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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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"from": "sidon_h16_k4_products",
"to": "sidon_h16_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_h16_k4_slos",
"to": "sidon_h16_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_pow7_k4_products",
"to": "sidon_pow7_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_pow7_k4_slos",
"to": "sidon_pow7_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_s6_k4_products",
"to": "sidon_s6_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_s6_k4_slos",
"to": "sidon_s6_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_s7_k4_products",
"to": "sidon_s7_k4_compare",
"type": "depends_on"
},
{
"from": "sidon_s7_k4_slos",
"to": "sidon_s7_k4_compare",
"type": "depends_on"
},
{
"from": "nonsidon_dense6_k4_products",
"to": "nonsidon_dense6_k4_compare",
"type": "depends_on"
},
{
"from": "nonsidon_dense6_k4_slos",
"to": "nonsidon_dense6_k4_compare",
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},
{
"from": "nonsidon_dense7_k4_products",
"to": "nonsidon_dense7_k4_compare",
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},
{
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},
{
"from": "primes_s7_k4_products",
"to": "primes_s7_k4_compare",
"type": "depends_on"
},
{
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"to": "primes_s7_k4_compare",
"type": "depends_on"
},
{
"from": "primes_s8_k4_products",
"to": "primes_s8_k4_compare",
"type": "depends_on"
},
{
"from": "primes_s8_k4_slos",
"to": "primes_s8_k4_compare",
"type": "depends_on"
}
]
}
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