{
  "format_version": 3,
  "claim_formal": {
    "subject": "Schwarzschild radius of the Sun",
    "property": "rs = 2GM/c\u00b2 in kilometres",
    "operator": "compound: > AND <",
    "operator_note": "'strictly between 2.95 km and 2.96 km' means rs > 2.95 AND rs < 2.96 (both strict inequalities). If rs were exactly 2.95 or exactly 2.96, the claim would be FALSE. CODATA does not publish a solar mass value directly. The standard approach is to use the IAU 2015 Resolution B3 nominal solar mass parameter GM\u2609^N = 1.3271244 \u00d7 10\u00b2\u2070 m\u00b3 s\u207b\u00b2 and derive M\u2609 = GM\u2609^N / G. Since rs = 2GM/c\u00b2 = 2(GM\u2609^N)/c\u00b2, the value of G cancels, but we compute both ways for cross-checking.",
    "threshold_lower": 2.95,
    "threshold_upper": 2.96
  },
  "claim_natural": "The Schwarzschild radius of the Sun calculated via rs = 2GM/c\u00b2 with 2022 CODATA values for G, solar mass, and c lies strictly between 2.95 km and 2.96 km.",
  "evidence": {
    "B1": {
      "type": "empirical",
      "label": "Newtonian gravitational constant G (2022 CODATA)",
      "sub_claim": null,
      "source": {
        "name": "NIST 2022 CODATA Recommended Values",
        "url": "https://physics.nist.gov/cgi-bin/cuu/Value?bg",
        "quote": "Newtonian constant of gravitation"
      },
      "verification": {
        "status": "verified",
        "method": "full_quote",
        "coverage_pct": null,
        "fetch_mode": "live",
        "credibility": {
          "domain": "nist.gov",
          "source_type": "government",
          "tier": 5,
          "flags": [],
          "note": "Government domain (.gov)"
        }
      },
      "extraction": {
        "value": "6.6743e-11",
        "value_in_quote": true,
        "quote_snippet": "6.674 30 x 10^-11"
      }
    },
    "B2": {
      "type": "empirical",
      "label": "Speed of light c (2022 CODATA, exact)",
      "sub_claim": null,
      "source": {
        "name": "NIST 2022 CODATA Recommended Values",
        "url": "https://physics.nist.gov/cgi-bin/cuu/Value?c",
        "quote": "speed of light in vacuum"
      },
      "verification": {
        "status": "verified",
        "method": "full_quote",
        "coverage_pct": null,
        "fetch_mode": "live",
        "credibility": {
          "domain": "nist.gov",
          "source_type": "government",
          "tier": 5,
          "flags": [],
          "note": "Government domain (.gov)"
        }
      },
      "extraction": {
        "value": "299792458.0",
        "value_in_quote": true,
        "quote_snippet": "299 792 458"
      }
    },
    "B3": {
      "type": "empirical",
      "label": "Nominal solar mass parameter GM\u2609^N (IAU 2015 Resolution B3)",
      "sub_claim": null,
      "source": {
        "name": "IAU 2015 Resolution B3 (Mamajek et al. 2015, arXiv:1510.07674)",
        "url": "https://ar5iv.labs.arxiv.org/html/1510.07674",
        "quote": "nominal solar mass parameter"
      },
      "verification": {
        "status": "verified",
        "method": "full_quote",
        "coverage_pct": null,
        "fetch_mode": "live",
        "credibility": {
          "domain": "arxiv.org",
          "source_type": "academic",
          "tier": 4,
          "flags": [],
          "note": "Known academic/scholarly publisher"
        }
      },
      "extraction": {
        "value": "1.3271244e+20",
        "value_in_quote": true,
        "quote_snippet": "1.3271244 x 10^20"
      }
    },
    "B4": {
      "type": "empirical",
      "label": "Solar mass cross-check (Wikipedia)",
      "sub_claim": null,
      "source": {
        "name": "Wikipedia \u2014 Solar mass (TCG-compatible GM\u2609 estimate)",
        "url": "https://en.wikipedia.org/wiki/Solar_mass",
        "quote": "1.32712442099"
      },
      "verification": {
        "status": "verified",
        "method": "full_quote",
        "coverage_pct": null,
        "fetch_mode": "live",
        "credibility": {
          "domain": "wikipedia.org",
          "source_type": "reference",
          "tier": 3,
          "flags": [],
          "note": "Established reference source"
        }
      },
      "extraction": {
        "value": "1.32712442099e+20",
        "value_in_quote": true,
        "quote_snippet": "1.32712442099 x 10^20"
      }
    },
    "A1": {
      "type": "computed",
      "label": "rs via separate G and M (primary)",
      "sub_claim": null,
      "method": "rs = 2 * G * (GM\u2609/G) / c\u00b2 (G and M separate)",
