# Theorem index

1. Additive block Gram identity.
2. Streaming sample-space kernel action.
3. Device-memory independence from total variant count.
4. Streaming `A V`.
5. Streaming `A^T U`.
6. Streaming Golub-Kahan equivalence.
7. Two-pass streamed dual action `A^T A V`.
8. Two-pass residualized sample-tile construction.
9. Exact matrix-packet decomposition `K = sum_h K_h`.
10. Exact memory-bounded polyphase Krylov composition.
11. Storage-phase commutation.
12. Frontier-to-I/O reduction.
13. Weighted phase-transfer envelope.
14. Thresholded-power certificate.
15. Certified approximate light cone.
16. Scalar depth-threshold law.
17. Krylov-polynomial certificate.
18. Certified phase pruning.
19. Minimal exact phase width from phase-local rank.
20. Exact low-rank inter-phase message action.
21. Exact QR-core update under appended variant blocks.
22. Exact range-core spectral reconstruction.
23. Device-memory planning asymptotic law.


## v0.7 spectral/tail bridge
- Block-norm operator certificate.
- Positive Weyl spectral interval for a pruned self-adjoint phase operator.
- Stochastic generalized-chi-square tail enclosure.
- Dual query/operator budget certification rule.
- Range-core singular-value certificate.
- Certified tail enclosure from a range-core residual.

## v0.9 realistic simulation validation
- corrected copy-LD simulator provenance audit;
- raw-genotype streamed-kernel regression under four LD scenarios;
- phenotype factor/kernel/eigenspace equivalence audit;
- realistic-LD K-COS tail validation through log10(p) approximately -458.