THEOREM_INDEX.md
Streaming Polyphase Factor Decomposition / SKAT
THEOREM_INDEX.md
1 # Theorem index
2
3 1. Additive block Gram identity.
4 2. Streaming sample-space kernel action.
5 3. Device-memory independence from total variant count.
6 4. Streaming `A V`.
7 5. Streaming `A^T U`.
8 6. Streaming Golub-Kahan equivalence.
9 7. Two-pass streamed dual action `A^T A V`.
10 8. Two-pass residualized sample-tile construction.
11 9. Exact matrix-packet decomposition `K = sum_h K_h`.
12 10. Exact memory-bounded polyphase Krylov composition.
13 11. Storage-phase commutation.
14 12. Frontier-to-I/O reduction.
15 13. Weighted phase-transfer envelope.
16 14. Thresholded-power certificate.
17 15. Certified approximate light cone.
18 16. Scalar depth-threshold law.
19 17. Krylov-polynomial certificate.
20 18. Certified phase pruning.
21 19. Minimal exact phase width from phase-local rank.
22 20. Exact low-rank inter-phase message action.
23 21. Exact QR-core update under appended variant blocks.
24 22. Exact range-core spectral reconstruction.
25 23. Device-memory planning asymptotic law.
26
27
28 ## v0.7 spectral/tail bridge
29 - Block-norm operator certificate.
30 - Positive Weyl spectral interval for a pruned self-adjoint phase operator.
31 - Stochastic generalized-chi-square tail enclosure.
32 - Dual query/operator budget certification rule.
33 - Range-core singular-value certificate.
34 - Certified tail enclosure from a range-core residual.
35
36 ## v0.9 realistic simulation validation
37 - corrected copy-LD simulator provenance audit;
38 - raw-genotype streamed-kernel regression under four LD scenarios;
39 - phenotype factor/kernel/eigenspace equivalence audit;
40 - realistic-LD K-COS tail validation through log10(p) approximately -458.