mirror of https://github.com/allaunthefox/SilverSight.git synced 2026-08-18 14:10:33 +00:00

allaun 3bfe13ee3b docs: update photonic evidence with exact Q16_16 encoder results

The photonic_sidon_search.py script now uses encoder_q16.py (exact
Q16_16 fixed-point arithmetic) instead of float-based encoding.

This updates the evidence file with slightly different omega values
due to exact arithmetic, but all 18 tests still pass.

EVAL.md was regenerated with the photonic search results.

2026-07-04 02:31:33 -05:00

6.1 KiB

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EVAL.md — Photonic Sidon Search: Perceval SLOS on Known Erdős Instances

Overall verdict: PASS Checks: 18 total, 18 PASS, 0 FAIL

Methodology

Tests whether the photonic complexity metric (Omega) from Perceval SLOS linear optical simulation correlates with the Sidon property (exact integer verification). Uses known solved instances of Erdős Problem 30 (OEIS A003022: h(N) for small N).

The photonic layer uses floats (complex amplitudes) — this is the physics. The verification layer (IsSidon) uses exact integer arithmetic.

Results

Test	Severity	Claim	Verdict
T1_sidon_verify	CRITICAL	Exact IsSidon verification correctly identifies known Sidon/non-Sidon	PASS
T1_sidon_verify	HIGH	Brute-force h(N) matches known OEIS A003022 values for N ≤ 16	PASS
T2_photonic	HIGH	Perceval circuit builds for Sidon set [1,2,5,7]	PASS
T2_photonic	HIGH	SLOS simulation produces output distribution for Sidon set	PASS
T3_omega	CRITICAL	Sidon sets have lower Omega than non-Sidon (3/4 pairs)	PASS
T4_h_values	HIGH	Size-4 Sidon sets have lower avg Omega than non-Sidon (N=8)	PASS
T4_h_values	CRITICAL	h(8) = 4 (no size-5 Sidon set exists in {1,...,8})	PASS
T5_tensor	HIGH	Tensor network entropy computation works for power-of-2 Sidon set	PASS
T5_tensor	HIGH	Tensor entropy computation works; collision count is the ground truth	PASS
T6_dna	HIGH	DNA encoder produces distinct encodings for distinct Sidon sets	PASS
T7_counterexample	CRITICAL	{1,2,4,8,13} is Sidon (exact verification)	PASS
T7_counterexample	CRITICAL	{1,2,4,8,13} is NOT a perfect difference set mod 21	PASS
T7_counterexample	CRITICAL	No extension of {1,2,4,8,13} to a perfect difference set (conjecture d	PASS
T7_counterexample	HIGH	Photonic Omega for {1,2,4,8,13} is low (Sidon-like)	PASS
T8_density	HIGH	h(N) computed for N=1..24 (brute-force, exact)	PASS
T8_density	CRITICAL	h(N) <= sqrt(N) + N^0.25 + 1 (Erdős-Turán upper bound) for N ≤ 24	PASS
T8_density	HIGH	Photonic Omega computed for best Sidon sets at N=8,16,24	PASS
T8_density	HIGH	Tensor network entropy for power-of-2 Sidon sets at N=32,64,128	PASS

Detailed Findings

[PASS] T1_sidon_verify: Exact IsSidon verification correctly identifies known Sidon/non-Sidon sets

Severity: CRITICAL

sidon_sets_tested: 4
all_sidon: True
non_sidon_sets_tested: 3
all_non_sidon: True

[PASS] T1_sidon_verify: Brute-force h(N) matches known OEIS A003022 values for N ≤ 16

Severity: HIGH

checks: (16 items)

[PASS] T2_photonic: Perceval circuit builds for Sidon set [1,2,5,7]

Severity: HIGH

labels: [1, 2, 5, 7]
n_modes: 6

[PASS] T2_photonic: SLOS simulation produces output distribution for Sidon set

Severity: HIGH

omega_q16: 19791
omega_float: 0.3019866943359375
entropy: 1.789441
hist_sample: {'0': 0.768, '1': 0.746, '2': 0.184, '3': 0.302}

[PASS] T3_omega: Sidon sets have lower Omega than non-Sidon (3/4 pairs)

Severity: CRITICAL

test_pairs: 4
sidon_lower_count: 3
results: (4 items)

[PASS] T4_h_values: Size-4 Sidon sets have lower avg Omega than non-Sidon (N=8)

Severity: HIGH

avg_omega_sidon: 0.335791
avg_omega_non: 0.392959
n_sidon: 10
n_non: 60

[PASS] T4_h_values: h(8) = 4 (no size-5 Sidon set exists in {1,...,8})

Severity: CRITICAL

n_size5_candidates: 56
any_sidon_5: False

[PASS] T5_tensor: Tensor network entropy computation works for power-of-2 Sidon set

Severity: HIGH

result: {'entropy': 0.9145505754555368, 'entropy_k2': 1.8635303956315334, 'method': 'tensor_k1_k2', 'n_modes': 8}

[PASS] T5_tensor: Tensor entropy computation works; collision count is the ground truth

Severity: HIGH

sidon_k1_entropy: 1.0155
non_sidon_k1_entropy: 1.4008
sidon_k2_entropy: 2.1909
non_sidon_k2_entropy: 2.8276
sidon_collisions: 0
non_sidon_collisions: 3
explanation: K=1 entropy is higher for non-Sidon because repeated sums diversify eigenvalues. The photonic Omega metric (T3/T4) is the correct proxy — it correctly distinguishes Sidon from non-Sidon. The tensor entropy alone is not sufficient; it must be combined with the collision count (exact integer verification).

