# Proof: The Schwarzschild radius of the Sun lies strictly between 2.95 km and 2.96 km

- **Generated:** 2026-03-28
- **Verdict:** PROVED
- **Audit trail:** [proof_audit.md](proof_audit.md) | [proof.py](proof.py)

## Key Findings

- The Schwarzschild radius rs = 2GM/c² evaluates to **2.953250 km** using the IAU 2015 nominal solar mass parameter and 2022 CODATA speed of light.
- 2.953250 km > 2.95 km and 2.953250 km < 2.96 km — both strict inequalities hold.
- Two independent computation paths (G and M separately vs GM☉ directly) yield identical results to 10 significant figures.
- A third computation using the more precise Wikipedia TCG-compatible GM☉ gives 2.953250 km, confirming the result.

## Claim Interpretation

**Claim:** "The Schwarzschild radius of the Sun calculated via rs = 2GM/c² with 2022 CODATA values for G, solar mass, and c lies strictly between 2.95 km and 2.96 km."

**Formal interpretation:** rs > 2.95 km AND rs < 2.96 km (both strict). If rs were exactly 2.95 or 2.96, the claim would be false.

**Source substitution:** CODATA does not publish a solar mass value. The standard approach uses the IAU 2015 Resolution B3 nominal solar mass parameter GM☉^N = 1.3271244 × 10²⁰ m³ s⁻² and derives M☉ = GM☉^N / G. Since rs = 2GM/c² = 2(GM☉^N)/c², the value of G cancels in the computation, but both paths are computed for cross-checking.

## Evidence Summary

| ID | Fact | Verified |
|----|------|----------|
| B1 | Newtonian gravitational constant G (2022 CODATA) | Yes |
| B2 | Speed of light c (2022 CODATA, exact) | Yes |
| B3 | Nominal solar mass parameter GM☉^N (IAU 2015 Resolution B3) | Yes |
| B4 | Solar mass cross-check (Wikipedia) | Yes |
| A1 | rs via separate G and M (primary) | Computed: 2.953250 km |
| A2 | rs via GM☉ directly (cross-check) | Computed: 2.953250 km |

## Proof Logic

The Schwarzschild radius is defined by rs = 2GM/c², where G is the gravitational constant, M is the mass of the object, and c is the speed of light.

**Constants used:**
- G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (B1, 2022 CODATA)
- c = 299 792 458 m s⁻¹ (B2, 2022 CODATA, exact by definition)
- GM☉^N = 1.3271244 × 10²⁰ m³ s⁻² (B3, IAU 2015 Resolution B3 nominal value)

**Primary computation (A1):** Derive M☉ = GM☉^N / G = 1.988410 × 10³⁰ kg, then compute rs = 2GM☉/c² = 2953.250 m = 2.953250 km.

**Cross-check (A2):** Compute rs = 2(GM☉^N)/c² directly, bypassing the G decomposition. Result: 2.953250 km — identical to A1 (G cancels algebraically).

**Independent source cross-check:** Using the Wikipedia TCG-compatible GM☉ = 1.32712442099 × 10²⁰ m³ s⁻² (B4), rs = 2.953250 km, agreeing within 5 × 10⁻⁸ km.

Since 2.95 < 2.953250 < 2.96, both strict inequalities hold.

## Counter-Evidence Search

- **G uncertainty:** The relative uncertainty in G (2.2 × 10⁻⁵) would shift rs by only ~0.00006 km. Since G cancels when using GM☉ directly, this uncertainty is irrelevant to the primary computation.
- **Time coordinate choice (TCB vs TDB):** Different time coordinates for GM☉ differ in the 8th significant digit, shifting rs by < 10⁻⁵ km — negligible.
- **External sources:** Wikipedia cites "approximately 3.0 km" and "2.95 × 10³ m"; NASA SpaceMath cites ~3 km. No authoritative source gives a value outside [2.9, 3.0] km.

## Conclusion

**PROVED.** The Schwarzschild radius of the Sun, computed as rs = 2GM/c² = 2.953250 km, lies strictly between 2.95 km and 2.96 km. All four sources are fully verified: NIST CODATA for G and c, IAU 2015 Resolution B3 for GM☉, and the Wikipedia cross-check for GM☉ (TCG-compatible).

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Generated by [proof-engine](https://github.com/yaniv-golan/proof-engine) v0.10.0 on 2026-03-28.