparently to bip if the binary isn't loadable (sdist installs without a C toolchain, Pyodide / WASM, the pure-Python fallback wheel).
• complex128 — FPU reference encoder with unit-norm complex Gaussian bases. Used for the algebraic identities (Syzygy operator, observer binding) and as a regression baseline.

Both backends implement the same algebraic substrate (cyclic-group representation of celestial phase-space, graph-Laplacian eigenbasis); they trade precision for speed.

Companion Project

ephemerides-spectral lives in the same docs/antikythera-maths/ folder as antikythera-spectral because the two share the spectral / cyclic-group framing and the Pyodide bridge contract. They are not consolidated: antikythera-spectral encodes a specific bronze-age mechanism (940-tooth Callippic gear DAG) while ephemerides-spectral encodes the live JPL DE441 ephemeris with phase-dependent (breathing) gravitational couplings. The chess-spectral notebook §20.13–§20.17 calls out the cross-pollination — chess uses Z_{640} (paying an explicit % 640 per op); ephemerides uses Z_{2^32} (free uint32 overflow).

Key Capabilities

• Graph Laplacian Propagator: Diagonal content = Newtonian mean motions + Mercury 43"/century post-Newtonian correction. Off-diagonal = gravitational fiber couplings (planet-sun, moon-planet, mean-motion resonances, asteroid-Jupiter).
• Phase 9 "Breathing" Couplings: Off-diagonal weights modulate with the resonant phase difference cos(n_a·φ_a − n_b·φ_b). Formally a state-dependent (non-autonomous) graph Laplacian / adaptive Kuramoto-family network with phase-difference-dependent coupling — see the research notebook §1.4 for the full positioning across spectral-graph-theory / dynamical-systems / DNLS-on-a-graph vocabularies. Implemented end-to-end without FPU using a 1024-entry int32 cosine LUT (Q1.14 amplitude, 4 KB).
• Sol Star System Roster (v0.5.0+): 38 bodies — Sun, 9 planets (incl. Pluto), 24 moons, 4 main-belt asteroids. The moon set covers Earth's Moon, Mars's Phobos / Deimos, all 4 Galileans (Io, Europa, Ganymede, Callisto) plus the 4 inner regulars (Metis, Adrastea, Amalthea, Thebe), the canonical 9 Saturnians (Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, Iapetus, Phoebe) plus the Janus / Epimetheus co-orbitals, Uranus's Titania, and Neptune's Triton.
• Mean-motion resonances (v0.5.0+): 7 entries in RESONANCES — Jupiter–Saturn 5:2, Neptune–Pluto 3:2, Io–Europa 2:1, Europa–Ganymede 2:1, Mimas–Tethys 4:2 (Cassini Division), Enceladus–Dione 2:1 (powers Enceladus tidal heating), Titan–Hyperion 4:3 (Hyperion's chaotic rotation). Natural-resonance gear group: Z_60 = Z_4 × Z_3 × Z_5.
• Runtime kernel patching (v0.4.0+): Diagnosed-fiber overlay — patches sit beside the published kernel as DATA, not code edits, and contribute per-body residue deltas at encode time. Inspired by Linux ksplice / kpatch; the kernel's published bytes never change. Bridge surface: apply_patch(name) / apply_custom_patch(...) / clear_patches(). Three patches in the bundled CATALOG authored from the v0.3.1 FFT residual analysis. v0.5.1 patch-shrinks-residual benchmark measured the catalog and showed partial vindication: J–S coupled patch shrinks both bodies' residuals by ~77% with phase-recovered authoring (research-side; stays out of the v0.5.x catalog until ≥80% on every body); Mars stays stuck at 3% due to FFT bin leakage. v0.5.2 adds windowed FFT + multi-bin patches for full predictive power.
• SPICE-free runtime (v0.5.0+): pip install works out of the box — both backends use codegen-baked initial phases shipped in _data/initial_phases.json. No SPICE kernel staging required for basic encoding. Skyfield + jplephem stay as optional [ephemeris] extras for callers who want runtime recalibration against custom kernels.
• Observer-Agnostic Views: Unitary binding to generate topocentric "Local View" hypervectors at any (lat, lon) on any body.
• Spectral Syzygy Window Search (v0.3.1+): find-syzygies --from-jd ... --to-jd ... enumerates candidate syzygies in closed form via the natural cyclic-group decomposition (synodic + draconic month), then confirms each by spectral projection. ~1000× faster than the v0.3.0 point-evaluation eclipse --jd pattern for window queries.

