This playbook codifies the canonical procedure for factorizing any integer n > 1
inside the factorization lab. Every step maps directly to TNFR physics:
Paley graph instrumentation, nodal decoding, operator strategies, and
TNFR-native verification metrics.
pip install -e . from the repository root.tnfr.dynamics.advanced_fft_arithmetic is loaded
automatically; distributed backends are optional).TNFR_PARTITION_* overrides only if you need custom block sizes.make.cmd smoke-tests passing—this validates the self-optimizing engine,
arithmetic formalism, and grammar rules before factoring new numbers.SpectralPaleyFactorizer.analyze(n).n to a Paley/Jacobi-compatible modulus, attaches EPI/νf
annotations, and records Laplacian eigenvalues via FFT.plan_paley_partitions deterministically divides the graph using
PartitionPlannerConfig. Telemetry (Φ_s, |∇φ|, K_φ, ξ_C) is stored per block.[UM, RA, IL, THOL]. The nodal decoder records ΔNFR
attenuation, coherence ratios, and inferred periodicity.operator_strategy_plan._verify_factors_tnfr collects deterministic invariants:
ΔNFR gain, Φ_s confinement vs parent, coherence windows, and periodicity locks.
Factors whose partitions satisfy the criteria become tnfr_certified_factors.analyze(..., trace_certificates=True) to persist:
partition_states, strategy_plan_snapshot, nodal_decoding_snapshot,
tnfr_verification_snapshot, and the invariant report.tnfr_verification_snapshot as the decisive evidence.python - <<'PY'
from tnfr_factorization import SpectralPaleyFactorizer
factorizer = SpectralPaleyFactorizer()
result = factorizer.analyze(221, trace_certificates=True)
print(result.tnfr_certified_factors)
print(result.certificate_path)
PYpython factorization-lab/benchmarks/full_spectrum_factorization.py \
--output full_spectrum_range.json \
--range-start 150 --range-stop 190Each entry in factorization-lab/results/benchmarks/ includes partition traces and the
serialized TNFR verification report for downstream audits.
SpectralPaleyFactorizer automatically records failed attempts in
results/failure_telemetry/ so operators can study Laplacian gaps,
partition coverage, and verifier bottlenecks. Control this behavior via
the TNFR_FAILURE_TELEMETRY environment variable:
| Value | Effect |
|---|---|
unset / 1 / true / on | Failure telemetry stays enabled (default) |
0 / false / off | Disables telemetry recording entirely |
To redirect artifacts, pass failure_telemetry_root=Path(...) when constructing
SpectralPaleyFactorizer. This keeps the JSON artifacts and manifest under a
per-run scratch directory while the default production pipelines continue to
log into results/failure_telemetry/.
| Criterion | Threshold |
|---|---|
| ΔNFR gain | ≥ 0.15 relative drop inside [UM, RA, IL, THOL] |
| Coherence | 0.72 ≤ coherence_ratio ≤ 1.38 |
| Φ_s delta | |Φ_s(local) − Φ_s(parent)| ≤ 0.35 |
| Evidence | ≥ 3 of the five flags (stabilized, coherence, dnfr_gain, phi, periodic) per partition |
| Coverage | ≥ 50% of partitions referencing a factor must endorse it |
Factors passing the criteria appear in tnfr_certified_factors and the certificate's
tnfr_verification_snapshot. Use these lists for downstream automation (e.g. deciding
whether to cascade into higher-level operators or to log a divergence).
| Symptom | Likely cause | Remedy |
|---|---|---|
tnfr_certified_factors empty | Partitions failed ΔNFR or coherence criteria | Inspect partition certificates (results/certificates/partitioned/…) for the offending block; adjust partition target size or run dissonance probes (OZ) before IL |
tnfr_verification_snapshot missing | trace_certificates=False or nodal decoder disabled | Re-run with trace_certificates=True; ensure [UM, RA, IL, THOL] is active in nodal_operator_sequence |
High phi_delta_max values | Parent Φ_s too low/high or partitions mis-sized | Tune TNFR_PARTITION_TARGET_SIZE or apply THOL stabilizers earlier |
| Self-optimizing engine unavailable | Optional dependency missing | Fallback sequence (emission→coupling→resonance→coherence→silence) still valid, but consider installing tnfr.engines.self_optimization |
theory/UNIFIED_GRAMMAR_RULES.md — nodal decoder completeness & grammar proofs.theory/TNFR_NODAL_FACTOR_COMPLETENESS.md — full statement of the TNFR-only
factorization theorem and verifier thresholds.docs/OPERATOR_CERTIFICATES.md — certificate schema and TNFR evidence fields.factorization-lab/benchmarks/full_spectrum_factorization.py — automation entry point.factorization-lab/tests/test_spectral_paley.py — regression coverage for decoder,
certificates, and verification metrics.