[{"type":"thinking","thinking":"Now write the E-001 verification script per the numerics conventions (deterministic, CSV+JSON output, db registration). Task 0.4: verify R(ψ₀)=4/3 and R(ψ_MT)=½+(1/√2)cot(1/√2) symbolically.\n\nScript: research/numerics/scripts/E-001-window-constants.py\n- Symbolic: define R(ψ) quotient; compute for ψ₀ and ψ_MT via sympy integration; assert equality with 4/3 and ½+(1/√2)cot(1/√2).\n- Numeric: mpmath high-precision values of 2−R and (3−R)/2.\n- Output CSV: window, R symbolic, R numeric, 2−R, (3−R)/2.\n- JSON sidecar with metadata.\n\nThen run, register experiment in db, commit. Also mark 0.4 [x].","signature":""},{"type":"text","text":"Stack installed. Writing the 0.4 verification script following the numerics conventions (deterministic, CSV+JSON dual output)."},{"type":"tool_use","id":"Write_78","name":"Write","input":{"file_path":"D:\\Python\\Quantum\\research\\numerics\\scripts\\E-001-window-constants.py","content":"\"\"\"E-001 — Task 0.4: symbolic + numeric verification of window constants.\n\nR(psi) := [∫ψ² + ∬|u−v|ψ(u)ψ(v)dudv] / (∫ψ)²   on [−1/2, 1/2], ψ even.\n\nClaims verified (paper Lemma 5.6; hand-derived in D-004 §7):\n  R(ψ₀)   = 4/3                        (ψ₀ = indicator)\n  R(ψ_MT) = 1/2 + (1/√2)cot(1/√2)      (ψ_MT = cos(√2 s))\nand the certificates 2 − R(ψ), (3 − R(ψ))/2.\n\nOutputs: research/numerics/data/E-001-window-constants.csv (+ .json sidecar)\n\"\"\"\nimport json\nimport sys\nfrom datetime import datetime, timezone\nfrom pathlib import Path\n\nimport mpmath as mp\nimport sympy as sp\n\nREPO = Path(__file__).resolve().parents[3]\nDATA = REPO / \"research\" / \"numerics\" / \"data\"\nDPS = 50\n\nu, v = sp.symbols(\"u v\", real=True)\nhalf = sp.Rational(1, 2)\n\n\ndef R_symbolic(psi):\n    \"\"\"Compute R(ψ) symbolically for even ψ on [-1/2, 1/2].\"\"\"\n    num1 = sp.integrate(psi**2, (u, -half, half))\n    # ∬|u−v|ψ(u)ψ(v) = 2∫_{u>v}(u−v)ψ(u)ψ(v)  (integrand symmetric)\n    inner = sp.integrate((u - v) * psi.subs(u, v), (v, -half, u))\n    num2 = 2 * sp.integrate(sp.simplify(psi * inner), (u, -half, half))\n    den = sp.integrate(psi, (u, -half, half)) ** 2\n    return sp.simplify((num1 + num2) / den)\n\n\ndef main() -> int:\n    mp.mp.dps = DPS\n    ok = True\n\n    psi0 = sp.Integer(1)\n    psiMT = sp.cos(sp.sqrt(2) * u)\n\n    R0 = R_symbolic(psi0)\n    RMT = R_symbolic(psiMT)\n    RMT_claim = sp.Rational(1, 2) + sp.cot(1 / sp.sqrt(2)) / sp.sqrt(2)\n\n    checks = []\n    checks.append((\"R(psi0) == 4/3\",\n                   sp.simplify(R0 - sp.Rational(4, 3)) == 0, R0))\n    checks.append((\"R(psiMT) == 1/2 + (1/sqrt2)cot(1/sqrt2)\",\n                   sp.simplify(RMT - RMT_claim) == 0, RMT))\n\n    rows = []\n    for name, R in [(\"psi0\", sp.Rational(4, 3)), (\"psiMT\", RMT_claim)]:\n        Rm = mp.mpf(sp.N(R, 60))\n        rows.append({\n            \"window\": name,\n            \"R_exact\": str(R),\n            \"R_numeric\": mp.nstr(Rm, 30),\n            \"2_minus_R\": mp.nstr(2 - Rm, 30),\n            \"distinct_(3-R)/2\": mp.nstr((3 - Rm) / 2, 30),\n        })\n\n    for label, passed, val in checks:\n        print(f\"[{'PASS' if passed else 'FAIL'}] {label}  (got {val})\")\n        ok &= passed\n\n    print(\"\\nCertificates:\")\n    for r in rows:\n        print(f\"  {r['window']:>6}: R = {r['R_numeric']}\")\n        print(f\"         2 - R = {r['2_minus_R']}   (3-R)/2 = {r['distinct_(3-R)/2']}\")\n\n    csv_path = DATA / \"E-001-window-constants.csv\"\n    json_path = DATA / \"E-001-window-constants.json\"\n    if csv_path.exists() and \"--force\" not in sys.argv:\n        print(f\"\\ncached: {csv_path} exists (use --force to recompute)\")\n        return 0 if ok else 1\n\n    with csv_path.open(\"w\", encoding=\"utf-8\", newline=\"\") as f:\n        f.write(\",\".join(rows[0].keys()) + \"\\n\")\n        for r in rows:\n            f.write(\",\".join(r.values()) + \"\\n\")\n\n    meta = {\n        \"experiment\": \"E-001\",\n        \"task\": \"0.4\",\n        \"description\": \"Symbolic+numeric verification of R(psi0)=4/3 and \"\n                       \"R(psiMT)=1/2+(1/sqrt(2))cot(1/sqrt(2)); certificates \"\n                       \"2-R and (3-R)/2\",\n        \"script\": \"research/numerics/scripts/E-001-window-constants.py\",\n        \"parameters\": {\"windows\": [\"psi0\", \"psiMT\"], \"dps\": DPS},\n        \"symbolic_checks\": {label: passed for label, passed, _ in checks},\n        \"timestamp_utc\": datetime.now(timezone.utc).isoformat(),\n        \"row_count\": len(rows),\n    }\n    json_path.write_text(json.dumps(meta, indent=2), encoding=\"utf-8\")\n    print(f\"\\nwrote {csv_path.name}, {json_path.name}\")\n    return 0 if ok else 1\n\n\nif __name__ == \"__main__\":\n    raise SystemExit(main())\n"},"extra_content":null}]