TNFR Spectral Factorization Package Summary

Item	Status	Notes
Research framing	✅	Paley spectral gap + TNFR coherence mapping documented in README and SPECTRAL_ROUTE.md
Package scaffolding	✅	Mirrors primality-test/ layout with docs + package namespace
Graph constructors	✅	Paley/Jacobi graph builder + node annotations implemented in spectral_paley.py
Spectral analyzers	✅	Laplacian eigenvalues + tetrad telemetry computed through FFT engine fallbacks
Factor recovery logic	✅	ΔNFR-aware heuristics with 8-criterion TNFR verification (§9.3); certificates include pressure decomposition, dual-lever analysis, conservation proxies
Theory alignment	✅	Arithmetic tetrad recalibration (§7.5), dual-lever (§8), pressure decomposition (§6), enriched telemetry (~15 fields)
Benchmarks/tests	✅	paley_gap_smoke.py, paley_gap_extended.py, and the new full_spectrum_factorization.py sweep (with certificate capture) plus regression tests
Publication assets	✅	.zenodo.json, LICENSE_SNAPSHOT.md, ZENODO_RELEASE_NOTES.md, and checksum workflow documented

Deliverables

1. Spectral TNFR Factorizer: Algorithm converting Paley-type graph spectra into factor candidates along with TNFR coherence certificates.
2. Documentation Set: Research notes (SPECTRAL_ROUTE.md), roadmap, and experiment guidelines.
3. Integration Hooks: Shared telemetry + operator infrastructure with the existing TNFR primality tooling.

Immediate Priorities

• Complex field Ψ: Compute Ψ = K_φ + i·J_φ on Paley graphs for unified analysis.
• Full conservation: Bridge Paley node attributes to canonical compute_noether_charge() / compute_energy_functional() (currently proxy values).
• Grammar-aware sequencing: Apply GrammarAwareDynamics to partition operator chains.
• Harden archive automation (Makefile target) so Zenodo bundles + checksums become single-command artifacts.