chess-spectral 1.6.0

Spectral lattice-fermion encoder for 2D and 4D chess (D4 / B4 symmetry, graph-Laplacian eigenbasis, 640-dim / 45 056-dim HDC)

chess_spectral (Python)

Python reference implementations of the 640-dim 2D and 45 056-dim 4D spectral chess encoders, plus the v1.5 quantum-mechanical front-end (chess_spectral.qm_4d + qm_4d_dynamics + qm_4d_bridge). Sibling of the C17 port in ../src/. Use the Python package for REPL / LLM / notebook analysis and Pyodide-bridge consumers; use the C binaries for batch throughput.

The pieces ship under two top-level packages:

• chess_spectral — 2D encoder + 4D encoder math + 4D phase operators + QM extension. Everything that's pure spectral / B_4 representation theory lives here.
• chess_spectral_4d — 4D game-state surface (move history, side-to-move, draw status, FEN4 round-trip, the Pyodide chess_spectral_4d.bridge module). Splits cleanly from the encoder so the 4D-rules concerns don't bleed into the spectral math.

Both packages share a single dist version derived from importlib.metadata; see Install below.

Install

From PyPI (recommended):

pip install chess-spectral

The base install pulls only numpy and scipy — sufficient for encoding, the 4D phase operators, the kinematic QM layer, and the full §17.1 bridge surface.

Optional extras:

# PGN ingest via chess_spectral.corpus (adds python-chess)
pip install "chess-spectral[corpus]"

# 4D phase-operator validation gates against the Oana & Chiru oracle
pip install "chess-spectral[test]"   # adds python-chess4d-oana-chiru

Package page: https://pypi.org/project/chess-spectral/

From source

Editable install from a local checkout:

pip install -e docs/chess-maths/chess-spectral/python/

From a git URL (pin a commit in production):

pip install "git+https://github.com/lemonforest/mlehaptics.git@COMMIT#subdirectory=docs/chess-maths/chess-spectral/python"

After install, two console scripts are on your $PATH:

chess-spectral --help            # 2D CLI
chess-spectral-4d --help         # 4D CLI

Both packages also expose __version__, derived dynamically from the installed dist:

>>> import chess_spectral, chess_spectral_4d
>>> chess_spectral.__version__ == chess_spectral_4d.__version__
True   # both derive from importlib.metadata.version("chess-spectral");
       # they cannot drift from each other or from the wheel.

In-place (no install)

The legacy workflow still works: every test and analysis script uses sys.path.insert to bootstrap off the python/ directory, so pytest docs/chess-maths/chess-spectral/python/tests/ runs without any install.

Quick start (2D, 640-dim)

>>> from chess_spectral import (
...     encode_640, channel_energies, read_encodings, fen_to_pos,
... )

>>> pos = fen_to_pos("rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1")
>>> enc = encode_640(pos)
>>> enc.shape
(640,)

>>> channel_energies(enc)
{'A1': 0.0, 'A2': 19.845, 'B1': 45.2825, 'B2': 45.2825,
 'E': 322.57, 'F1': 88.77, 'F2': 1851.01, 'F3': 1507.65,
 'FA': 19.92, 'FD': 0.0}

# Read a whole game that was encoded by either C or Python
>>> hdr, arr = read_encodings("game.spectralz")  # transparent gzip
>>> arr.shape
(161, 640)

Quick start (4D, 45 056-dim)

The 4D encoder runs on the Z_8^4 hypercubic lattice with B_4 hyperoctahedral symmetry adaptation (per Oana & Chiru, AppliedMath 6(3):48, 2026). Output is a 45 056-dim float32 vector partitioned into 11 channels of 4096 modes each: A1, STD4_X/Y/Z/W, FIB_SYM_1/2/3, FA_PAWN_W, FA_PAWN_Y, FD_DIAG.

>>> from chess_spectral.fen_4d import parse
>>> from chess_spectral.encoder_4d import (
...     encode_4d, channel_energies_4d, CHANNELS_4D,
... )

>>> pos = parse("4d-fen v1: K@4,0,0,0; k@4,7,7,7")
>>> v = encode_4d(pos)
>>> v.shape, v.dtype
((45056,), dtype('float32'))

>>> energies = channel_energies_4d(v)   # per-channel L2 energies
>>> sorted(energies)
['A1', 'FA_PAWN_W', 'FA_PAWN_Y', 'FD_DIAG',
 'FIB_SYM_1', 'FIB_SYM_2', 'FIB_SYM_3',
 'STD4_W', 'STD4_X', 'STD4_Y', 'STD4_Z']