Resolution Scaling

Temporal resolution of a residue shift scales inversely with hypervector dimension D:

D	Earth resolution	Use case
2^16	~8 minutes	default; long-term mapping
2^19	~1 minute	medium-cadence events
2^25	~1 second	high-cadence local readout

Installation

pip install ephemerides-spectral

For full ephemeris support (skyfield + JPL DE-kernels):

pip install "ephemerides-spectral[ephemeris]"

CLI Usage

The package ships a rich ephemerides-spectral console script. Use --help on the top-level or any sub-command:

ephemerides-spectral --help
ephemerides-spectral encode --help
ephemerides-spectral breathing --help

Sub-command Cheat-Sheet

# Package version + frozen-data manifest
ephemerides-spectral version

# All 26 bodies in the Sol Star System Laplacian
ephemerides-spectral bodies

# Earth temporal resolution at the default D=65536
ephemerides-spectral resolution --body earth

# Encode J2000 with the integer ALU backend (default)
ephemerides-spectral encode --jd 2451545.0

# Same JD with the FPU complex128 reference encoder
ephemerides-spectral encode --jd 2451545.0 --backend complex128

# Topocentric view from London at J2000
ephemerides-spectral local-view --jd 2451545.0 --body earth --lat 51.5 --lon -0.1

# Syzygy alignment probability AT a JD (point evaluation; encode-then-check)
# v0.4+ ROADMAP: window search via the natural cyclic-group decomposition
ephemerides-spectral eclipse --jd 2451545.0

# Off-diagonal couplings (Laplacian fiber bundle)
ephemerides-spectral couplings

# Phase 9 breathing modulation (Jupiter-Saturn 5:2 by default)
ephemerides-spectral breathing --jd 2458850.0

# Override resonance: 3:2 Neptune-Pluto
ephemerides-spectral breathing --jd 2451545.0 \
    --pair-a neptune --pair-b pluto --n-a 3 --n-b 2

# Mars Sol Date / Mars Coordinated Time at a JD (v0.3.0)
ephemerides-spectral time-mars --jd 2451549.5     # → MSD ≈ 44795.99
ephemerides-spectral time-mars --msd 50000        # invert: MSD → JD_UTC

# Mean lunar synodic + sidereal age/phase at a JD (v0.3.0)
ephemerides-spectral time-lunar --jd 2451545.0

# Lunar-time kernel metadata (LTE440 + LTC status; v0.3.0)
ephemerides-spectral lunar-kernels

# Resonance-derived natural cyclic group (v0.3.0)
ephemerides-spectral natural-group     # → Z_30 = Z_2 × Z_3 × Z_5

# Spectral-native syzygy window search (v0.3.1+)
# Replaces the v0.3.0 point-evaluation `eclipse --jd` for window queries.
# ~1000× faster than encode-then-check; uses the closed-form Saros /
# Metonic / synodic / draconic-month enumeration.
ephemerides-spectral find-syzygies --from-jd 2460311 --to-jd 2460676

# Diagnosed-fiber runtime kernel patching (v0.4.0+)
# Patches sit beside the published kernel as DATA, not code edits, and
# contribute per-body residue deltas at encode time. The kernel's
# published bytes never change. Three patches in the bundled CATALOG
# authored from v0.3.1's de441_error_spectrum FFT (Mars 7.96 yr,
# Mercury 10.69 yr, Jupiter–Saturn 9.56 yr coupled).
ephemerides-spectral patches catalog
ephemerides-spectral patches apply --name jupiter-saturn-9.56yr-coupled
ephemerides-spectral patches active
ephemerides-spectral patches clear

All sub-commands emit JSON to stdout; pass --no-pretty (top-level flag, before the sub-command) for compact single-line output suitable for piping into jq or downstream tooling. Every response carries an ok field; ok: false returns exit code 1 with an error message.

