{
  "file_path": "D:\\Python\\Quantum\\NGUYEN.md",
  "old_string": "- [~] 5.1 Lean 4 formalization of all new lemmas (build on zeta-23-lean).\n      \u2192 SKELETON STAGE COMPLETE (session 010, D-061): NguyenRH1 package\n      (research/lean/NguyenRH1/) \u2014 9 statements compile against\n      Mathlib + Zeta23 types. **TIER (i) COMPLETE (session 011)**:\n      chain_rule_sqrt_shift, sInfty_lower_bound, marginTilde_convex\n      PROVED (~1100 lines; full support library \u2014 see journal-011).\n      **TIER (ii) STEPS 1+2 COMPLETE (session 012, D-062)**:\n      lambda_pos_finite_height_verified PROVED modulo the single named\n      analytic hypothesis SfBoundProp + the declared computational\n      perimeter (assembly-first split per session-012-notes; FAlt\n      majorant swap; secant two-point base; base points discharged by\n      certified interval bounds in LiBasePoints.lean \u2014 margin\u0303(8\u00d710\u2074)\n      \u2265 8001 certified, margin\u0303(10\u2075) \u2265 85 501 certified).\n      Remaining: tier ii\u2032 (SfBoundProp contour layers L0\u2013L3 \u2014\n      POST-PUBLICATION per session-012-end-notes review; Trudgian\n      N(T)/S(T) = declared perimeter, D-062 \u00a74), (iii) valley,\n      (iv) Suzuki.",
  "new_string": "- [~] 5.1 Lean 4 formalization of all new lemmas (build on zeta-23-lean).\n      \u2192 SKELETON STAGE COMPLETE (session 010, D-061): NguyenRH1 package\n      (research/lean/NguyenRH1/) \u2014 9 statements compile against\n      Mathlib + Zeta23 types. **TIER (i) COMPLETE (session 011)**:\n      chain_rule_sqrt_shift, sInfty_lower_bound, marginTilde_convex\n      PROVED (~1100 lines; full support library \u2014 see journal-011).\n      **TIER (ii) STEPS 1+2 COMPLETE (session 012, D-062)**:\n      lambda_pos_finite_height_verified PROVED modulo the single named\n      analytic hypothesis SfBoundProp + the declared computational\n      perimeter (assembly-first split per session-012-notes; FAlt\n      majorant swap; secant two-point base; base points discharged by\n      certified interval bounds in LiBasePoints.lean \u2014 margin\u0303(8\u00d710\u2074)\n      \u2265 8001 certified, margin\u0303(10\u2075) \u2265 85 501 certified).\n      **TIER ii\u2032 LAUNCHED (session 014, user directive \u2014 BEFORE\n      submission, option (a); design D-064)**: TWO DISCOVERIES \u2014\n      (1) liCoeff encoding defect (unordered tsum NOT Summable \u27f9 junk;\n      LiVerifiedUpTo/SfBoundProp FALSE as encoded; paired-form fix =\n      ii\u2032-1a); (2) crux identity Sf(n) = Res\u2081(n) EXACT (numerically\n      verified vs E-015/E-021) \u27f9 assembly TAIL-FREE. Routes R1\u2013R5;\n      sub-stage map ii\u2032-1a..7 (~9\u201316 sessions); perimeter unchanged\n      (Trudgian N(T)/S(T) declared, D-062 \u00a74). Freeze protocol: paper\n      files + existing proofs untouched until ii\u2032-7 (liCoeff fix\n      excepted). Remaining after ii\u2032: (iii) valley, (iv) Suzuki."
}