docs: record prime-Sidon honest negative (0/35 after Bonferroni)

Claude Code completed the prime-Sidon spectral detection test:
- 35 test cases
- 0/35 significant after Bonferroni correction
- Adversarial review caught a tautology in original methodology
- Null hypothesis properly added
- Negative finding is properly bounded

ENE database: session prime-sidon-negative-001 (promoted)
GitHub: commit a0d95049

This is a third measured data point for the octagon:
- Sidon sets: YES (4/4)
- Graph coloring: YES (Hoffman)
- Prime distribution: NO (0/35) ← NEW
- Graph isomorphism: NO (cospectral)
- Text: NO (3.088 b/B)

The octagon is NOT universal. It works for some problems and
fails for others. The research question: what determines which
problems have spectral signatures?

docs/living/DIRECTION_LOG.md

@@ -73,3 +73,41 @@ embedding that makes nonlinear properties spectrally detectable.
 **Why:** Braille/T9 on text: 4.167 b/B (dead). But the p-adic
 valuations (prime factorization) ARE the prime decomposition — the
 invariant signature. DNA carries invariants, not compressed bytes.
+
+## 2026-07-03: Prime-Sidon Hypothesis → Honest Negative
+
+**Was:** The prime number distribution has a Sidon-related spectral
+signature detectable via Perceval SLOS.
+
+**Result:** Honest negative. 35 test cases, 0/35 significant after
+Bonferroni correction. The adversarial review caught a tautology
+in the original methodology (which would have produced false
+positives), added the null hypothesis, and the negative finding
+is properly bounded.
+
+**What this means:** The prime distribution does NOT have a
+Sidon-detectable spectral signature through the SLOS pipeline.
+This is a measured negative — it clears the question off the board.
+
+**Recorded in:**
+- ENE database: session prime-sidon-negative-001 (promoted)
+- ENE packages: prime-sidon-pkg-001 (verified, promoted)
+- ENE receipts: negative_result (verified)
+- ENE ingest_events: prime-ingest-001 (recorded)
+- GitHub: commit a0d95049
+
+**Implication for the octagon:** primes don't have the spectral
+signature that Sidon sets do. The octagon works for Sidon (4/4)
+but NOT for primes (0/35). This is a third data point:
+
+| Problem | Octagon works? | Evidence |
+|---------|----------------|----------|
+| Sidon sets | YES | 4/4 (measured) |
+| Graph coloring | YES | Hoffman bound (known) |
+| Prime distribution | NO | 0/35 after Bonferroni (measured) |
+| Graph isomorphism | NO | Cospectral graphs (known) |
+| Text | NO | 3.088 b/B (measured) |
+
+The octagon is NOT universal. It works for some problems and
+fails for others. The research question is now: what determines
+which problems have spectral signatures?

docs/living/TARGETS.md

@@ -96,3 +96,11 @@ is the P vs NP experimental program's first NP-complete test case.
 with eigenvalue product computation (O(n^m)). Only works for linear
 systems. Needs: verify eigenvalue products match SLOS output on
 the Sidon crossing matrix.
+
+## ~~Prime-Sidon spectral detection~~ [DEAD — 2026-07-03]
+
+**Result:** Honest negative. 35 test cases, 0/35 significant after
+Bonferroni. The prime distribution does NOT have a Sidon-detectable
+spectral signature through SLOS. Adversarial review caught a tautology
+in the original methodology, null was properly added, negative is
+bounded. ENE session: prime-sidon-negative-001 (promoted).