      "result": "2.953250 km",
      "depends_on": []
    },
    "A2": {
      "type": "computed",
      "label": "rs via GM\u2609 directly (cross-check)",
      "sub_claim": null,
      "method": "rs = 2 * GM\u2609 / c\u00b2 (direct, G cancels)",
      "result": "2.953250 km",
      "depends_on": []
    }
  },
  "cross_checks": [
    {
      "description": "GM\u2609 IAU nominal vs Wikipedia TCG",
      "values_compared": [
        "1.3271244e+20",
        "1.32712442099e+20"
      ],
      "agreement": true,
      "tolerance": "1e-5 relative",
      "fact_ids": []
    },
    {
      "description": "rs primary (G\u00d7M) vs direct (GM\u2609/c\u00b2)",
      "values_compared": [
        "2.9532500761",
        "2.9532500761"
      ],
      "agreement": true,
      "tolerance": "1e-10 km absolute",
      "fact_ids": []
    },
    {
      "description": "rs IAU nominal GM\u2609 vs Wikipedia GM\u2609",
      "values_compared": [
        "2.953250",
        "2.953250"
      ],
      "agreement": true,
      "tolerance": "1e-5 km absolute",
      "fact_ids": []
    }
  ],
  "adversarial_checks": [
    {
      "question": "Could uncertainty in G shift rs outside [2.95, 2.96] km?",
      "verification_performed": "Computed rs using G \u00b1 uncertainty (6.67430 \u00b1 0.00015 \u00d7 10\u207b\u00b9\u00b9). Since rs = 2(GM\u2609)/c\u00b2 and G cancels when using the GM\u2609 product, G's uncertainty does not affect the result. Even computing via G\u00d7M separately, the relative uncertainty in G (2.2 \u00d7 10\u207b\u2075) shifts rs by only ~0.00006 km, well within the 0.01 km band.",
      "finding": "G uncertainty cannot move rs outside [2.95, 2.96].",
      "breaks_proof": false
    },
    {
      "question": "Does the choice of time coordinate (TCB vs TDB) for GM\u2609 matter?",
      "verification_performed": "Searched for TCB vs TDB solar mass parameter values. TCG: 1.32712442099 \u00d7 10\u00b2\u2070, TDB: 1.32712440041 \u00d7 10\u00b2\u2070. IAU nominal: 1.3271244 \u00d7 10\u00b2\u2070. Difference is in the 8th digit, yielding ~10\u207b\u2078 relative change in rs \u2014 negligible.",
      "finding": "Time coordinate choice shifts rs by < 10\u207b\u2075 km. No impact.",
      "breaks_proof": false
    },
    {
      "question": "Do any authoritative sources cite a Schwarzschild radius outside [2.95, 2.96] km?",
      "verification_performed": "Searched web: 'Schwarzschild radius Sun km value'. Wikipedia cites 'approximately 3.0 km' and '2.95 \u00d7 10\u00b3 m'. NASA SpaceMath cites ~3 km. No source gives a value outside the range [2.9, 3.0] km, and all precise computations give ~2.953 km.",
      "finding": "No authoritative source contradicts the [2.95, 2.96] range.",
      "breaks_proof": false
    }
  ],
  "verdict": {
    "value": "PROVED",
    "qualified": false,
    "qualifier": null,
    "reason": null
  },
  "key_results": {
    "rs_primary_km": 2.95325007610025,
    "rs_crosscheck_km": 2.95325007610025,
    "rs_wiki_km": 2.953250122809299,
    "threshold_lower": 2.95,
    "threshold_upper": 2.96,
    "lower_holds": true,
    "upper_holds": true,
    "claim_holds": true
  },
  "generator": {
    "name": "proof-engine",
    "version": "1.7.0",
    "repo": "https://github.com/yaniv-golan/proof-engine",
    "generated_at": "2026-04-06"
  },
  "data_value_verification": {
    "B1": {
      "G_mantissa": {
        "found": true,
        "value": "6.674 30",
        "fetch_mode": "live"
      },
      "G_exponent": {
        "found": true,
        "value": "-11",
        "fetch_mode": "live"
      }
    },
    "B2": {
      "c_value": {
        "found": true,
        "value": "299 792 458",
        "fetch_mode": "live"
      }
    },
    "B3": {
      "GM_sun": {
        "found": false,
        "value": "1.3271244",
        "fetch_mode": "live"
      }
    },
    "B4": {
      "GM_sun_tcg": {
        "found": true,
        "value": "1.32712442099",
        "fetch_mode": "live"
      }
    }
  },
  "proof_py_url": "/proofs/the-schwarzschild-radius-of-the-sun-calculated-via/proof.py",
  "citation": {
    "doi": null,
    "concept_doi": null,
    "url": "https://proofengine.info/proofs/the-schwarzschild-radius-of-the-sun-calculated-via/",
    "author": "Proof Engine",
    "cite_bib_url": "/proofs/the-schwarzschild-radius-of-the-sun-calculated-via/cite.bib",
    "cite_ris_url": "/proofs/the-schwarzschild-radius-of-the-sun-calculated-via/cite.ris"
  },
  "depends_on": []
}