The 4D game-state surface (move history, draw detection, FEN4 round-trip, promotion-piece argument) lives in chess_spectral_4d:

>>> from chess_spectral_4d import GameState4D, apply_move, MoveHistory4D
>>> from chess_spectral_4d import bridge

# Load a placement from a FEN4 string (white-to-move by default)
>>> result = bridge.load_state("4d-fen v1: K@4,0,0,0; k@4,7,7,7")
>>> state = result['state']
>>> isinstance(state, GameState4D)
True

# apply_move(state, from_sq, to_sq, *, promote_to='Q') is the v1.4 API
>>> # state2 = apply_move(state, from_sq=4, to_sq=5, promote_to='Q')

# Draw status: priority threefold > 50-move > insufficient > stalemate
>>> bridge.get_draw_status(state, has_legal_moves=True)
{'ok': True, 'status': 'none'}

For raw move-rule logic (legal-move generation, check detection) on Z_8^4, see chess_spectral.phase_operators_4d below.

Quick start (QM extension, v1.5+)

The QM extension ships in two layers, mirroring the standard physics split:

• Kinematics — chess_spectral.qm_4d. What states and operators look like: state space, observables, measurement structure, the B_4 group action. Lifts encoder output to ψ ∈ ℂ^{45056}, exposes the 11-channel decomposition as a built-in projection-valued measure (PVM), builds five Hermitian piece-reach observables (rook / bishop / queen / king / knight) on the per-channel ℂ^{4096} factor, and ships the 384-element B_4 unitary representation as a cached LUT.
• Dynamics — chess_spectral.qm_4d_dynamics. How states change: the 11 per-channel u_move_* builders for move-as-unitary transitions (discrete) plus evolve_under_h0 for Zeno-style continuous time evolution between move boundaries.

Consumers that want a Pyodide-JSON-shaped surface use the chess_spectral.qm_4d_bridge dispatch layer described in the next section.

>>> from chess_spectral.fen_4d import parse
>>> from chess_spectral.qm_4d import (
...     state_to_psi,
...     prob_channel, measure_channel_distribution,
...     channel_projector,
...     H_rook_4, H_bishop_4, H_queen_4, H_king_4, H_knight_4,
...     measure_observable_distribution,
...     b4_unitary_rep_4096, b4_unitary_rep_full,
...     expectation, is_normalized, is_hermitian, is_unitary,
... )

>>> pos = parse("4d-fen v1: K@4,0,0,0; k@4,7,7,7; R@0,0,0,0")
>>> psi = state_to_psi(pos, side_to_move=True)
>>> psi.shape, psi.dtype
((45056,), dtype('complex128'))
>>> is_normalized(psi)
True

# Born-rule channel measurement: probability mass per channel
>>> prob_channel(psi, c=0)            # A1 channel
3.3e-08
>>> probs = measure_channel_distribution(psi)   # all 11 channels
>>> abs(probs.sum() - 1.0) < 1e-10
True

# ⟨ψ|H_rook|ψ⟩ on the rook channel block
>>> # expectation(H_rook_4, psi[0:4096])    # H_piece_4 is sparse 4096x4096

# Born-rule eigenbasis distribution: |⟨φ_k|ψ⟩|² grouped by eigenvalue
>>> # eigvals, probs = measure_observable_distribution(H_rook_4, psi[0:4096])

# B_4 group action (384 elements). 4096-dim per-channel block, or the
# I_11 ⊗ U_4096(g) Kronecker extension to the full 45 056-dim space.
>>> # U = b4_unitary_rep_full(g)            # cached; sparse 45056x45056

The Hermitian piece-reach observables H_rook_4, H_bishop_4, H_queen_4, H_king_4, H_knight_4 are built on demand and cached. They are real-symmetric on ℂ^{4096} with integer / near-integer spectra (Hermiticity verified at floating residual ~5e-15; Pre-flight 2 in qm_4d.py). Pawn observables break Hermiticity under the standard inner product (directed push) — the pseudo-Hermitian η-metric construction is deferred to v1.7+ per ADR-005.

b4_unitary_rep_4096(g) and b4_unitary_rep_full(g) realize the order-384 hyperoctahedral group as sparse unitaries on ℂ^{4096} and ℂ^{45056} respectively (the latter is I_{11} ⊗ U_{4096}(g) — same B_4 action applied independently to each of the 11 channels). Both are cached per group element. measure_observable_distribution(H, ψ) diagonalizes any Hermitian observable on ℂ^{4096} and returns the Born-rule probability distribution over distinct eigenvalues.