Python API

from ephemerides_spectral import default_encode, bridge

# One-liner: encode a JD as a system state under the default backend.
state = default_encode(jd=2451545.0)            # uint32[26] residues (BIP)
state = default_encode(jd=2451545.0, backend="complex128")  # complex128[D]

# JSON-friendly bridge surface (Pyodide / web frontend)
bridge.get_version()                             # version + manifest
bridge.list_bodies()                             # 26-body roster
bridge.get_resolution(body="mars", D=65536)      # sec/residue
bridge.get_system_state(jd_tdb=2451545.0)        # encode + per-body residues
bridge.get_local_view(jd_tdb=2451545.0, body="earth", lat=51.5, lon=-0.1)
bridge.get_eclipse_probability(jd_tdb=2451545.0)
bridge.list_couplings()                          # Laplacian fibers
bridge.get_breathing_modulation(jd_tdb=2451545.0)  # Phase 9 LUT inspector

# v0.3.0 surface
bridge.jd_to_mars_time(jd_utc=2451549.5)         # MSD + MTC (Allison & McEwen 2000)
bridge.mars_time_to_jd(msd=50000)                # MSD → JD_UTC inverse
bridge.get_lunar_phase(jd_tdb=2451545.0)         # mean synodic + sidereal phase
bridge.list_lunar_kernels()                      # LTE440 metadata + LTC status
bridge.get_natural_resonance_group()             # Z_30 = Z_2 × Z_3 × Z_5

# v0.4.0 surface — runtime kernel patching (overlay on the spectral kernel)
bridge.list_catalog_patches()                    # bundled CATALOG (3 patches)
bridge.apply_patch("mars-7.96yr-diagonal")       # load from CATALOG
bridge.apply_custom_patch(name="my-patch", kind="sinusoid",
                          body="earth", amplitude_deg=0.93,
                          period_days=1940.2)    # FFT-diagnosed custom patch
bridge.list_active_patches()                     # what's currently overlaid
bridge.clear_patches()                           # wipe back to byte-exact baseline

Every bridge method returns a Pyodide-JSON-serialisable dict with ok: True/False. Caller-side errors return {ok: False, error: "..."} rather than raising — designed for crossing the Python/JS boundary cleanly.

Performance & Footprint

ephemerides-spectral is designed for high-performance galactic mapping on edge devices where large SPICE kernels (the 3.3 GB DE441) are prohibitive.

Memory Footprint

Component	Format	RAM / Flash	Description
State (BIP)	uint32[D]	256 KB	At D=65536; pure cyclic-group residues.
State (complex128)	complex128	1.0 MB	At D=65536; FPU reference encoder.
Channel Bases	mixed	~26 MB	Full 26-body roster; pageable from Flash.
Laplacian (L)	complex128	< 15 KB	26 × 26 interaction matrix.
Cosine LUT (Phase 9)	int32[1024]	4 KB	Off-diagonal breathing modulation.
DE441 Truth	BSP	3,300 MB	Original JPL source (calibration only).

Compression vs DE441: > 100:1. Once calibrated, the HDC instrument functions as standalone algebraic truth — no kernel needed for propagation, local-view extraction, or syzygy detection.

Microcontroller Compatibility

The BIP backend is the natural production target for embedded use:

• ESP32-S3 / ESP32-C6 (8 MB+ PSRAM): full 26-body BIP state in PSRAM, microsecond-latency phase updates via uint32 adds.
• ARM Cortex-M7 (Teensy 4.1, etc.): integer multiply-accumulate suits the omega * delta_t step path natively; cosine LUT fits in tightly-coupled memory.
• RISC-V / Edge AI accelerators: (φ_1 + φ_2) mod 2^32 is a single uint32 add — directly mappable to vector-extension lanes.

Instead of searching 3.3 GB of Chebyshev coefficients, these devices evolve the entire Sol Star System phase-space using integer additions and a 4 KB cosine table.

Honest accuracy: DE441 full-epoch sweep (v0.3.0)

research/de441_sweep.py runs the BIP integer-ALU encoder at 15 sample points spanning J2000 ± 14,000 yr (just inside DE441's ~30,000-yr coverage window) and compares per-body ecliptic-longitude residues against DE441 ground truth. Results — sorted by max error, descending:

Body	n	median (rad)	p95 (rad)	max (rad)	max (deg)
jupiter	15	1.357	2.937	3.070	175.92
saturn	15	1.415	2.990	3.062	175.46
neptune	15	0.691	2.748	2.778	159.18
pluto	15	0.791	2.524	2.721	155.92
moon	15	1.084	2.559	2.670	153.00
mercury	15	0.356	1.444	1.461	83.74
mars	15	0.117	0.250	0.253	14.52
uranus	15	0.047	0.120	0.141	8.06
venus	15	0.024	0.114	0.124	7.11
earth	15	0.011	0.104	0.115	6.59

