python-chess4d-oana-chiru 0.3.1

Python reference implementation of Oana & Chiru (2026) — A Mathematical Framework for Four-Dimensional Chess (DOI 10.3390/appliedmath6030048).

python-chess4d-oana-chiru

Python reference implementation of:

Oana & Chiru, A Mathematical Framework for Four-Dimensional Chess, MDPI AppliedMath 6(3):48, 2026. DOI 10.3390/appliedmath6030048.

The source paper lives in hoodoos/ (treat as read-only reference).

Coordinate convention

Internally 0-based: B = {0,…,7}^4 ⊂ Z^4 (4096 cells). The paper's 1-based {1,…,8}^4 notation is preserved in docstrings and converted only at the UI boundary. See CLAUDE.md for the indexing gotcha (the reference UI is also 0-based; the central mixed-color slice block is at theoretical (z, w) ∈ {4, 5}×{4, 5} / UI (z, w) ∈ {3, 4}×{3, 4}).

Status

0.3.0 — core engine, legality, and corpus tooling are in. Implemented: all six piece types with paper-faithful move generation (rook / bishop / knight / queen / king / pawn), multi-king legality per §3.4 Def 3 (a move is legal iff no king of the mover is attacked afterwards), X-axis castling with global attack safety, Y- and W-axis en passant, pawn promotion on the terminal rank of each forward axis, draw detection (50-move rule + threefold repetition via 4D state hash), .c4d move notation with round-trip I/O, chess-spectral integration (optional), and a random-playout corpus generator writing the chess-maths-the-movie nested layout.

Not yet implemented: search / evaluation, a UI, Oana-Chiru 4D-aware opening books. See CLAUDE.md for architectural invariants.

Spectral encoding (optional)

chess4d integrates with the chess-spectral framework (developed in the sibling mlehaptics repo) for physics-grounded analysis of 4D positions. The encoder maps a GameState to an 11-channel, 45 056-dimensional float32 spectral vector and writes streams of frames as spectralz v4 files. Install with the spectral extra (pulls chess-spectral directly from GitHub, plus numpy and scipy):

pip install -e .[spectral]

Encode a single position:

from chess4d import initial_position
from chess4d.spectral import encode_position

gs = initial_position()
vec = encode_position(gs)  # (45056,) float32

Encode a game and write it to a spectralz v4 file:

from chess4d.spectral import write_spectralz

write_spectralz("game.spectralz", start_state, move_list)

The 11 channels cover the six piece types (with pawns split by forward axis per Oana & Chiru Def. 11) plus board-parity and side-to-move signals. See the chess-spectral notebooks in the mlehaptics repo for channel semantics and reconstruction examples.

Corpus generation

chess4d-corpus-gen writes a reproducible random-playout corpus in the chess-maths-the-movie nested layout:

./corpus/<run_id>/
  manifest.json                    # run metadata + per-game rows
  c4d/game_NNN.c4d                 # compact 4D move notation
  ndjson/game_NNN.ndjson           # per-ply pos4 snapshots + moves
  spectralz/game_NNN.spectralz     # 45 056-dim per-ply encoding (optional)

<run_id> is auto-minted as corpus_YYYYMMDD_HHMMSS_seedN (or ..._unseeded) and can be overridden with --run-id. Generation is two-pass: the playout pass writes c4d + NDJSON unconditionally, then an optional encoding pass reads the NDJSON and produces spectralz frames with absolute ply numbers.

# default: full-game spectralz for every ply
chess4d-corpus-gen --n-games 10 --seed 42 --output ./corpus

# only encode the final 30 plies per game (c4d + NDJSON still full)
chess4d-corpus-gen --n-games 1 --max-plies 500 --encode-last 30

# playout only — c4d + NDJSON, no spectralz, no [spectral] extra needed
chess4d-corpus-gen --n-games 10 --seed 42 --no-encode

# reproducible named run
chess4d-corpus-gen --n-games 10 --seed 42 --run-id fixed-corpus-v1

Retro-encoding an existing corpus

Because encoding reads from the NDJSON sidecar, you can turn a --no-encode corpus into a spectralz corpus at any point without replaying the games:

# encode every ply of every game in an existing run
chess4d-corpus-encode ./corpus/corpus_20260419_180342_seed42

# tail-only: encode just the final 30 plies of each game
chess4d-corpus-encode ./corpus/corpus_20260419_180342_seed42 --last-n 30

The standalone CLI is driven entirely by NDJSON and updates manifest.json in place. For a given (seed, last_n), the retro-encoded spectralz bytes are identical to those produced by chess4d-corpus-gen --encode-last N on the same inputs.

The NDJSON schema is chess4d-ndjson-v1: line 1 is the format header, line 2 is a game_header record with termination / ply count / seed, and subsequent lines carry per-ply records with the applied move, side_to_move, and a full pos4 dict (2-char pawn values Pw/Py/pw/py, 1-char non-pawns, keyed by linear square index (x<<9) | (y<<6) | (z<<3) | w).

Development

pip install -e .[dev]
pytest -v
mypy --strict src/chess4d
ruff check src tests

License

Unlicense (public domain). See LICENSE.