Move-as-unitary dynamics (Phase 4, Track B) live in chess_spectral.qm_4d_dynamics. The module ships per-channel builders for all 11 channels and both non-capture and capture moves:

• u_move_a1 — A_1 channel via projector-sandwich (B1).
• u_move_std4 — STD4_X/Y/Z/W via similarity-transform; same-orbit is strict-unitary, cross-orbit returns a measurement-only marker (B3a, ADR-003 amendment).
• u_move_fa_pawn — FA_PAWN_W/Y via axis-parity-odd projector sandwich (B3b).
• u_move_fib_meas — FIB_SYM_1/2/3 via measurement-only re-encode (B3c, per the Phase 3.5 amendment to ADR-003 §3.3).
• u_move_fd_diag — FD_DIAG via rank-1 update + renormalization (B3d/e).
• evolve_under_h0 + H_FREE_4D — Zeno-style continuous evolution between move boundaries, where H_0 = -Δ is the lattice Laplacian (B2, ADR-002).

§17.1 Pyodide bridge surface (v1.5)

chess_spectral.qm_4d_bridge is the consumer-facing bridge — the 7 §17.1 QM-extension methods plus 6 §17.5 dev/debug methods — designed for Pyodide consumers (e.g., the chess4D-OC visualizer) that need Pyodide-JSON-serializable returns and Float32 ψ-amplitudes ready for Float32Array shader uploads.

>>> from chess_spectral.qm_4d_bridge import (
...     # §17.1 (QM-extension surface)
...     get_qm_state, get_qm_density, apply_move_qm, apply_move_qm_full,
...     measure_at, get_density_matrix_of, get_probability_current,
...     get_qm_expectation,
...     # §17.5 (dev / debug surface)
...     get_version, get_encoder_shape, get_fen4_state, load_fen4,
...     load_jsonl_fixture, has_legal_moves,
... )

# Round-trip: load a FEN4, get ψ as Float32 interleaved, apply a move,
# get the updated ψ.
>>> r = load_fen4("4d-fen v1: K@0,0,0,0; k@7,7,7,7; R@1,0,0,0")
>>> state = r['state']

>>> r = get_qm_state(state, side_to_move=True)
>>> r['basisDim'], r['psi'].dtype, r['psi'].shape
(45056, dtype('float32'), (90112,))   # 2 × 45 056 — real+imag interleaved
>>> abs(r['normSq'] - 1.0) < 1e-6
True

# Per-cell density: |ψ|² summed across the 11 channels per cell
>>> r = get_qm_density(state)
>>> r['density'].shape, abs(r['density'].sum() - 1.0) < 1e-6
((4096,), True)

# Apply a move and get the assembled ψ_post (Float32 interleaved).
# move format: (from_sq, to_sq) as ints OR ((x,y,z,w), (x,y,z,w))
>>> # r = apply_move_qm_full(state, move=(1, 2))
>>> # r['ok'], r['psi'].shape
>>> # (True, (90112,))

# §17.5 debug surface
>>> get_version()['version']         # e.g., '1.5.0'
>>> get_encoder_shape()['totalDim']  # 45056
>>> get_encoder_shape()['channels']  # [{'name': 'A1', 'offset': 0, 'dim': 4096}, ...]

Wire format (ComplexArray, Float32Array-friendly): every ψ return is a 1-D Float32 array of length 2 * 45056 = 90112, where psi[2k] is Re(ψ_k) and psi[2k+1] is Im(ψ_k). This matches the §17.1 contract documented in the research notebook §17.1.

apply_move_qm vs apply_move_qm_full. The low-level apply_move_qm returns a per-channel dispatch dict (mixed csr_matrix

• marker dict values) for consumers that want to reason about per- channel structure. The high-level apply_move_qm_full does the block-by-block assembly (csr_matrix → U_chan @ ψ_pre[block]; marker dict → psi_post_block splice) and returns the assembled ψ_post as Float32 interleaved. Most consumers want the _full variant.

The B5 milestone (April 2026) closed the last unshipped channels, so the bridge no longer raises for any move type — non-captures and captures both succeed via the channels' B5 capture-path branches. See qm_4d_bridge.py for per-method docstrings and qm_4d_dynamics.py for the per-channel construction details.

Deferred to v1.7+:

• get_density_matrix_of (reduced density matrix; needs partial- trace machinery on channel labels).
• get_qm_density(piece_id=...) (per-piece marginal; same blocker).

Both raise NotImplementedError with a pointer to the v1.7 milestone.

