mirror of https://github.com/allaunthefox/SilverSight.git synced 2026-08-07 18:35:45 +00:00

allaun f1a050277b feat(slos): eigenvalue products predict SLOS concentration ordering - verified with Spearman correlation, cross-validated with exact tensor network

48 test points across K=1..4 and 12 label sets (Sidon power sets,
Sidon constructions, dense non-Sidon, prime-based).

Results:
  K=1: ρ=-0.85 (products→SLOS), ρ=-0.94 (SLOS↔tensor)
  K=2: ρ=-0.88 (products→SLOS), ρ=-0.94 (SLOS↔tensor)
  K=3: ρ=-0.93 (products→SLOS), ρ=-0.98 (SLOS↔tensor)
  K=4: ρ=-0.93 (products→SLOS), tensor N/A (K>3)

Key: all Spearman correlations are negative and strengthen with K.
Sidon sets produce 1.5-2.3× higher KL divergence than same-size non-Sidon.
Primes are intermediate: partially Sidon-like but weaker.

DAG: 192 nodes, 96 edges, all individually checkpointed for resume.
Resume with: python3 scripts/perceval_slos_verify.py --resume

Receipt: docs/research/SLOS_SIDON_VERIFICATION_RECEIPT.md

Build: N/A (Python/perceval verification, no Lean build)

2026-07-03 17:55:26 -05:00

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SLOS Sidon Verification Receipt

Status: VERIFIED — all claims backed by local SLOS simulation and exact tensor network Date: 2026-07-03 System: Provider-nixos (neon-rs1000), Perceval v1.2.4, quimb v1.14.0 Script: scripts/perceval_slos_verify.py Artifacts: .openresearch/artifacts/slos_computation_dag.json (192 nodes, 96 edges)

Core Claim

Eigenvalue product concentration predicts SLOS output concentration ordering for Sidon vs non-Sidon label sets, verified across K=1..4 and 12 test cases.

Test Cases (12 label sets, 4 photon numbers = 48 test points)

Category	Label sets	Sizes
Sidon powers of 2	`sidon_pow2`, `sidon_pow7`, `sidon_pow8`	4, 7, 8
Sidon constructions	`sidon_h8`, `sidon_h16`, `sidon_s6`, `sidon_s7`	4, 5, 6, 7
Non-Sidon consecutive	`nonsidon_seq`, `nonsidon_dense6`, `nonsidon_dense7`	4, 6, 7
Prime-based	`primes_s7`, `primes_s8`	7, 8

Spearman Rank Correlations

Test	K=1	K=2	K=3	K=4
Products → SLOS KL	ρ = -0.846	ρ = -0.880	ρ = -0.930	ρ = -0.930
SLOS ↔ Tensor (exact)	ρ = -0.944	ρ = -0.937	ρ = -0.979	N/A (K>3)

All correlations are negative: lower eigenvalue product distinct_ratio → higher SLOS KL divergence from uniform (more concentrated output). Correlation strengthens with K.

Key Comparisons (same-size sets, K=2)

Size	Sidon	KL	Non-Sidon	KL	Ratio
4	sidon_pow2	1.13	nonsidon_seq	0.50	2.3×
4	sidon_h8	0.91	nonsidon_seq	0.50	1.8×
6	sidon_s6	1.95	nonsidon_dense6	0.93	2.1×
7	sidon_pow7	2.94	nonsidon_dense7	1.92	1.5×
7	primes_s7	2.12	nonsidon_dense7	1.92	1.1×
8	sidon_pow8	3.30	nonsidon_dense7	1.92	1.7×

Method Agreement

The Spearman ρ = -0.979 between SLOS (100k-shot sampling) and exact tensor network entropy at K=3 confirms that the SLOS sampling noise is negligible — the two methods produce nearly identical orderings. This is a cross-method validation: the result is not an artifact of Perceval's specific SLOS implementation.

DAG Structure

192 nodes recording the full computation graph:

48 eigenvalue product nodes (12 sets × 4 K values)
48 SLOS circuit nodes
48 SLOS result nodes (100k shots each)
48 comparison nodes (Spearman + tensor cross-validation)

Each node is individually checkpointed. Resume with --resume after interruption.

claim_boundary

slos-sidon-verification:spearman-correlation-cross-method

This receipt is bounded to the claim that eigenvalue product distinct_ratio predicts SLOS concentration ordering across the tested label sets and photon numbers. It does not claim universality beyond the 12 test cases, nor does it claim physical realizability on quantum hardware.

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