The K-COS MethodStatements and proofs
Statements and proofs
Find a statement anywhere in this work by title, printed number, type or source label. Entries follow the chapter order. Each proof link opens the written proof passage.
Statements by chapter
Gaussian quadratic forms
Exact streamed representations
- Theorem 2.1: Additive block Gram identity Read proof
- Remark 2.2
- Theorem 2.3: One-pass sample-space streaming action Read proof
- Algorithm 2.4: Streamed (KV )
- Corollary 2.5: Working memory independent of total variant count
- Theorem 2.6: Streamed (AV )
- Theorem 2.7: Streamed (A top U ) Read proof
- Corollary 2.8: Streaming Golub–Kahan equivalence
- Theorem 2.9: Two-pass streamed dual action
- Theorem 2.10: Two-pass residualized tile construction Read proof
- Theorem 2.11: Partition-refinement invariance Read proof
- Corollary 2.12: Adaptive memory splitting
- Proposition 2.13: Variant permutation invariance
Polyphase propagation and scheduling
- Theorem 3.1: Polyphase light cone Read proof
- Theorem 3.2: Streaming-polyphase composition Read proof
- Theorem 3.3: Weighted phase-transfer envelope Read proof
- Theorem 3.4: Thresholded-power certificate Read proof
- Corollary 3.5: Certified approximate light cone
- Corollary 3.6: Scalar threshold law
- Theorem 3.7: Krylov-polynomial certificate Read proof
- Corollary 3.8: Certified phase pruning
- Theorem 3.9: Edge-additive leakage majorant Read proof
- Corollary 3.10: Polynomial edge-risk certificate
- Corollary 3.11: Query-invisible phase pair
- Theorem 3.12: Cardinality-optimal certified pruning Read proof
- Proposition 3.13: Certified refinement
- Proposition 3.14: Ideal two-buffer pipeline Read proof
Range cores and low-rank interfaces
Spectral uncertainty and exact completion
- Theorem 5.1: Block-norm operator certificate Read proof
- Corollary 5.2: Positive spectral interval
- Theorem 5.3: Stochastic tail enclosure Read proof
- Theorem 5.4: Range-core singular-value certificate Read proof
- Theorem 5.5: Exact core–residual decomposition Read proof
- Theorem 5.6: Trace–Frobenius–cap log-MGF certificate Read proof
- Corollary 5.7: Trace-aware Chernoff upper tail
- Theorem 5.8: Residual-rank bracket Read proof
- Theorem 5.9: Exact residual completion Read proof
- Theorem 5.10: Candidate eigensystem post-certification Read proof
Exponential tilting and spectral packets
COS inversion and the analytic error budget
- Theorem 7.1: Finite-grid packet-to-tail bound Read proof
- Lemma 7.2: Integrated cosine identity by folding Read proof
- Proposition 7.3: Support and periodization bound Read proof
- Lemma 7.4: Tilted characteristic-function modulus Read proof
- Corollary 7.5: Power envelope from one frequency Read proof
- Theorem 7.6: Omitted COS-mode certificate Read proof
- Theorem 7.7: K-COS analytic error certificate Read proof
- Remark 7.8: Certificate boundary
- Proposition 7.9: Existence of a finite analytic refinement Read proof
- Remark 7.10