CLI

The 2D CLI (chess-spectral, entry point chess_spectral.cli:main) mirrors the C spectral CLI subcommand-for-subcommand. Output is byte-identical to the C binary on the same input — the spectral csv command produces the same bytes on either side.

chess-spectral csv         game.spectralz -o game.csv
chess-spectral encode      -i game.ndjson -o game.spectralz -z
chess-spectral encode-fen  --fen "..."   -o single.spectral
chess-spectral compare     a.spectralz b.spectralz
chess-spectral query       game.spectralz --ply 30
chess-spectral heatmap     game.spectralz --ply 30 --channel A1
chess-spectral analyze     game.spectralz
chess-spectral export      game.spectralz -o game.json
chess-spectral version

The 4D CLI (chess-spectral-4d):

chess-spectral-4d tables-verify  --phase all
chess-spectral-4d encode-fen4    --fen4 "4d-fen v1: K@0,0,0,0; ..."
chess-spectral-4d encode-moves4  --moves game.ndjson4 -o game.spectralz4 -z
chess-spectral-4d corpus-gen     --games game1.ndjson4 game2.ndjson4 ...
chess-spectral-4d version

Both CLIs follow the --help discipline: every subcommand and every argument has non-empty help text. Run <cmd> --help (or <cmd> <subcommand> --help) before invoking; the immolation suite gates this in CI.

Layout

chess_spectral/                # 2D + 4D encoder math + QM extension
  __init__.py                  # __version__ via importlib.metadata
  encoder.py                   # encode_640(pos) → np.ndarray(640,)
  frame.py                     # v2 .spectral[z] binary I/O + transparent gzip
  csv_export.py                # dist_prev / cos_prev / energies CSV
  cli.py                       # `chess-spectral` (2D CLI)
  phase_operators/             # 2D §11 phase-space move generator (1.2.0+)

  encoder_4d.py                # encode_4d(pos4) → float32(45056,)
  frame_4d.py                  # v3/v4 .spectralz4 binary I/O (legacy reader)
  frame_v5.py                  # v5 unified wire format (2D + 4D, 3 encoding modes; default for new writes from v1.6)
  tables_4d.py                 # B_4 group, lattice tables, eigenmodes
  fen_4d.py                    # FEN4 v1 placement-literal parser + serialize
  phase_operators_4d/          # 4D §13 phase-operator move engine (1.3.0+)

  qm_4d.py                     # Track A kinematic QM front-end (1.5.0+)
  qm_4d_dynamics.py            # Track B per-channel U_move builders (1.5.0+)
  qm_4d_bridge.py              # §17.1 + §17.5 Pyodide bridge surface (1.5.0+)

chess_spectral_4d/             # 4D game-state surface (1.4.0+)
  __init__.py                  # GameState4D, Move4D, MoveHistory4D, apply_move, bridge
  move_history.py              # ply log, side-to-move, 50-move clock, repetition hash
  apply_move.py                # apply_move(state, from_sq, to_sq, *, promote_to='Q')
  bridge.py                    # load_state, get_draw_status, get_move_history,
                               #   is_insufficient_material_2d
  cli.py                       # `chess-spectral-4d` (4D CLI)

pyproject.toml                 # PEP 621 packaging metadata
tests/                         # pytest suite (see test count below)

Test count (post-v1.5): 45 895 tests collected. Breakdown: ~44 876 parametric 4D phase-operator tests (the bulk), 81-test end-to-end immolation suite (test_smoke_e2e.py, expanded from 41 for v1.5 surface coverage), 272 v1.5 QM tests across the kinematic front-end (test_qm_4d.py, test_qm_4d_z2_grading.py), the Track B B1..B5 dynamics gates (test_qm_4d_dynamics_b{1,2,3a,3b,3c,3d,5}.py), and the §17.1/§17.5 bridge surface (test_qm_4d_bridge_v15.py), plus 102 fast tests, 260 pawn-axis / phase-4d-check / phase-4d- unobstructed tests, 92 2D phase_operators tests, and 210 v1.4 game-state tests. Run via pytest docs/chess-maths/chess-spectral/python/tests/.

Phase operators (2D, §11)

chess_spectral.phase_operators ships a phase-space move generator and check detector (added in 1.2.0). The primitives compute all moves and check relationships as modular arithmetic on a single integer per square — phi(r, c) = r·67 + c·7 mod 640 — rather than geometric coordinates. They are a drop-in equivalent to python-chess's pseudo_legal_moves + is_check, validated at 100% on the reference corpus, and compose naturally with the spectral encoder's coprime phase structure.

import chess
from chess_spectral.phase_operators import (
    occupation_aware_moves_c,   # pseudo-legal dests from a square
    available_castles,          # legal castles for side-to-move
    phasecast_is_check,         # is the mover's king attacked?
    move_leaves_king_in_check,  # would this move expose our king?
)

board = chess.Board()
dests = occupation_aware_moves_c(board, "N", 0, 1, +1)
# -> frozenset({(2, 0), (2, 2)})   (a3 and c3)

phasecast_is_check(board)  # False on the starting position

Validation coverage and rationale: see PHASE_OPERATOR_SUPPLEMENT.md.

