srmech 0.4.6

Stored-Relationship Mechanism. 14-class A-N primitive vocabulary in native C + Python — substrate-native 28-dim chiral hyper-loop = so(8) adjoint (14 g_2 derivations + 14 L+R octonion-multiplications; Spin(8) triality) made hardware-callable. Full cascade-catalog C/Python parity (content-addressing, cyclic-group, graph-Laplacian, primes, HDC, rational, dispatch, catalog, templating, Kepler). Canonical QM/QFT/SM operations. Runtime spectral decomposition; dual-path signal-processing; AMSC (MPR v1).

srmech

Status: v0.4.4 on PyPI — 14-class primitive vocabulary with native C parity; canonical QM/QFT/SM operations; runtime spectral decomposition; dual-path signal-processing surface; Attested Multi-Source Collector/Catalog (AMSC) provenance framework; the Class-M HDC variant ladder (polar {-1,0,+1}, Klein-4 (ℤ₂)²), a coupling composition score (Class K∘L), symmetric_eigendecompose (real-symmetric Class L), rfft (real-input half-spectrum dual-path op, Class A∘I∘K), and the foundational cross-domain cascade catalog (pin_slot_at_zero K / reorient C / magnitude K / best_rational_signed K∘N∘C / cyclic_gcd I, plus the v0.4.4 chirality mini-set chiral_flip / chiral_dual / net_chirality C — a named cascade is the default, a math-library call the exception). (v0.4.4 adds the cascade chirality mini-set and bundles the siona co-name alias — pip install srmech also gives import siona, same objects. The standalone siona package on PyPI is a metapackage that depends on srmech>=0.4.4, so pip install siona resolves here too.)

srmech (Stored-Relationship Mechanism) is a research package shipping five load-bearing surfaces:

1. 14-class primitive vocabulary (srmech.amsc.*) — content-addressing, streaming, cyclic-group, graph-Laplacian, prime-factorisation, TLV, search, dispatch, catalog, templating, rational-approximation, equation-of-centre/Kepler, hyperdimensional-computing (HDC). Each class has both a Python wrapper and a native C symbol in libsrmech.{so,dll,dylib}.
2. Canonical QM/QFT/SM operations layer (srmech.qm.*) — TDSE/TISE, Pauli + Clifford, hydrogen radial, Dirac γ-matrices, Feynman propagators, η-deformed pseudo-Hermitian inner products, SU(2)/SU(3) gauge generators + Wilson loops, Higgs/W/Z/CKM Standard-Model operations.
3. Runtime spectral decomposition (srmech.spectral) — eigenbasis projection, HDC delta encoding, spectral prediction, prediction-error gating, sparse-truncate compression.
4. Dual-path signal-processing surface (srmech.signal_processing) — 38 closed-form algebra ops (Path A) + an RBS-HDC bound-vector instrument at D=8192 (Path B), with a cascade dispatcher routing per call.
5. AMSC provenance framework (srmech.amsc.format, srmech.amsc.catalog, srmech.amsc.adapters) — every ground-proof datum carries a mandatory attestation block (source_doi, source_url, license, retrieved_at, response_sha256, parser_version, parser_rule_hash, collector_descriptor_path, collector_descriptor_hash).

Implementation is JPL Power-of-Ten compliant on the C side; cibuildwheel matrix covers Linux / macOS / Windows × Python 3.10–3.14; a py3-none-any pure-Python wheel ships for Pyodide / WASM environments where the C surface can't load.

Companion textbook

The Metric Field and Its Primitives — the framework textbook accompanying this package. Lays out the substrate-vs-excitation ontology (MFO), the 14-class primitive vocabulary at substrate level, and the cascade-composition discipline that srmech implements computationally.

