Carrier-ratchet → 0 roadmap (#564) — workflow-generated, ground-truthed against source¶

Status: head = v0.7.5rc113 (rbs_lm flipped, CEIL_NUMPY_CARRIER = 15). Target = 0. Generated by the carrier-ratchet-to-zero workflow (run wf_e69d32fa-8fe, 2026-06-11): 15 parallel per-file investigation agents + a synthesizer, ground-truthed against the actual srmech source.

The load-bearing CORRECTION (every per-file spec got this wrong)¶

The specs assumed dense_matmul_complex / dense_norm / dense_dot_real/_complex are "already numpy-free, just drop the top import." FALSE — those helpers call np.ascontiguousarray / np.sum / np.zeros internally and RAISE numpy-absent (the rc70 runnable ≠ loadable trap). The ONLY genuinely numpy-free 2-D kernels are the mat_* family over Mat (mat_matmul / mat_solve / mat_hermitian_eigendecompose / mat_eigvals / mat_svd / mat_lstsq). Every consumer flip routes through mat_*, NOT dense_*.

Other corrections: - potentials.py was the OMITTED 15^th carrier (hydrogen radial + harmonic-oscillator; calls hermitian_eigendecompose). Same numpy-as-ACCURACY shape as ica_jade. Handled in rc119. - Both "stays-gated" specs (ica_jade + potentials) are WRONG vs "want ZERO": mat_hermitian_eigendecompose is unconditionally numpy-free (native Jacobi C + _hermitian_eig_py fallback), so the eigh dependency is a CARRIER swap, not a floor. - so8 has DUAL numpy use — (a) rank assertions (matrix_rank) → exact RREF over ℚ (rc120, mathematically identical, no float-tol drift); (b) float SVD-nullspace / Gram-Schmidt geometry → carrier-swap to mat_svd + mat_norm, NOT exact-RREF (per [[feedback_cascade_svd_nullspace_accuracy_not_route_matrix_rank]]). Keep nullspace on float mat_svd. - No mat_norm/mat_dot exists (dense_norm/dot are carriers) → rc114 foundation. - No exact RREF/rank helper exists (matrix_cascades has char_poly/eigvals_exact, no rank) → rc120. - hdc.loop_left/right/conj use _lazy_numpy (np.asarray/np.ascontiguousarray) → raise numpy-absent → rc121 foundation before octonion→so8→triality.

Discipline (every rc)¶

Bump version at 5 SSOT locations incl. the scaffolding pin BEFORE running the suite ([[feedback_srmech_version_bump_hits_five_locations_run_suite_after]]).
Verify "runs numpy-GENUINELY-absent" via the _BLOCK_NUMPY meta-path subprocess (test_signal_processing_numpy_free_reachable_rc71 pattern), NOT monkeypatch sys.modules['numpy']=None (which only proves runtime-math-free, not fresh-import-free — [[feedback_carrier_ratchet_misses_require_numpy_subpackage_gates]]).
qm matrix layer → TOML [class] (rc75 Hurwitz precedent): EXTEND class_catalog/, reuse make_class, NO per-module carrier flips for the [class] ops, NO duplicate coupling codepath, NO duplicated loader. (spin/relativistic/sm/single_particle are factory-style operator builders, NOT [class] objects → they flip onto Mat directly, consistent with "group sensibly".)
No bare abs() (Class-K sign-branch). No new hashlib.sha256 (route amsc.format.sha256_bytes).
Mat.to_numpy/HV.to_numpy stay LOSSY export-convenience only; numpy = test-oracle + opt-in bridge.
Each rc: flip → 5-file bump → full suite → PR → 8-job CI → --merge (no squash) → tag at 2-parent merge → TestPyPI → clean numpy-absent verify. git add docs/srmech/ ONLY (never -A).

The 15-rc order (rc114 → rc128)¶

rc	files	CEIL	difficulty	foundation_first
rc114	`amsc/laplacian.py`+`amsc/mat.py`: mat_norm / mat_dot_real / mat_dot_complex (Σ	xᵢ	² via `rational.sqrt`, pure-Python reduction, no abs)	15→15
rc115	`qm/spin.py` (Mat Pauli) + `qm/bell.py` (exact `eigvals_exact`)	15→13	moderate	rc114
rc116	`qm/single_particle.py` + `qm/sm.py` (Mat carrier-construction; maybe `Mat.identity`/`Mat.diag`)	13→11	moderate	rc114
rc117	`qm/relativistic.py` (Dirac γ exact Mat; γ from spin's σ)	11→10	mechanical	rc114, rc115
rc118	`qm/gauge.py` → TOML [class] `su2_gellmann.toml`+`su3_gellmann.toml` (template for later reframes)	10→9	design-heavy	rc114
rc119	`qm/potentials.py` (15^th) + `ica_jade.py` → `mat_hermitian_eigendecompose`; flip rc71 assert to "runs". SPLIT ica_jade→rc119b if einsum-Jacobi too heavy	9→7	design-heavy	rc114
rc120	`amsc/cascade/matrix_cascades.py`: exact RREF-rank over ℚ (`mat_rank_exact`)	7→7	moderate	— (FOUNDATION, gates so8 rank)
rc121	`amsc/hdc.py`/cascade: numpy-free octonion mult (native ctypes fed stdlib array + int8-table fallback off `cd_basis_product`)	7→7	design-heavy	— (FOUNDATION, gates octonion→so8→triality)
rc122	`qm/octonion.py` (exact int8 table bytearray + numpy-free mult/conj/norm)	7→6	moderate	rc121, rc114
rc123	`qm/so8.py` (exact-RREF rank assertions + Mat/`mat_svd` nullspace geometry — DUAL fix)	6→5	design-heavy	rc120, rc121/122, rc114
rc124	`qm/triality.py` (Mat + `mat_lstsq` companion fit; einsum→`mat_matmul`/loops)	5→4	design-heavy	rc122, rc123, rc114
rc125	`qm/pseudo_hermitian.py` (non-Hermitian eigvals via `mat_eigvals`; Gram solve via `mat_solve`)	4→3	design-heavy	rc114
rc126	`qm/propagators.py` → TOML [class] (reuse rc118 loader; D@S=iI_4 via `mat_matmul`)	3→2	design-heavy	rc115, rc117, rc118, rc114
rc127	`spectral/__init__.py` (HV/list coeff carrier + struct-pack; `np.argsort`→pure-Python stable sort; `mat_hermitian_eigendecompose`)	2→1	moderate	rc114
rc128	`mcp/_coercion.py` CAPSTONE (boundary dual-path; lazy-numpy only behind ndarray back-compat) → flip `CEIL_NUMPY_CARRIER` 1→0 + numpy-absent fresh-import asserts for whole qm/spectral/mcp surface + audit eager `_require_numpy` gates	1→0	design-heavy	ALL rc115–rc127

Spine (must land first; if one slips, its consumers can't flip)¶

rc114 mat_norm/mat_dot → gates nearly every consumer
rc120 exact RREF rank → gates so8
rc121 numpy-free octonion mult → gates octonion→so8→triality (strict chain rc121→122→123→124)

Design-heavy (do NOT rush; split if a verify wobbles)¶

rc118 (first TOML reframe — sets the template), rc119 (einsum Jacobi re-expression), rc121 (native feeding + int8 fallback), rc123 (deepest float coupling, dual rank/nullspace), rc124 (mat_lstsq), rc125 (general non-Hermitian eigvals), rc126 (second TOML reframe — reuse not duplicate), rc128 (capstone).