README.md

TNFR spectral factorization lab — archived

Reference only; not maintained or part of the current application workflow. The source and historical outputs remain at their original paths to preserve uncommitted changes and recorded path associations. The retirement record identifies retained source, recovery revisions, retired integration tests and concrete counterexamples.

This pipeline combines supplied Jacobi-residue graphs, spectral heuristics, arithmetic statistics and partition workflows. Its acceptance and completeness labels are not reliable factor certificates. It establishes neither autonomous factor recovery from the nodal equation nor a complexity improvement or a cryptographic capability. This page records the archived implementation's scope; it is not an installation or execution recommendation.

The maintained arithmetic utility and number-theory owner retain exact arithmetic and independently proved residue-graph results. The Paley, CRT and cyclotomy constructions have their own hypotheses; sharing a graph operator does not validate this application's candidate pipeline.

Results and verification

The retirement is based on implementation counterexamples, not only a change of research priority:

• The structural verifier can accept candidate 6 for target 35 while its own support_divisible field is false.
• An integer size_hint can enable an exception to the stabilization condition.
• A composite signature for 35 with candidates [5, 7, 11] can report completeness although their product is 385.
• Both modes compute arithmetic telemetry by factoring the input. Integer-size candidates, divisibility checks and trial-division fallback remain involved; a spectral result does not isolate the source of factor information.

Archived result	Actual boundary
candidate_factors	Heuristic seeds, arithmetic refinements and partition hints; neither complete nor necessarily prime
tnfr_certified_factors, tnfr_verification	Configured acceptance scores with a separate divisibility observation; the acceptance rule need not require divisibility
factor_signature, composite_signature	Serialized records; hashes check recorded content, not the truth of powers or completeness
certificate_path, partition paths	Analysis/workflow records; a proposed word is not an executed operator trace

Independent proper-divisor, primality, product and multiplicity checks are necessary before interpreting any historical factor list. Passing them would not show that recovery came from a TNFR mechanism.

Setup and public interfaces

The engine no longer adds this directory to its import path. The deprecated tnfr.factorization.factorize, TNFR.factorize and Network.factorize interfaces remain compatibility bridges for a separately supplied legacy tnfr_factorization package. Missing or archived-checkout implementations produce retirement guidance; an external implementation produces a deprecation warning. Keeping these names does not maintain or certify the archived lab. See the API migration.

Generic manifest preparation, dry-run assessment and report validation remain engine responsibilities. They do not bootstrap this lab, reconstruct a residue graph from a modulus, or apply a proposed operator word implicitly.

The retained source owners are the lab API, candidate pipeline, partition planner, seed handling and snapshot records. Their original CLI and helper files are historical source, not supported entry points. The lab has no separate setup.py or pyproject.toml.

Candidate policy and configuration

Historical pure=True changes a process-wide environment policy for the call. It skips arithmetic-statistic hints and gcd refinement in the initial candidate stage, but does not make the complete pipeline arithmetic-free:

• _compute_arithmetic_telemetry factors the input to obtain Omega, tau and sigma in both modes.
• Even-number hints, integer-size seeds and later partition-size divisibility checks remain.
• Empty initial candidates reach trial division without a pure-mode guard; its default bound is isqrt(n).
• TNFR_PURE_MODE_VERIFY_DIVISIBILITY filters one initial stage, not every later candidate or final acceptance label.

Automatic modulus selection rounds upward to at least n and 5, with residue 1 mod 4, without proving primality. Distinct inputs can therefore share a graph (35 and 37 both select modulus 37). Explicit overrides enforce only the lower bound 5, while prime-modulus Paley identities require their own domain. Support is supplied arithmetically, not formed by a nodal law.

The low-level constructor defaults to a node cap of 4097; None removes it. The historical high-level wrapper and CLI pass None when omitted. CLI zero also removes the cap, unlike the constructor. These differences matter when interpreting retained records, as do cache, backend and mode.

Archived JSON projections encode nonfinite diagnostics as null with numeric_availability reasons. When projection changes the payload, numeric_projection.retained_hash_scope distinguishes internal hash inputs from exported bytes. This is neither provenance authentication nor a guarantee that the underlying diagnostic has physical meaning.

Telemetry and mechanism boundaries

The lab's field names differ from canonical tnfr.physics.fields:

Lab field	Computation or source
phi_s	Normalized edge density, without nodewise pressure or path distance
phase_gradient	Selected spectral gap divided by node count
phase_curvature	Largest supplied eigenvalue divided by node count
coherence_length	Positive backend value, otherwise inverse selected gap
Arithmetic EPI, capacity, pressure	Static factor/divisor readouts without phase or autonomous evolution
Energy/Noether proxies	Algebraic lab features, without an established balance or conserved charge

On regular unit-weight graphs the fallback combinatorial spectrum is d * spectrum(L_rw). Its inverse selected gap is not the normalized diffusion timescale 1 / (nu * lambda_2(L_rw)) without degree/time conversion. The selection discards eigenvalues at or below 1e-9, so it need not select the true second eigenvalue.

Partition pressure reduction includes a fixed attenuation surrogate. It is not operator execution or a convergence theorem. Grammar-valid proposals, configured thresholds and finite score changes do not prove U5, autonomous selection, conservation or a factorization mechanism.

Verification and evidence

Archived tests and benchmark source are retained for interpretation and recovery, outside the maintained test selection and automatic validation maps. Their finite passing cases do not override the counterexamples above. Do not rerun frozen producers to update these records.

Historical JSON, notebook records and captured paths retain their original bytes. Partition hashes cover selected members, telemetry and metadata in supplied order, excluding other state; they are not complete checkpoints. Snapshot demonstrations use synthetic persistence records.

The current testing policy covers independent core arithmetic controls, the basic primality utility and compatibility admission. The root LICENSE.md remains authoritative.