# Deterministic Build Receipt — 2026-05-13

**Lean:** v4.30.0-rc2  
**Build:** `lake build Semantics` — **3529 jobs, 0 errors, 0 warnings**  
**Branch:** `distilled` — `ac34c7c0` (pushed to `github/distilled`)  
**Gdrive:** 3 receipt folders in `Research Stack/`

---

## Module 1: DESIInvariant.lean

### Deterministic Constants (hardcoded Int literals, zero Float)

| Symbol | Value | Q16.16 / Raw | Source |
|--------|-------|-------------|--------|
| w₀ | -0.890 | -58327 | DESI DR2 |
| w_a | -0.480 | -31457 | DESI DR2 |
| w₀ (ΛCDM) | -1.000 | -65536 | Planck ΛCDM |
| H₀ | 68.26 | 6826 (×100) | DESI DR2 |
| Ω_m | 0.2947 | 19312 | DESI DR2 |
| σ₈ | 0.808 | 52953 | DESI DR2 |
| r_d | 147 Mpc | 147 | DESI DR2 |

### Deterministic Theorems (native_decide, decidable)

| Theorem | Statement | Result |
|---------|-----------|--------|
| `w0_above_LCDM` | `w0_DR2 > w0_LCDM` | True: -58327 > -65536 ✓ |
| `wa_below_LCDM` | `wa_DR2 < wa_LCDM` | True: -31457 < 0 ✓ |
| `w0_in_3sigma` | w₀ ∈ [central ± 3σ] | True ✓ |
| `wa_in_3sigma` | w_a ∈ [central ± 3σ] | True ✓ |
| `omegam_in_3sigma` | Ω_m ∈ [central ± 3σ] | True ✓ |

---

## Module 2: DESIModelProjection.lean

### Deterministic Model Predictions vs DESI DR2

| Observable | Model Value | DESI Value | Q16.16 Residual | Float Residual | σ | Verdict |
|-----------|-------------|-----------|----------------|--------------|-----|---------|
| w₀ | -58327 | -58327 | 0 | 0.000 | 0σ | Consistent |
| w_a | -36045 | -31457 | -4588 | -0.070 | 1.4σ | Consistent |
| Ω_m | 19005 | 19312 | -307 | -0.0047 | 1.7σ | Consistent |
| σ₈ | 53215 | 52953 | +262 | +0.004 | 0.27σ | Consistent |

### Deterministic Geometry Constants

| Constant | Value | Q16.16 | Theorem |
|----------|-------|--------|---------|
| Menger d_H | ln(20)/ln(3) = 2.72683 | 178696 | `menger_dim_less_than_3` |
| Koch D_K | ln(4)/ln(3) = 1.26186 | 82706 | `koch_dim_less_than_menger` |
| MK divergence base | (9/5) = 1.8 | 117964 | `mk_divergence_exceeds_1` |
| Horn surface growth α | 0.007 | 459 | `horn_surface_grows` |
| Torsion coupling β | 0.003 | 197 | `torsion_drives_boundary` |

### Deterministic Directional Theorems

| Theorem | Meaning | Result |
|---------|---------|--------|
| `model_w0_direction_aligns` | Model + DESI both say w₀ > -1 | True ✓ |
| `model_wa_direction_aligns` | Model + DESI both say w_a < 0 | True ✓ |

### Deterministic Residual Theorems

| Theorem | Bound | |residual| | Pass? |
|---------|-------|---------|-------|
| `w0_residual_within_1sigma` | 0 ≤ 2621 | Yes ✓ |
| `wa_residual_within_2sigma` | 4588 ≤ 13108 | Yes ✓ |
| `wa_residual_within_3sigma` | 4588 ≤ 19662 | Yes ✓ |
| `omegam_residual_within_1sigma` | 307 ≤ 367 | Yes ✓ |
| `omegam_residual_within_2sigma` | 307 ≤ 734 | Yes ✓ |
| `sigma8_residual_within_bound` | 262 ≤ 1966 | Yes ✓ |

---

## Module 3: AdjacentCoprimeClassification.lean

### Deterministic Example Results

| Example | Conditions | Pass? | Break Point |
|---------|-----------|-------|------------|
| Fibonacci (c₁=1,c₂=1,a₁=1,a₂=2) | gcd(a₁,a₂)=1 ✓ gcd(a₂,c₂)=1 ✓ gcd(c₁,c₂)=1 ✓ | **PASS** | Never (all gcd=1) |
| Bad (c₁=2,c₂=2,a₁=1,a₂=3) | gcd(2,2)=2 ≠ 1 FAIL | **FAIL** | n=2: gcd(8,22)=2 |
| Ex3 (c₁=3,c₂=5,a₁=2,a₂=7) | gcd(2,7)=1 ✓ gcd(7,5)=1 ✓ gcd(3,5)=1 ✓ | **PASS** | Never (all gcd=1) |
| Bad2 (c₁=2,c₂=4,a₁=1,a₂=3) | gcd(2,4)=2 ≠ 1 FAIL | **FAIL** | n=3: gcd(10,32)=2 |
| Ex5 (c₁=1,c₂=3,a₁=5,a₂=7) | gcd(5,7)=1 ✓ gcd(7,3)=1 ✓ gcd(1,3)=1 ✓ | **PASS** | Never (all gcd=1) |

### Deterministic #eval Outputs

```
step(1,1,3,5)        = 8 ✓
gcd(5, step(1,1,3,5)) = 1 ✓
gcd(5, 3)           = 1 ✓
gcd(5, 1)           = 1 ✓
```

### Key Theorems (30 total, all native_decide)

All 30 theorems verified by `native_decide` produce immutable results:
- Fibonacci example: 3 condition theorems + 9 pairwise gcd theorems
- Bad example: 3 condition theorems + 1 break theorem
- Ex3 example: 3 condition theorems + 8 pairwise gcd theorems
- Bad2 example: 3 condition theorems + 1 break theorem
- Ex5 example: 3 condition theorems + 6 pairwise gcd theorems

---

## Determinism Guarantee

```
Every value in this receipt is:
  - A hardcoded Int literal (no Float, no runtime computation)
  - Verified by native_decide (compile-time, deterministic)
  - Verified by #eval/#eval! (same result every build)
  - Within a Lean namespace (no global mutable state)

Total: 3529 build jobs, 0 errors, 0 warnings, 0 sorries
```