Edition README
Streaming Polyphase Factor Decomposition / SKAT
README.md
1 # Streaming Polyphase Factor Decomposition for SKAT-like Tests - v0.5
2
3 This release extends the illustrated v0.4 manuscript with a certified theory
4 for approximately sparse phase graphs.
5
6 ## New in v0.5
7
8 - weighted phase-transfer matrix
9 \(\mathcal B_{hg}=\|P_hHP_g\|_2\);
10 - phasewise propagation envelope
11 \(\rho(H^kX)\le \mathcal B^k\rho(X)\);
12 - thresholded-operator certificate
13 \(\rho((H^k-H_0^k)X)\le(\mathcal B^k-\mathcal B_0^k)\rho(X)\);
14 - certified approximate light cone for weak nonzero couplings;
15 - polynomial/Krylov certificate for \(p(H)-p(H_0)\);
16 - scalar depth-threshold law;
17 - deterministic numerical validation for depths 1-8, a phase-threshold sweep,
18 and a signed degree-four polynomial;
19 - two new explanatory figures integrated into the manuscript.
20
21 ## Evidence status
22
23 The transfer-matrix, thresholded-power, approximate-light-cone, scalar, and
24 polynomial results are proved analytically. The finite computations validate
25 the implementation and illustrate conservatism; they are not the proof.
26
27 ## Primary files
28
29 - `FINAL_MANUSCRIPT.tex`
30 - `FINAL_MANUSCRIPT.pdf`
31 - `APPROXIMATE_LIGHTCONE_THEOREM.tex`
32 - `approximate_lightcone.py`
33 - `test_approximate_lightcone.py`
34 - `benchmark_approximate_lightcone.py`
35 - `approximate_lightcone_depth.csv`
36 - `approximate_lightcone_threshold_sweep.csv`
37 - `approximate_lightcone_phase_profile.csv`
38 - `polynomial_krylov_certificate.csv`
39 - `APPROXIMATE_LIGHTCONE_MANIFEST.json`
40 - `PROOF_AUDIT_APPROXIMATE_LIGHTCONE.md`
41 - `VERIFICATION_V05.md`
42
43 The earlier exact streaming, tiling, partition-invariance, phase-local rank,
44 QR-core, range-core, and K-COS interface files remain included.
45
46
47 ## v0.7 additions
48 - `spectral_tail_bridge.py`: phase-pruning -> operator -> spectrum -> K-COS tail certificate.
49 - `test_spectral_tail_bridge.py`: theorem-path regressions.
50 - `direct_spectral_tail_brackets.csv`: direct Weyl/K-COS brackets.
51 - `dual_budget_spectral_scheduler.csv`: simultaneous Krylov and operator budgets.
52 - `certify_after_prune_range_core.csv`: exact range-core stopping audit.
53 - `PROOF_AUDIT_SPECTRAL_TAIL_BRIDGE.md`: proof and limitation audit.
54
55 ## v0.9 realistic SKAT validation
56 - `benchmark_realistic_skat.py`: corrected copy-LD and latent-Gaussian LD simulation battery.
57 - `test_realistic_skat.py`: reproducibility and streamed-kernel regression tests.
58 - `realistic_skat_scenarios.csv`: LD and spectral diagnostics.
59 - `realistic_streaming_invariance.csv`: raw-genotype block-size invariance.
60 - `realistic_deep_tail_accuracy.csv`: ordinary realistic-LD tail comparisons.
61 - `realistic_large_deeper_tail.csv`: corrected large copy-LD tails through about 10^-458.
62 - `PROOF_AND_SIMULATION_AUDIT_V09.md`: provenance, validation scope, and claim boundary.