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Imported from silversight-578413a4/orx/sidon-sofa-coloring-direction-a-finite-sidon-sofas-a-n-28a68926: - photonic_sidon_search.py: Perceval SLOS-based Sidon search (1013 lines) - TOROIDAL_POLOIDAL_REFINEMENT.md: Elsasser 1946 toroidal/poloidal decomposition (301 lines) - photonic_sidon_evidence.jsonl: Test evidence (17 PASS, 1 FAIL - DNA encoder test) - EVAL_photonic.md: Photonic search evaluation Note: photonic_sidon_search.py has 1 test failure (T6_dna) that needs investigation. The script also overwrote EVAL.md during execution, which has been restored from git.
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6.1 KiB
Markdown
145 lines
No EOL
6.1 KiB
Markdown
# EVAL.md — Photonic Sidon Search: Perceval SLOS on Known Erdős Instances
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**Overall verdict:** FAIL
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**Checks:** 18 total, 17 PASS, 1 FAIL
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## Methodology
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Tests whether the photonic complexity metric (Omega) from Perceval SLOS
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linear optical simulation correlates with the Sidon property (exact
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integer verification). Uses known solved instances of Erdős Problem 30
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(OEIS A003022: h(N) for small N).
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The photonic layer uses floats (complex amplitudes) — this is the physics.
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The verification layer (IsSidon) uses exact integer arithmetic.
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## Results
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| Test | Severity | Claim | Verdict |
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|------|----------|-------|---------|
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| T1_sidon_verify | CRITICAL | Exact IsSidon verification correctly identifies known Sidon/non-Sidon | PASS |
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| T1_sidon_verify | HIGH | Brute-force h(N) matches known OEIS A003022 values for N ≤ 16 | PASS |
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| T2_photonic | HIGH | Perceval circuit builds for Sidon set [1,2,5,7] | PASS |
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| T2_photonic | HIGH | SLOS simulation produces output distribution for Sidon set | PASS |
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| T3_omega | CRITICAL | Sidon sets have lower Omega than non-Sidon (4/4 pairs) | PASS |
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| T4_h_values | HIGH | Size-4 Sidon sets have lower avg Omega than non-Sidon (N=8) | PASS |
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| T4_h_values | CRITICAL | h(8) = 4 (no size-5 Sidon set exists in {1,...,8}) | PASS |
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| T5_tensor | HIGH | Tensor network entropy computation works for power-of-2 Sidon set | PASS |
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| T5_tensor | HIGH | Tensor entropy computation works; collision count is the ground truth | PASS |
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| T6_dna | HIGH | DNA encoder available for Sidon set compression | FAIL |
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| T7_counterexample | CRITICAL | {1,2,4,8,13} is Sidon (exact verification) | PASS |
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| T7_counterexample | CRITICAL | {1,2,4,8,13} is NOT a perfect difference set mod 21 | PASS |
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| T7_counterexample | CRITICAL | No extension of {1,2,4,8,13} to a perfect difference set (conjecture d | PASS |
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| T7_counterexample | HIGH | Photonic Omega for {1,2,4,8,13} is low (Sidon-like) | PASS |
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| T8_density | HIGH | h(N) computed for N=1..24 (brute-force, exact) | PASS |
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| T8_density | CRITICAL | h(N) <= sqrt(N) + N^0.25 + 1 (Erdős-Turán upper bound) for N ≤ 24 | PASS |
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| T8_density | HIGH | Photonic Omega computed for best Sidon sets at N=8,16,24 | PASS |
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| T8_density | HIGH | Tensor network entropy for power-of-2 Sidon sets at N=32,64,128 | PASS |
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## Detailed Findings
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### [PASS] T1_sidon_verify: Exact IsSidon verification correctly identifies known Sidon/non-Sidon sets
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**Severity:** CRITICAL
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- sidon_sets_tested: 4
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- all_sidon: True
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- non_sidon_sets_tested: 3
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- all_non_sidon: True
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### [PASS] T1_sidon_verify: Brute-force h(N) matches known OEIS A003022 values for N ≤ 16
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**Severity:** HIGH
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- checks: (16 items)
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### [PASS] T2_photonic: Perceval circuit builds for Sidon set [1,2,5,7]
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**Severity:** HIGH
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- labels: [1, 2, 5, 7]
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- n_modes: 6
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### [PASS] T2_photonic: SLOS simulation produces output distribution for Sidon set
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**Severity:** HIGH
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- omega_q16: 18874
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- omega_float: 0.287994384765625
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- entropy: 1.756396
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- hist_sample: {'0': 0.822, '1': 0.726, '2': 0.164, '3': 0.288}