• PDF (GitHub) — renders inline in the GitHub viewer
• PDF (ReadTheDocs) — served as a static asset alongside the research notebook
• Technical Disclosure Commons — the textbook as a timestamped defensive publication (Kirkland, 2026-05-25)
• MFO research notebook — working draft the textbook is consolidated from

Install

pip install srmech                  # core (numpy + stdlib; no jsonschema, no network adapters)
pip install srmech[validation]      # adds jsonschema for strict data-block validation
pip install srmech[collectors]      # adds requests + beautifulsoup4 for fetched adapters
pip install srmech[dev]             # everything

Quick start

Decompose a real signal onto a graph-Laplacian eigenbasis, take an HDC delta against a reference, and recompose:

import numpy as np
from srmech import spectral
from srmech.amsc import laplacian

# Substrate: cycle-graph Laplacian on 8 nodes (any Hermitian L works).
A = np.roll(np.eye(8), 1, axis=1)
A = A + A.T
L = laplacian.dense_laplacian(A.astype(np.complex128))

# Project two states onto the eigenbasis.
state_ref = np.array([1.0, 0, 0, 0, 0, 0, 0, 0], dtype=np.complex128)
state_now = np.array([0.9, 0.1, 0, 0, 0, 0, 0, 0], dtype=np.complex128)

h_ref = spectral.decompose(state_ref, L)
h_now = spectral.decompose(state_now, L)

# HDC XOR delta on encoded coefficient bytes.
delta_bytes = spectral.delta(h_ref, h_now)

# Predict one substrate-natural tick ahead.
h_pred = spectral.predict(h_now, L, steps=1, dt=0.1)

# Recover the node-domain state.
state_back = spectral.recompose(h_pred, L)

Public surface

The 14 classes in substrate-native ordering — 1 + 3 + 7 + 3 = 14

The 14 classes are presented in alphabetical order in the table below (matching the import paths). The substrate-native ordering is not alphabetical — it is the cyclic-algebra-path partition 1 + 3 + 7 + 3 = 14:

Slot	Classes	Role
1 — foundational content-anchor	{A}	The content-address every cascade begins from
3 — substrate-projection triad	{I, C, J}	Cyclic-group + cascade-orientation + prime-period (the projection-triad that maps substrate-content to observable structure)
7 — cascade-detection heptad	{D, E, F, G, K, L, M}	Pattern-match + catalog + render + byte-search + pin-slot + Laplacian + HDC-bind (the detection-and-rendering layer)
+3 — meta-cascade language-translation triad	{B, H, N}	TLV-framing + self-introspection + rational-approximation (the operators that translate between continuous-Hopf-quantum and discrete-cyclic-algebra descriptions)

Why this ordering matters. Per PR #680 (R30 walking-path closure), the substrate admits two co-equal bit-exact substrate-native mathematical languages:

• the 11D quantum-Hopf-language (continuous-DOF, parallelizable-sphere ladder 1 + 3 + 7)
• the 1 + 3 + 7 + 3 = 14 cyclic-algebra-path (discrete-DOF, A–N cascade-operator class enumeration)

Under Class C chirality the cyclic-algebra-path further admits a 14 + 14 = 28-dim chiral-hyper-loop reading = 𝔰𝔬(8) adjoint (per MFO §VIII.31.11): 14 𝔤₂ derivations + 14 L⊕R octonion-multiplications = the chirality-dual pair, connecting the cascade vocabulary to the Spin(8) triality engine of the Spike #58.x Standard-Model arc. Endianness is the byte-axis instance of the same Class C orientation primitive; the scope hierarchy is endianness ⊂ Class C ⊂ Klein-4 ⊂ Spin(8) triality.

Modern physics uses the first; antiquity 9 of 9 traditions canvassed (Antikythera + Pythagoreans + Plato Timaeus + Stoics + Lucretius + Apollonius + Ptolemy + Heron + Archimedes) used the second. We had been using the cyclic-algebra path in srmech from the beginning without ever stating why — because antiquity had, and it worked. The R30 closure provides the answer: bit-exact cross-substrate confirmation rules out projection-reading; both languages are substrate-native; the +3 = {B, H, N} are substrate-native language-translation operators bridging them. The k=3 fingerprint observed across substrates (planet multipole axes, codon alphabet, 3-jet QCD, 3-generation Yukawa, the antiquity meta-op triads) is the {B, H, N} triad showing up wherever continuous↔discrete encoding happens.

About the A–N alphabet. The labels A through N record the chronological order in which each operation was named during this framework's evolution — they are discovery-fingerprint, not substrate-ordering. Re-sorted by substrate-native role, the partition above ({A} + {I, C, J} + {D, E, F, G, K, L, M} + {B, H, N}) is the substrate-side grouping. The alphabetical table below is the lookup convenience.