Earth phase error scales roughly linearly with horizon:

Δt (yr)	Earth err (deg)
0	0.000
±1	0.001–0.004
±10	0.006–0.008
±100	0.065–0.069
±1000	0.65–0.68
±5000	2.93–3.31
±10000	4.70–5.71
±14000	5.48–6.59

Three regimes, honestly named

• Sub-10° at multi-millennium horizons (Earth, Venus, Uranus): bodies whose mean motion + small eccentricity + the static gravitational fiber couplings approximate the actual orbit well. Earth benefits from being the calibration body for Mercury's PN diagonal.
• Tens of degrees (Mars 14.5°, Mercury 83.7°): dynamics include eccentricity + long-period perturbations the Phase-9 model captures only partially. Mars has no resonance entry; Mercury's PN diagonal is linear whereas its actual perihelion precession at multi-millennium scales has higher-order terms.
• Phase-scrambled (Jupiter, Saturn, Neptune, Pluto, Moon all hit >150°): bodies whose secular drift is dominated by resonant perturbations the Phase-9 model approximates phenomenologically. The α = 0.1 modulation depth is the right order of magnitude but wrong-in-detail; over ±14,000 yr that wrong-detail accumulates to a ~3 rad phase deficit.

This measures how much of multi-millennium ephemeris our v0.3.0 model captures, not how accurate the BIP encoder is at its design horizon. v0.3.0 is calibrated for the ±20-yr horizon (0.0002 rad ≈ 0.012° Earth phase floor); the multi-millennium errors are the cost of running a model trained for short-horizon dynamics far past its design point. The v0.4+ first-principles per-resonance α derivation is the planned fix — see ROADMAP.

Encoding timings (BIP integer-ALU path, default D = 65536)

Δt (yr)	encode wall time
0	0.2 ms
±1	0.7–1.3 ms
±10	4.2–6.8 ms
±100	44.7–45.8 ms
±1000	447–483 ms
±5000	2.38–2.44 s
±10000	4.34–4.44 s
±14000	6.18–6.37 s

Linear in |Δt| — one 30-day chunk per integration step. At the v0.1.0 design horizon (±20 yr, ~243 chunks) the encode is ~1.85 ms; at ±14,000 yr (~170k chunks) it's ~6.4 s. Median across the sweep: 447 ms; max: 6.4 s.

v0.4.1+ C native path drops these by ~1000× (encode at +20 yr: 46 ms BIP → 0.04 ms C). The full DE441 FFT-residual sweep (1024 samples) takes ~14 seconds on the C native path versus ~5 minutes on Python BIP — the truth-lookup against skyfield is the new bottleneck.

Patch-shrinks-residual benchmark — VINDICATED on planets (v0.5.2)

Earn the right to predict the missing data. — measured.

The v0.4.0 catalog patches claimed to predict missing physics; v0.5.1 audited them and surfaced two authoring bugs (amplitude off by 2×, phase=0 assumption wrong); v0.5.2 fixed both with least-squares fitting at the exact target period. Result: VINDICATED on every targeted planet body.

Patch	v0.4.0 (mag-only)	v0.5.1 (phase-recovered)	v0.5.2 (LS-fit)
Mars 7.96 yr	+2.5%	+2.7%	+99.2%
Mercury 10.69 yr	−49.9% (peak GREW)	+39.6%	+99.9%
Jupiter 9.56 yr	+30.9%	+77.1%	+97.6%
Saturn 9.56 yr	−0.4%	+76.4%	+96.0%

The vindicated patches ship as CATALOG_V2 alongside the original v0.4.0 CATALOG. Use the -v2 suffix:

bridge.apply_patch("mars-7.96yr-diagonal-v2")              # 99.2% shrinkage
bridge.apply_patch("mercury-10.69yr-diagonal-v2")          # 99.9%
bridge.apply_patch("jupiter-saturn-9.56yr-coupled-v2")     # 97.6% J / 96.0% S

Empirical findings worth noting:

• J–S correlation = +1 (in-phase), not −1 as v0.4.0 assumed. Anti-correlated-libration intuition was empirically wrong.
• LS-fit amplitudes are 25–55% larger than FFT-bin extraction — the energy that was leaking into adjacent bins.
• Mars's true residual amplitude is 10.69° (LS) vs 3.45° (FFT-bin rank-1) — a 3× underestimate, the worst leakage case in the catalog.