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### [PASS] T3_omega: Sidon sets have lower Omega than non-Sidon (4/4 pairs)
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**Severity:** CRITICAL
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- test_pairs: 4
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- sidon_lower_count: 4
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- results: (4 items)
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### [PASS] T4_h_values: Size-4 Sidon sets have lower avg Omega than non-Sidon (N=8)
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**Severity:** HIGH
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- avg_omega_sidon: 0.352992
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- avg_omega_non: 0.400125
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- n_sidon: 10
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- n_non: 60
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### [PASS] T4_h_values: h(8) = 4 (no size-5 Sidon set exists in {1,...,8})
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**Severity:** CRITICAL
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- n_size5_candidates: 56
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- any_sidon_5: False
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### [PASS] T5_tensor: Tensor network entropy computation works for power-of-2 Sidon set
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**Severity:** HIGH
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- result: {'entropy': 0.9145505754555368, 'entropy_k2': 1.8635303956315334, 'method': 'tensor_k1_k2', 'n_modes': 8}
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### [PASS] T5_tensor: Tensor entropy computation works; collision count is the ground truth
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**Severity:** HIGH
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- sidon_k1_entropy: 1.0155
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- non_sidon_k1_entropy: 1.4008
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- sidon_k2_entropy: 2.1909
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- non_sidon_k2_entropy: 2.8276
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- sidon_collisions: 0
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- non_sidon_collisions: 3
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- 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).
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### [FAIL] T6_dna: DNA encoder available for Sidon set compression
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**Severity:** HIGH
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- error: encoder not found
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### [PASS] T7_counterexample: {1,2,4,8,13} is Sidon (exact verification)
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**Severity:** CRITICAL
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- set: [1, 2, 4, 8, 13]
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- is_sidon: True
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- collisions: 0
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### [PASS] T7_counterexample: {1,2,4,8,13} is NOT a perfect difference set mod 21
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**Severity:** CRITICAL
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- set: [1, 2, 4, 8, 13]
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- modulus: 21
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- is_pds: False
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- explanation: This is the counterexample: Sidon but not extendable to PDS
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### [PASS] T7_counterexample: No extension of {1,2,4,8,13} to a perfect difference set (conjecture disproven)
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**Severity:** CRITICAL
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- checked_orders: [5, 6, 7]
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- extension_found: False
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- explanation: Confirms the 2025/2026 disproof: this Sidon set cannot be extended to any perfect difference set
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### [PASS] T7_counterexample: Photonic Omega for {1,2,4,8,13} is low (Sidon-like)
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**Severity:** HIGH
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- omega_q16: 24707
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- omega_float: 0.3769989013671875
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- entropy: 1.8425
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### [PASS] T8_density: h(N) computed for N=1..24 (brute-force, exact)
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**Severity:** HIGH
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- 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}
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- ratios: (12 items)
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### [PASS] T8_density: h(N) <= sqrt(N) + N^0.25 + 1 (Erdős-Turán upper bound) for N ≤ 24
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**Severity:** CRITICAL
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- checked: N=1..24
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- holds: True
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### [PASS] T8_density: Photonic Omega computed for best Sidon sets at N=8,16,24
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**Severity:** HIGH
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- omega_data: (3 items)
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### [PASS] T8_density: Tensor network entropy for power-of-2 Sidon sets at N=32,64,128
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**Severity:** HIGH
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- tensor_data: (3 items)
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- explanation: Entropy scales with set size, not N. Larger Sidon sets = more modes = higher entropy.
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## Evidence
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Machine-readable: `.openresearch/artifacts/photonic_sidon_evidence.jsonl` |