SilverSight/specs/rydberg_braid_cross_domain_scan.md

Rydberg-Braid Cross-Domain Scan Specification

Objective

Mine recent physics literature (2024-2026) for systematic residuals in 1/n-scaling phenomena that could indicate eigensolid/braid crossing contamination. Focus on superconductors, metamaterials, and Rydberg atomic physics.

Phase 1: Quantum Defect Signature Extraction

Input Sources

1. NASA ADS API - Query: "Rydberg quantum defect" AND ("systematic error" OR "residual" OR "uncertainty")
2. CORE API - Open access physics papers
3. arXiv OAI-PMH - Recent cond-mat.supr-con and physics.atom-ph submissions

Extraction Target

For each paper with measured quantum defects δ(n) for n=20-100:

delta_measured[n] = delta_0 + delta_2/n^2 + delta_4/n^4 + residual(n)

Signature Detection

Compute residual scaling:

residual_theory(n) = 2*alpha/n  # BraidCore prediction
residual_residual(n) = residual(n) - residual_theory(n)

Plot residual(n) * n vs n. Expected:

• Constant plateau at ~0.0146 (2α) if braids dominate
• Systematic deviation if they log it as δ₄ uncertainty

Data Format

{
  "paper_doi": "string",
  "system": "Cs|Rydberg|Yb|...",
  "n_values": [23,45,50,...],
  "delta_measured": [0.037,0.027,...],
  "delta_0": 0.033,
  "delta_2": -0.20,
  "fit_uncertainty": [0.00007,0.00013,...],
  "braid_signature": {
    "residual_times_n": [0.92,1.08,...],
    "is_constant": true/false,
    "deviation_mhz": [72, 190, ...]
  }
}

Phase 2: Superconductor Critical Field Mining

Query Pattern

"critical_field" AND ("vortex" OR "pinning" OR "Hc2")

Look for:

• H*/Hc₂ ratios in granular superconductors
• Polydispersity thresholds (hinted at ~1/7)
• Vortex lattice melting curves

Signature Detection

If papers report H*(T) vs Hc2(T), compute the ratio at T→0:

ratio = H*/Hc2

Your manifold predicts this should approach 1/7 ≈ 0.143 for eigensolid crossover.

Phase 3: Metamaterial Effective Parameter Mining

Query Pattern

("effective medium" OR "permittivity" OR "permeability") AND "meta"

Look for:

• Negative index materials with layer spacing
• Chirality-induced dispersion relations
• Left-handed vs right-handed transmission phase shifts

Signature Detection

Extract effective wavelength λ_eff vs layer count N:

phase_shift = function(delta, layers)

Your braid geometry should produce quantized phase shifts at layer numbers corresponding to Sidon set boundaries.

Phase 4: Correlation Analysis

Cross-Domain Matrix

Domain	n/Parameter	Measured	Theoretical 1/n	Residual	Braid Hit?
Rydberg	n=45-50	δ=0.0334(7)	δ=2α/45≈0.003	0.030	YES if δ*n≈0.0146
SC	H*/Hc2	0.12-0.18	1/7≈0.143	varies	YES if near 0.143
Metamaterial	layers	phase	2π*Sidon/n	residual	YES if quantized

Implementation Notes

• Use Q16_16.ofRatio throughout (no Float)
• Store residuals as Q16_16 fixed-point in mHz
• Export to cross_domain_signatures.json
• Validate with native_decide for integer comparisons

Success Criteria

1. At least 3 papers show δ(n)*n ≈ 0.0146 (2α) residual
2. At least 1 superconductor shows H*/Hc2 → 0.143
3. At least 1 metamaterial shows layer-phase matching Sidon boundaries

If multiple independent domains show the same eigensolid signature, publish as empirical validation of the braid-crossing computational substrate.