See the v0.5.2 patch-shrinks-residual analysis on the project docs for the full math derivation, methodology, and moon-residual open question.

Status

• v0.5.2 (current) — Patch-shrinks-residual benchmark VINDICATED on planets via LS-fit catalog (Mars 99.2%, Mercury 99.9%, J–S 97.6/96.0%). CATALOG_V2 ships alongside v0.4.0. Moon-kernel infrastructure (mar099s / jup365 / sat441) added; moon-residual root cause queued for v0.5.x. See the project CHANGELOG and package CHANGELOG.
• v0.5.1 — Patch-shrinks-residual benchmark: PARTIAL vindication (J–S 77%, Mercury 40%, Mars stuck on FFT leakage); two v0.4.0 authoring bugs surfaced.
• v0.5.0 — All major Jovian + Saturnian moons join the encoder (26 → 38 bodies). Three new resonances (Cassini Division, Enceladus tidal heating, Hyperion chaos). SPICE-free runtime via codegen-baked initial phases.
• v0.4.1 — C-side runtime kernel patching (ABI v2). 237× speedup on patched encodes vs BIP.
• v0.4.0 — Diagnosed-fiber runtime overlay (Python side). Patches as data, ksplice/kpatch-style.
• v0.3.1 — C-in-wheel + spectral syzygy window search + DE441 error-spectrum FFT.
• v0.3.0 — Mars Sol Date / Mars Coordinated Time, mean lunar primitives, LTE440 awareness, DE441 full-epoch sweep, natural-resonance gear group.
• v0.2.0 — Phase 9 coverage extension to four resonance pairs (J–S 5:2, N–P 3:2, Io–Europa 2:1, Europa–Ganymede 2:1).
• v0.1.0 — first PyPI release. 26-body Sol Star System Laplacian + Phase 9 breathing couplings + ALU-native BIP encoder.

Roadmap

• v0.4+ first-principles per-resonance α — replaces phenomenological α = 0.1 with values derived from a Hamilton/Delaunay-variable Lagrangian (Lie-series perturbation theory around each resonance). The DE441 sweep above is the empirical motivation: bodies inside the resonance set phase-scramble at multi-millennium horizons because their α values are wrong-in-detail.
• v0.4+ DE441 vs DE442 spectral error signature (experiment) — build two BIP instruments, one calibrated only from DE441, one only from DE442; encode the same JD on both; project the per-body residue deltas onto the encoder's eigenbasis. If the deltas have a coherent spectral signature, DE442's corrections to DE441 live in a specific eigenmode subspace — which means we could predict where ephemeris error correction is structurally needed without needing the corrected kernel.
• v0.4+ spectral syzygy window search — replaces the v0.3.0 point-evaluation eclipse --jd (encode-then-check) with a find-syzygies --from-jd ... --to-jd ... window search that uses the encoder's natural cyclic-group decomposition (Saros 6585.32 d, Metonic 19 yr, synodic month 29.53 d, lunar nodes 18.6 yr). The bronze antikythera's Saros dial doesn't encode-and-check either — it just turns gears whose ratios are the Saros cycle. The HDC-native pattern is to enumerate window-multiples of the slow modes in closed form from the Q-format omega values, then confirm each candidate by spectral projection. This reduces the cost from O(window_days × encode_cost) to O(n_syzygies × confirmation_cost).
• v0.5+ CORDIC topocentric rendering — the cosine LUT is half a CORDIC kernel; the rotation half can subsume the topocentric lat / lon observer-bind, taking that path off the FPU entirely.
• v0.5+ LTC (Lunar Coordinated Time) — pending NASA + international space-agency standardisation (target ~2026–2028 per April 2024 White House directive). LTE440 (Lin et al. 2025) ships the underlying SPICE-format conversion ephemeris with 0.15 ns accuracy through 2050; the bridge gains an LTC namespace mirroring MarsTime once the LTC epoch + day-length convention are formalised.
• Phase 10 resonance coverage — Jupiter–Uranus 7:1, Saturn–Uranus 3:1, Saros / Metonic / Earth–Moon precession entries. Each adds a row to the RESONANCES table; the integer-LUT machinery is shared.
• Bit-serial hardware port (Verilog/SystemC) — the cosine LUT becomes block RAM, the omega * step becomes a fixed-precision multiplier.

License

GPL-3.0-or-later.