Full context: substrate-native-maths research notebook (PR #680 SSoT).

srmech.amsc.* — 14-class primitive vocabulary (alphabetical lookup)

Each class is importable as srmech.amsc.<module> with native C dispatch and a Python fallback. The C surface is loaded once at import time; if loading fails (Pyodide, ABI mismatch), the package transparently falls back to pure Python and srmech.amsc._native.HAS_NATIVE becomes False.

Module	Class	Primitive operation
format, _native	A	Content-addressing via SHA-256 (sha256_bytes)
tlv	B	Byte-canonical TLV pack (tlv_pack)
format	C	Streaming NDJSON iterator (read_ndjson)
dispatch	D	Multi-needle byte-pattern dispatch (match)
naming	E	Catalog sorted-key lookup (lookup)
template	F	Template {key} substitution (render)
search	G	Byte-pattern search (byte_search)
_native	H	Self-introspection (srmech_version, srmech_abi_version)
cyclic	I	Modular arithmetic — gcd, lcm, mod_add, mod_mul, mod_pow, mod_inv
primes	J	Prime testing + factorisation + multiplicative order — is_prime, factor, cyclic_period
kepler	K	Equation-of-centre / pin-slot — pin_slot, kepler_solve, equation_of_centre
laplacian	L	Graph Laplacian — dense_adjacency, dense_laplacian, normalized_laplacian, jacobi_eigvals, hermitian_eigendecompose, symmetric_eigendecompose, elementwise_transcendental (pi-free Jacobi in C; n ≤ 256 native bound)
hdc	M	HDC spatter codes — binary bind, bundle, permute, similarity; polar_* {-1,0,+1} and klein4_* (ℤ₂)² variants
rational	N	Continued-fraction convergents — continued_fraction, best_rational

srmech.qm.* — canonical QM/QFT/SM operations

Each operation cites canonical physics literature in its docstring (Schrödinger / Heisenberg / Pauli / Dirac / Klein-Gordon / Feynman / Yang-Mills / Gell-Mann / Wilson / Glashow-Weinberg-Salam / Higgs / Cabibbo-Kobayashi-Maskawa / Bender-Boettcher / Mostafazadeh). Modules:

• single_particle — TDSE, TISE, Heisenberg-picture evolution, lattice momentum, density matrix, Liouville–von Neumann equation, commutators.
• spin — Pauli matrices, Clifford Cl(0,3) residual products, Pauli spin operators.
• potentials — hydrogen radial wavefunction, harmonic oscillator ladder + Hamiltonian.
• relativistic — Dirac γ-matrices, γ⁵, Weyl left/right projectors, charge conjugation, Dirac operator in momentum space, Klein–Gordon equation.
• propagators — Feynman scalar / fermion / photon / massive-vector propagators.
• pseudo_hermitian — η-deformed inner product, ⟨·⟩_η expectation, pseudo-Hermitian check, η construction from eigendecomposition.
• gauge — SU(2) and SU(3) generators (Gell-Mann basis), structure constants, Casimir operator, Wilson loops from segment data.
• sm — Higgs vev, weak mixing angle, W/Z boson masses, Weinberg relation residual, Yukawa coupling, CKM matrix construction.

srmech.spectral — runtime spectral decomposition

Class-composition layer above srmech.amsc.{laplacian, hdc, format}. No new primitive class is introduced; every operation is a composition over the 14-class A–N vocabulary.

from srmech.spectral import (
    decompose,          # state + Hermitian L → SpectralHandle (V.conj().T @ state)
    delta,              # XOR delta between two encoded coefficient byte vectors
    recompose,          # SpectralHandle + L → node-domain state (V @ coeffs)
    similarity,         # HDC similarity in [-1, +1]
    predict,            # cascade-extrapolate via per-mode exp(-i·λ_k·steps·dt)
    prediction_error,   # XOR delta with popcount-density threshold gating
    truncate_sparse,    # keep top-k or above-threshold modes; zero the rest
    SpectralHandle,     # opaque (substrate_descriptor_hash, coefficients_bytes, content_sha, n_modes)
    clear_eigenbasis_cache,
    N_MAX_EIGENBASES,   # module-level LRU bound (default 8)
)