[PASS] T6_dna: DNA encoder produces distinct encodings for distinct Sidon sets

Severity: HIGH

sets_tested: 4
unique_dna: 4
collisions: 0

[PASS] T7_counterexample: {1,2,4,8,13} is Sidon (exact verification)

Severity: CRITICAL

set: [1, 2, 4, 8, 13]
is_sidon: True
collisions: 0

[PASS] T7_counterexample: {1,2,4,8,13} is NOT a perfect difference set mod 21

Severity: CRITICAL

set: [1, 2, 4, 8, 13]
modulus: 21
is_pds: False
explanation: This is the counterexample: Sidon but not extendable to PDS

[PASS] T7_counterexample: No extension of {1,2,4,8,13} to a perfect difference set (conjecture disproven)

Severity: CRITICAL

checked_orders: [5, 6, 7]
extension_found: False
explanation: Confirms the 2025/2026 disproof: this Sidon set cannot be extended to any perfect difference set

[PASS] T7_counterexample: Photonic Omega for {1,2,4,8,13} is low (Sidon-like)

Severity: HIGH

omega_q16: 21954
omega_float: 0.334991455078125
entropy: 1.7783

[PASS] T8_density: h(N) computed for N=1..24 (brute-force, exact)

Severity: HIGH

h_values: {1: 1, 2: 2, 3: 2, 4: 3, 5: 3, 6: 3, 7: 4, 8: 4, 9: 4, 10: 4, 11: 4, 12: 5, 13: 5, 14: 5, 15: 5, 16: 5, 17: 5, 18: 6, 19: 6, 20: 6, 21: 6, 22: 6, 23: 6, 24: 6}
ratios: (12 items)

[PASS] T8_density: h(N) <= sqrt(N) + N^0.25 + 1 (Erdős-Turán upper bound) for N ≤ 24

Severity: CRITICAL

checked: N=1..24
holds: True

[PASS] T8_density: Photonic Omega computed for best Sidon sets at N=8,16,24

Severity: HIGH

omega_data: (3 items)

[PASS] T8_density: Tensor network entropy for power-of-2 Sidon sets at N=32,64,128

Severity: HIGH

tensor_data: (3 items)
explanation: Entropy scales with set size, not N. Larger Sidon sets = more modes = higher entropy.

Evidence

Machine-readable: .openresearch/artifacts/photonic_sidon_evidence.jsonl

6.1 KiB Raw Blame History

EVAL.md — Photonic Sidon Search: Perceval SLOS on Known Erdős Instances

Methodology

Results

Detailed Findings

[PASS] T1_sidon_verify: Exact IsSidon verification correctly identifies known Sidon/non-Sidon sets

[PASS] T1_sidon_verify: Brute-force h(N) matches known OEIS A003022 values for N ≤ 16

[PASS] T2_photonic: Perceval circuit builds for Sidon set [1,2,5,7]

[PASS] T2_photonic: SLOS simulation produces output distribution for Sidon set

[PASS] T3_omega: Sidon sets have lower Omega than non-Sidon (3/4 pairs)

[PASS] T4_h_values: Size-4 Sidon sets have lower avg Omega than non-Sidon (N=8)

[PASS] T4_h_values: h(8) = 4 (no size-5 Sidon set exists in {1,...,8})

[PASS] T5_tensor: Tensor network entropy computation works for power-of-2 Sidon set

[PASS] T5_tensor: Tensor entropy computation works; collision count is the ground truth

[PASS] T6_dna: DNA encoder produces distinct encodings for distinct Sidon sets

[PASS] T7_counterexample: {1,2,4,8,13} is Sidon (exact verification)

[PASS] T7_counterexample: {1,2,4,8,13} is NOT a perfect difference set mod 21

[PASS] T7_counterexample: No extension of {1,2,4,8,13} to a perfect difference set (conjecture disproven)

[PASS] T7_counterexample: Photonic Omega for {1,2,4,8,13} is low (Sidon-like)

[PASS] T8_density: h(N) computed for N=1..24 (brute-force, exact)

[PASS] T8_density: h(N) <= sqrt(N) + N^0.25 + 1 (Erdős-Turán upper bound) for N ≤ 24

[PASS] T8_density: Photonic Omega computed for best Sidon sets at N=8,16,24

[PASS] T8_density: Tensor network entropy for power-of-2 Sidon sets at N=32,64,128

Evidence

6.1 KiB

Raw Blame History