# 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
```json
{
  "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.