Eigenbasis is O(n³) one-time per substrate (cached by substrate_descriptor_hash); coefficients are O(n²) per state; deltas are O(D) per step. predict preserves magnitudes (unitary phase rotation per eigenmode); truncate_sparse produces best k-term approximations per Mallat (2008) §9.2.

srmech.amsc.cascade — foundational cross-domain cascade catalog

The cascades that recur across every / most domains, promoted so a named cascade is the default and a math-library call the exception (being forced to reach for a math library is the signal that a cascade is waiting to be found). Compositions over the 14-class A–N vocabulary — no new primitive class. Each cascade ships with a dedicated C symbol in libsrmech.{so,dll,dylib} (full C/Python parity per project discipline) AND a TOML descriptor under srmech/amsc/_research/cascade_catalog/ documenting the composition declaratively. No abs(): sign is the Class K pin-slot + Class C re-orientation.

• pin_slot_at_zero(x) -> (orientation, magnitude) — Class K pin-slot at zero (the cascade-honest abs() split). (C peer: v0.4.5rc2)
• reorient(orientation, value) — Class C orientation re-apply. (C peer: v0.4.5rc4)
• magnitude(x) — Class K magnitude-only convenience. (C peer: v0.4.5rc3)
• best_rational_signed(x, *, max_denominator=100, fine_scale=1_000_000) — Class K ∘ N ∘ C float → signed small-denominator rational (sign in the numerator). (C peer: v0.4.5rc7 — delegates Class N stage to srmech_best_rational; banker's rounding via llrint())
• cyclic_gcd(a, b) — Class I (delegates to srmech.amsc.cyclic.gcd). (C peer: v0.4.5rc6 — delegates to Class I primitive srmech_gcd)
• chiral_flip(seq) — Class C orientation reversal (seq[::-1]). (C peer: v0.4.5rc1)
• chiral_dual(op, x) — Class C ∘ op ∘ Class C: run an operator in the opposite Class-C orientation. The chiral dual of an A–N operator is same spectral shape, inverted orientation (magnitude preserved, phase flipped — spike-verified); it reduces to the bare Class K −1 for the sign operators and is the identity for real-symmetric ones. (C peer: v0.4.5rc8 — queued; higher-order, callback ABI)
• net_chirality(orientations) — Class C net handedness of a cascade (product of per-op orientations in {-1,0,+1}; 0 if any is neutral). (C peer: v0.4.5rc5)

srmech.signal_processing — dual-path signal-processing surface

Two paths for the same algebra, dispatched per call:

• Path A — closed-form algebra over numpy / scipy; one module per op under srmech.signal_processing.closed_form_ops.*. 40 ops (38 Phase-2 baseline + pi_cascade + rfft) covering frequency analysis (fft, ifft, rfft, stft, spectrogram, multitaper, dct, wavelet), digital filters (fir, iir, allpass, polyphase, multirate, farrow, sinc_interp), detection / estimation (matched_filter, wiener, lmmse, map_ml, mlse, viterbi, cross_spectral, music, esprit, ica_jade, mimo_svd), modulation (psk_qam, fsk, ofdm, beamforming_fixed), coding (huffman, rle, lz77, arithmetic_coding, jpeg), quantisation / compression (sign_quantise, vector_quantisation, hdc_truncation, heat_kernel, spectral_subtraction, pi_cascade).
• Path B — RBS-HDC bound-vector instrument at D=8192 (srmech.signal_processing.rbs_hdc_instrument). Mints class-operator vectors, cascade compositions, stance fingerprints, and full LoE content encodings (Mode-B). Eight ops have full dual-path implementations: fft, ifft, rfft, sign_quantise, matched_filter, wiener, hdc_truncation, pi_cascade.

