Streaming Polyphase Factor Decomposition / SKAT

Streaming Polyphase Factor Decomposition for SKAT-like Tests - v0.5

This release extends the illustrated v0.4 manuscript with a certified theory for approximately sparse phase graphs.

New in v0.5

• weighted phase-transfer matrix \(\mathcal B_{hg}=\|P_hHP_g\|_2\);
• phasewise propagation envelope \(\rho(H^kX)\le \mathcal B^k\rho(X)\);
• thresholded-operator certificate \(\rho((H^k-H_0^k)X)\le(\mathcal B^k-\mathcal B_0^k)\rho(X)\);
• certified approximate light cone for weak nonzero couplings;
• polynomial/Krylov certificate for \(p(H)-p(H_0)\);
• scalar depth-threshold law;
• deterministic numerical validation for depths 1-8, a phase-threshold sweep, and a signed degree-four polynomial;
• two new explanatory figures integrated into the manuscript.

Evidence status

The transfer-matrix, thresholded-power, approximate-light-cone, scalar, and polynomial results are proved analytically. The finite computations validate the implementation and illustrate conservatism; they are not the proof.

Primary files

• FINAL_MANUSCRIPT.tex
• FINAL_MANUSCRIPT.pdf
• APPROXIMATE_LIGHTCONE_THEOREM.tex
• approximate_lightcone.py
• test_approximate_lightcone.py
• benchmark_approximate_lightcone.py
• approximate_lightcone_depth.csv
• approximate_lightcone_threshold_sweep.csv
• approximate_lightcone_phase_profile.csv
• polynomial_krylov_certificate.csv
• APPROXIMATE_LIGHTCONE_MANIFEST.json
• PROOF_AUDIT_APPROXIMATE_LIGHTCONE.md
• VERIFICATION_V05.md

The earlier exact streaming, tiling, partition-invariance, phase-local rank, QR-core, range-core, and K-COS interface files remain included.

v0.7 additions

• spectral_tail_bridge.py: phase-pruning -> operator -> spectrum -> K-COS tail certificate.
• test_spectral_tail_bridge.py: theorem-path regressions.
• direct_spectral_tail_brackets.csv: direct Weyl/K-COS brackets.
• dual_budget_spectral_scheduler.csv: simultaneous Krylov and operator budgets.
• certify_after_prune_range_core.csv: exact range-core stopping audit.
• PROOF_AUDIT_SPECTRAL_TAIL_BRIDGE.md: proof and limitation audit.

v0.9 realistic SKAT validation

• benchmark_realistic_skat.py: corrected copy-LD and latent-Gaussian LD simulation battery.
• test_realistic_skat.py: reproducibility and streamed-kernel regression tests.
• realistic_skat_scenarios.csv: LD and spectral diagnostics.
• realistic_streaming_invariance.csv: raw-genotype block-size invariance.
• realistic_deep_tail_accuracy.csv: ordinary realistic-LD tail comparisons.
• realistic_large_deeper_tail.csv: corrected large copy-LD tails through about 10^-458.
• PROOF_AND_SIMULATION_AUDIT_V09.md: provenance, validation scope, and claim boundary.