Phase operators (4D, §13)

chess_spectral.phase_operators_4d (1.3.0+) is the 4D analogue — mixed-radix tower with modulus 145451 and ladder coefficient 14 (vs the 2D framework's 8). Validated against python-chess4d-oana-chiru at 44 803 (state, origin, piece) cases for occupation-aware moves and 232 cases for check detection.

from chess_spectral.phase_operators_4d import (
    phi4,
    P_rook4, P_bishop4, P_queen4, P_king4, P_knight4,
    P_pawn4_white, P_pawn4_black,
    occupation_aware_moves_a_4d,    # phase-op candidates ∩ chess4d oracle
    phasecast_is_check_4d,
    move_leaves_king_in_check_4d,
)

Full design + experimental record: PHASE_OPERATOR_SUPPLEMENT_4D.md.

When to use what

The 2D and 4D encoders are independent build targets that share table generation discipline. Pick by what you're encoding; the QM extension sits on top of the 4D encoder.

	2D (chess_spectral)	4D (chess_spectral + chess_spectral_4d)
Encoding dim	640	45 056
Lattice	Z_8 × Z_8	Z_8^4
Symmetry group	D_4 (order 8)	B_4 hyperoctahedral (order 384)
Game rules	python-chess (fen_to_pos)	Oana & Chiru (python-chess4d-oana-chiru)
Channels	10 (A1, A2, B1, B2, E, F1, F2, F3, FA, FD)	11 (A1, STD4_X/Y/Z/W, FIB_SYM_1/2/3, FA_PAWN_W/Y, FD_DIAG)
Phase operators	phase_operators (1.2.0+)	phase_operators_4d (1.3.0+)
QM extension	not yet shipped	qm_4d + qm_4d_dynamics + qm_4d_bridge (1.5.0+)

Python vs C — same encoders on either side, byte-identical output:

	C (../src/)	Python (this package)
Throughput	µs/encode	ms/encode
REPL / notebooks	✗	✓
LLM-pasteable	binary	code
scipy.linalg exploration	✗	✓
Embeds in mobile / web (Pyodide)	✓	✓ (Pyodide)
Exact numerical reference	tables baked at build	rebuilt from primitives

Develop new channels in Python first (faster iteration, scipy.linalg at hand, no rebuild loop). Once the math is frozen, port to C and verify parity via the test suite — the critical test is test_csv_matches_c_byte_for_byte (2D) / test_e2e_spectralz4_parity.py (4D), which assert the C-produced encoded bytes equal the Python-produced bytes.

See also

• Cross-disciplinary applications — research notebook §15 (chess_spectral_research_notebook.md) for the framing of chess-spectral as a H(4, 8) Hamming-scheme toolkit with B_4-equivariant frozen featurizer and Born-rule loss hooks.
• §17 bridge contracts — same notebook, §17.1 / §17.5 for the consumer-facing method specs that this package implements.
• 4D notebook — chess_spectral_4d_notebook.md for the 4D-specific research record (encoder injectivity, B_4 spectral identity, qm_4d pre-flight findings).
• Track B ADRs — docs/adr/qm_4d/ for the design record of the v1.5 QM extension:
  • ADR-001 phase convention for unitary moves
  • ADR-002 time-evolution semantics (continuous H_0 between move boundaries; evolve_under_h0)
  • ADR-003 per-channel move transformation (+ Phase 3.5 orbit-restriction amendment for cross-orbit STD4 / FIB_SYM measurement-only re-encode)
  • ADR-004 Z_2 superselection structure (side-to-move sign multiplier, resolves the 8-collision encoder hash issue)
  • ADR-005 pawn pseudo-Hermitian η-metric (deferred to v1.7+)
  • PHASE_3_5_PROBE_RESULTS.md — empirical probe record that drove the ADR-003 amendment.
• Pawn-axis split (v1.1.1) — Oana & Chiru Definition 11; the encoder splits the pawn antisymmetric channel into W-axis and Y-axis sub-channels (FA_PAWN_W, FA_PAWN_Y) and grew from 40 960-dim to 45 056-dim. See encoder_4d.py header for the rationale.