# R3: Tier-3 Mineral Control Result

Date: 2026-04-02
Packet: ULP-CTM-159
Work Group: D (Tier-3 Control Execution)

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## Reconstruction Method

For each selected mineral, apply the reconstruction function phi(S(t), BC) -> R(t):
1. Specify S(t): formation temperature (T) and pressure (P)
2. Specify BC: chemical composition of the system (bulk composition of melt, solution, or vapor)
3. Use published phase diagrams to predict the equilibrium crystal structure R(t)
4. Compare prediction with observed crystal structure

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## Selected Minerals And Results

### Polymorph Sets (Same composition, different structures at different conditions)

| # | System | S(t): T, P | BC: Composition | Predicted R(t) | Observed R(t) | Correct? |
|---|--------|-----------|----------------|----------------|---------------|----------|
| 1 | SiO2 | 25°C, 1 atm | Pure SiO2 | alpha-quartz (trigonal) | alpha-quartz | YES |
| 2 | SiO2 | 1700°C, 1 atm | Pure SiO2 | cristobalite (cubic) | cristobalite | YES |
| 3 | SiO2 | 600°C, 20 kbar | Pure SiO2 | coesite (monoclinic) | coesite | YES |
| 4 | CaCO3 | 25°C, 1 atm | Pure CaCO3, low Mg | calcite (trigonal) | calcite | YES |
| 5 | CaCO3 | 25°C, 10 kbar | Pure CaCO3 | aragonite (orthorhombic) | aragonite | YES |
| 6 | Carbon | 25°C, 1 atm | Pure C | graphite (hexagonal) | graphite | YES |
| 7 | Carbon | 5 GPa, 1500°C | Pure C | diamond (cubic) | diamond | YES |
| 8 | Al2SiO5 | 500°C, 4 kbar | Pure Al2SiO5 | kyanite (triclinic) | kyanite | YES |
| 9 | Al2SiO5 | 800°C, 2 kbar | Pure Al2SiO5 | sillimanite (orthorhombic) | sillimanite | YES |
| 10 | Al2SiO5 | 400°C, 1 kbar | Pure Al2SiO5 | andalusite (orthorhombic) | andalusite | YES |

### Common Rock-Forming Minerals

| # | System | S(t): T, P | BC: Composition | Predicted R(t) | Observed R(t) | Correct? |
|---|--------|-----------|----------------|----------------|---------------|----------|
| 11 | NaCl | 25°C, 1 atm | NaCl from evaporite | halite (cubic) | halite | YES |
| 12 | Fe2O3 | Surface conditions | Oxidizing | hematite (trigonal) | hematite | YES |
| 13 | FeS2 | Hydrothermal, ~300°C | Fe + S in solution | pyrite (cubic) | pyrite | YES |
| 14 | Mg2SiO4 | 1300°C, 30 kbar | Peridotite bulk comp | forsterite/olivine | olivine | YES |
| 15 | CaMgSi2O6 | 1200°C, 1 atm | Basaltic melt | diopside (monoclinic) | diopside | YES |
| 16 | KAlSi3O8 | 700°C, 2 kbar | Granitic melt | orthoclase (monoclinic) | orthoclase | YES |
| 17 | NaAlSi3O8 | 700°C, 2 kbar | Granitic melt | albite (triclinic) | albite | YES |
| 18 | ZrSiO4 | 800°C, granitic | Zr-bearing melt | zircon (tetragonal) | zircon | YES |
| 19 | CaSO4 2H2O | 25°C, 1 atm | Ca + SO4 solution | gypsum (monoclinic) | gypsum | YES |

### Boundary / Complication Cases

| # | System | S(t): T, P | BC: Composition | Predicted R(t) | Observed R(t) | Correct? |
|---|--------|-----------|----------------|----------------|---------------|----------|
| 20 | SiO2 | Rapid cooling from melt | Pure SiO2 | Glass (amorphous) given rapid cooling BC; quartz/cristobalite given slow cooling BC | Glass if rapid; crystal if slow | YES (BC includes cooling rate) |

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## Reconstruction Success Rate

| Category | Count | Correct | Rate |
|----------|-------|---------|------|
| Polymorph sets | 10 | 10 | 100% |
| Common minerals | 9 | 9 | 100% |
| Boundary cases | 1 | 1 | 100% (with BC including cooling rate) |
| **Total** | **20** | **20** | **100%** |

**Success rate: 20/20 = 100%**

Threshold: > 80%. Result: 100%.

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## Interpretation Against Thresholds

| Metric | Threshold | Observed | Verdict |
|--------|----------|---------|---------|
| Reconstruction success | > 80% | 100% | **PASS** |

The pre-S6 reconstruction function phi(S(t), BC) -> R(t) exists and succeeds completely for the selected mineral set. Given T, P, and composition, the equilibrium crystal structure is fully determined.

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## Why 100% Is Not Suspicious

One might worry that 100% success means the test was too easy or the minerals were cherry-picked. Three responses:

1. **The minerals were selected for well-constrained formation conditions** (per protocol). The selection criterion was "formation conditions known from published petrology." This naturally selects minerals where the phase diagram is well-characterized — but that IS the point. Pre-S6, R(t) should be deterministic from S(t) + BC. The fact that well-characterized minerals achieve 100% reconstruction is exactly the expected result.

2. **The boundary case (rapid cooling -> glass) was included specifically to test the BC-dependence edge.** The result was correct: the phase diagram predicts glass at rapid cooling rates and crystal at slow cooling rates. The BC (cooling rate) is the determinant.

3. **Minerals with disputed phase boundaries or poorly constrained formation conditions were excluded** (per the exclusion criteria in R0). Including them would add noise without adding signal — the test is designed to ask whether phi EXISTS for well-constrained pre-S6 systems, not whether ALL pre-S6 systems are well-constrained.

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## The Paired Comparison

| | Pre-S6 (Crystal) | Post-S6 (Bacterium) |
|---|---|---|
| Can S(t) + BC reconstruct R(t)? | **YES** | **NO** |
| Reconstruction success rate | 100% (20/20) | ~0% (0/5 pairs have matching genomes) |
| Independence ratio | ~0.00 (all structure is S(t)+BC-determined) | ~0.999 (essentially all sequence is S(t)+BC-free) |
| phi exists? | **YES** | **NO** |

**The contrast is the result.**

The same formal question — can S(t) + BC determine R(t)? — yields opposite answers in the two regimes:
- Pre-S6: YES. Crystal structures are thermodynamically determined. R(t) is a function of S(t) + BC.
- Post-S6: NO. Genome sequences are overwhelmingly not thermodynamically determined. R(t) carries ~99.9% independent information.

The transition from dependent to independent occurs at the S6 boundary — the point where self-replicating, encoding, record-bearing life appears.

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## Tier-3 Final Verdict

**PASS.** Reconstruction success 100% (threshold: > 80%). The pre-S6 control confirms that R(t) IS reconstructable from S(t) + BC in the physical regime. The contrast with the post-S6 arm is overwhelming.