{
  "prefix": {
    "pe": "https://proofengine.info/proofs/thank-god-2026-has-no-square-root-is-mathematically-meaningful/",
    "prov": "http://www.w3.org/ns/prov#",
    "xsd": "http://www.w3.org/2001/XMLSchema#",
    "schema": "http://schema.org/"
  },
  "entity": {
    "pe:claim": {
      "prov:type": "pe:Claim",
      "prov:label": "\"Thank God 2026 has no square root\" is mathematically meaningful",
      "prov:value": "\"Thank God 2026 has no square root\" is mathematically meaningful"
    },
    "pe:evidence-A1": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "isqrt(2026)\u00b2 \u2260 2026 (primary: no integer square root)",
      "pe:factId": "A1",
      "pe:evidenceType": "computed",
      "pe:method": "math.isqrt(2026) = 45; verified 45\u00b2 = 2025 \u2260 2026 and 46\u00b2 = 2116 \u2260 2026",
      "pe:result": "True"
    },
    "pe:evidence-A2": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "Prime factorisation of 2026 has no repeated factors (cross-check)",
      "pe:factId": "A2",
      "pe:evidenceType": "computed",
      "pe:method": "Prime factorisation: 2026 = 2\u00b9 \u00d7 1013\u00b9; both exponents are odd \u2192 not a perfect square (cross-check)",
      "pe:result": "True"
    },
    "pe:evidence-A3": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "45\u00b2 = 2025 (predecessor year is a perfect square \u2014 context)",
      "pe:factId": "A3",
      "pe:evidenceType": "computed",
      "pe:method": "math.isqrt(2025) = 45; verified 45\u00b2 = 2025 (context: predecessor year is a perfect square)",
      "pe:result": "True"
    },
    "pe:evidence-A4": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "\u221a2026 is irrational (consequence of A1/A2)",
      "pe:factId": "A4",
      "pe:evidenceType": "computed",
      "pe:method": "Valuation argument: v\u2082(2026) = 1 (odd); if \u221a2026 = p/q then 2\u00b7v\u2082(p) = 1 + 2\u00b7v\u2082(q) \u2014 even = odd, contradiction",
      "pe:result": "True"
    },
    "pe:verdict": {
      "prov:type": "pe:Verdict",
      "prov:label": "Verdict: PROVED",
      "prov:value": "PROVED"
    }
  },
  "activity": {
    "pe:determine-verdict": {
      "prov:type": "pe:VerdictDetermination",
      "prov:label": "Determine verdict from evidence",
      "prov:endTime": "2026-03-28"
    }
  },
  "agent": {
    "pe:proof-engine": {
      "prov:type": "prov:SoftwareAgent",
      "prov:label": "Proof Engine",
      "schema:version": "0.10.0",
      "schema:url": "https://github.com/yaniv-golan/proof-engine"
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  "wasGeneratedBy": {
    "pe:gen-verdict": {
      "prov:entity": "pe:verdict",
      "prov:activity": "pe:determine-verdict"
    }
  },
  "wasDerivedFrom": {},
  "wasAttributedTo": {
    "pe:attr-verdict": {
      "prov:entity": "pe:verdict",
      "prov:agent": "pe:proof-engine"
    }
  },
  "used": {
    "pe:used-A1": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A1"
    },
    "pe:used-A2": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A2"
    },
    "pe:used-A3": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A3"
    },
    "pe:used-A4": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A4"
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}