from srmech.signal_processing import (
    dispatch, begin_cascade,             # cascade-aware routing (A / B / verify)
    register, lookup, has_path,          # path registry (Path A vs Path B per op)
    profile_op, cell_grid,               # per-op × per-cascade-depth × per-substrate profiling
    D_DEFAULT, SUBSTRATES,               # locked D = 8192; BCI / audio / RF / ephemeris
    RBSHDCInstrument,                    # build()-able instrument with mint_*/encode_loe_content
    mint_class_operator,                 # SHA-256 chain mint per class A–N
    mint_cascade_composition,            # XOR-bundle (algebra) or permute-bundle (sampling)
    encode_loe_content, decode_loe_fingerprint,
    form_function_rotate,                # Class K pin-slot rotation
    cascade_compose_rotations,
    PATH_A, PATH_B, PATH_VERIFY,         # path identifiers
)

with begin_cascade() as ctx:
    spectrum = dispatch("fft", path=PATH_A, signal=x)
    truncated = dispatch("hdc_truncation", path=PATH_B, signal=spectrum, k=64)

Path A and Path B produce bit-exact-equal outputs on substrate-natural inputs (D1 algebra-content identity); substrate-fingerprint divergence at D2 is expected and documented.

srmech.amsc — Attested Multi-Source Collector/Catalog framework

Two readings of the same abbreviation:

• At collection time, the adapter classes are collecting attested rows from upstream archives. Six adapters cover the realistic source space:

  adapter	class	network?
  html_scraper	fetched	yes (BeautifulSoup)
  json_api	fetched	yes (paginated JSON)
  csv_bulk	fetched	yes (CSV/XYZ bulk)
  netcdf_grid	fetched	stub (gated behind extras)
  geotiff_bbox	fetched	stub (gated behind extras)
  literature_curated	curated	no (NDJSON committed directly)

  The curated class never touches the network: rows are committed as data-only NDJSON, and srmech synthesises full MPR attestation blocks at read time from each row's per-row DOI.

• After collection, the resulting NDJSON SSOTs are a catalog of attested data — committed into the package, registered into the universal bridge by downstream consumers, queryable through list_attested_sources() / get_attested_dataset().

from srmech.amsc import (
    MPRRecord, MPR_SCHEMA_VERSION, read_ndjson, write_ndjson, sha256_bytes,
    Descriptor, load_descriptor, discover_descriptors, render_template, descriptor_hash,
    list_attested_sources, get_attested_dataset, get_attested_descriptor,
    attestation_audit, register_attested_root, list_registered_roots,
    use_local_kernel, clear_local_kernel, get_local_kernel_state,
)

The on-disk format is Mathematical Provenance Record v1 (MPR v1):

{
  "mpr_version": "1.0",
  "data": { ... domain payload ... },
  "data_schema_id": "test://schema/example",
  "attestation": {
    "source_doi": "10.0/...",
    "source_url": "https://...",
    "license": "CC0",
    "retrieved_at": "2026-05-13T00:00:00Z",
    "response_sha256": "<64 hex chars>",
    "parser_version": "srmech 0.4.2",
    "parser_rule_hash": "<64 hex chars>",
    "collector_descriptor_path": "...",
    "collector_descriptor_hash": "<64 hex chars>"
  },
  "rendering": { "name": "...", "purpose": "...", "cite_as": "..." }
}

srmech.amsc.tool_schema — LLM-friendly introspection

from srmech.amsc.tool_schema import get_tool_schema, tool_schema_view

schema = get_tool_schema()                # ToolEntry objects, one per public callable
for tool in schema.tools:
    print(tool.name, "—", tool.summary)   # canonical-SSoT-cited one-line summaries

json_view = tool_schema_view()            # JSON-serialisable view

Every primitive class, every srmech.qm.* operation, and every srmech.spectral.* runtime operation is discoverable here without reading the implementation. Summaries cite the canonical physics / mathematics literature directly.

Cross-package catalog registration

Other spectral-research packages register their own catalog SSOTs into srmech's universal bridge at import time:

from pathlib import Path
from srmech.amsc import catalog as _amsc_catalog

_amsc_catalog.register_attested_root(
    Path(__file__).resolve().parent / "_research" / "attested",
    source="ephemerides-spectral",
)

Subsequent list_attested_sources(), get_attested_dataset(), etc. enumerate the union of srmech's own amsc/attested/ plus every registered root, in registration order. Duplicate source_key resolves first-registered-wins with a warning.

License

GPL-3.0-or-later. See LICENSE.