logo-maths — HDC split-object pattern applied to LOGO¶

Python research spike that generalizes the chess-spectral split-object-with-fiber-matrix pattern to a new domain. See logo_research_notebook.md for the full experimental log and ../../docs/chess-maths/chess_spectral_research_notebook.md for the pattern's original write-up.

Iteration 2 added (2026-04-14): self-containment, F₁ HDC retrieval fix (45% → 91% top-1), fiber-as-transport-map experiments (L6a–e), three-body topology (L6f–h), and a retraction of iteration-1's L1 "reversibility via single-vector flip" claim.

Iteration 3 added (2026-04-14): held-out generalization (L7a, 4/4 PASS — L6d's D4 character claim survives the memorization gate) and partial-trace fibers (L7b, ⅕ PASS — fibers drift with trace length but do NOT extrapolate forward; snapshot baseline beats fiber-prediction by 0.855 cos on spiral_square). The trajectory hypothesis for chess needs reformulating before porting.

Layout¶

logo_ast.py               AST node dataclasses + walk()
logo_parser.py            tokenizer + recursive-descent parser
logo_interp.py            tree-walk interpreter → Trace + rule firings
logo_irrep.py             D4 irrep projection (8 perms + char table) — self-contained
logo_hdc/
    hd.py                 MAP-B primitives (atom, bind, bundle_sum, sim, ...)
    quantum_atoms.py      Part A: command atoms + role-level unbind/swap
    codebook.py           Part B: structured rule HVs
    split.py              SplitObject (left + right + fiber)
    fiber.py              build_fiber_matrix, svd_report, fiber_to_hdc
                          (fiber_to_hdc has per-row L1 normalization, default on)
logo_encode_vocab.py      Part A encoder: program → vocab_lex/vocab_ctx HVs
logo_encode_syntax.py     Part B encoder: program → syn_lex/syn_ctx HVs
logo_encode_geometry.py   Part C encoder: trace → 320-dim D4-irrep HV
logo_corpus.py            21 hand-curated LOGO programs by family/symmetry
logo_build_splits.py      Corpus → F₁ coincidence stream
logo_fiber2.py            Syntax × geometry fiber; value-enriched features
logo_transport.py         Fiber-as-transport-map experiments + 3-body topology
logo_csv_export.py        Per-program CSV emitter (now with transport columns)
logo_py.py                CLI (parse / trace / encode / fiber1 / fiber2 / transport / csv)
samples/                  Generated artifacts (CSV, etc.)

CLI quick-ref¶

python logo_py.py parse      square        # dump the AST
python logo_py.py trace      square        # turtle trace JSON
python logo_py.py encode     square        # channel-energy summary
python logo_py.py fiber1                   # F₁ SVD + per-row-normalized HDC retrieval
python logo_py.py fiber2                   # F₂ SVD + per-program self-sim
python logo_py.py transport                # polygon-pair transport table (default)
python logo_py.py transport --chain        # vocab → syntax → geometry chain
python logo_py.py transport --characterize # per-feature transport(N) D4 split
python logo_py.py transport --modes        # per-SVD-mode attribution
python logo_py.py transport --topology     # chain-collapse, holonomy, chirality
python logo_py.py transport --holdout pentagon,octagon    # L7a: rebuild fiber without those programs
python logo_py.py transport --partial 30,60               # L7b: fiber at N=30 predicting g at N=60
python logo_py.py transport --drift 10,60                 # L7b: fiber drift between anchors
python logo_py.py transport --spiral-extrapolate 10,60    # L7b.5: fiber vs snapshot baseline
python logo_py.py csv -o samples/corpus.csv

src args accept a filesystem path, a corpus entry name, or - for stdin. The transport flags can be combined; --pairs accepts a custom a,b;c,d list.

Predictions tested¶

Phase	Prediction	Outcome
L1 (iter 1)	`bind(a_FORWARD, flip) ≈ a_BACK` after cleanup	✗ RETRACTED — measured cos −0.004 vs BACK; replaced with role-level `unbind_role` / `swap_role_value` (cos 1.0 exact for the swap)
L2	Part A and Part B independently inferable	✓ ≥ 80% cleanup on both
L3	F₁ rank 3-4, interpretable modes, nullspace = inert rules	✓ rank 7 (exceeded), modes semantic, nullspace correct
L3 (iter 2)	F₁ HDC retrieval recovers low-energy couplings	✓ 5/11 → 10/11 with per-row L1 normalization
L4	F₂ surfaces program output symmetry	✓ in subdominant modes (after DC-mode deflation)
L4	Polygon D4-irrep decomposition matches theory	✓ pure A1 for Dₙ with n multiple of 4, A1+E split for D3/D5
L6a (iter 2)	cos(Δg_pred_deflated, Δg_actual) > 0.30 for adjacent polygons	✓ 6/6 pairs (worst 0.473)
L6b (iter 2)	deflated transport ≥ raw transport for ≥ 4/6 pairs	✓ 4/6
L6c (iter 2)	chain transport cos > 0.10 (square → spiral_square)	✓ 0.516
L6d (iter 2)	transport(N) qualitatively recovers D4 character class	✓ for 4/12/5/3; messier for 8 and 6 (small-corpus artefact)
L6e (iter 2)	modes 4-7 carry > 80% of polygon transport energy	✗ MISS — 47-60% across pairs; signal spread across modes 1, 3, 6, 7, 8
L6f (iter 2)	chain collapse: cos ≈ 0.95 narrow → 0.99 wide	≈ 0.99 / 0.99; rules already saturate the mediation budget at this corpus size
L6g (iter 2)	cycle holonomy cos ≈ 0.93, ‖Δ‖ ≈ 0.37	✓ 0.942 / 0.340 (rank-1 cycle SVD: s_1/s_0 ≈ 0)
L6h (iter 2)	small chirality commutator (corpus-bias caveat)	0.082 — near-symmetric with small chiral signal
L7a.1 (iter 3)	`transport(5)` A1+E share drifts ≤ 20pp under holdout(pentagon,octagon)	✓ 0.1pp (86% → 85%)
L7a.2 (iter 3)	`transport(8)` A1 fraction ≥ 50% under holdout	✓ 69.7% (actually grows from 60%)
L7a.3 (iter 3)	`\|transport(5/8)\|` norms don't collapse (≥ 30% of full)	✓ 0.727 / 1.077
L7a.4 (iter 3)	Pair cos under held-out fiber > 0.25	✓ triangle→pentagon +0.568
L7b.1 (iter 3)	Polygon mean cos(pred, target) > 0.40 at (30, 60)	✗ +0.307
L7b.2 (iter 3)	Spiral mean cos(pred, target) > 0.20 at (30, 60)	✗ +0.085
L7b.3 (iter 3)	Fiber drift `‖M_l − M_e‖_F / ‖M_e‖_F` > 0.10 between N=10 and N=60	✓ 0.250
L7b.4 (iter 3)	Spiral-marker features (MAKE, repeat_n=60) dominate top-5 drift	✗ generic structural rules dominate
L7b.5 (iter 3)	spiral_square: fiber-pred beats snapshot baseline by > 0.10	✗ gain = −0.855 (fiber actively worse than "use earlier snapshot")

Dependencies¶

numpy. That's it. The spike is fully self-contained — no sibling-package imports, no sys.path manipulation. The D4 projection lives in logo_irrep.py.