← Session 27 — ii′-5c/5d: Davenport disc + FE-reflection bounds
thinking (1421 chars)
Now I have the design. Let me look at the current LiDisc.lean capstone and relevant parts, plus check what exists in LiContour.lean (zeroMult_neg_two) and the Zeta23 seams I'll need:
1. `RvM.completedRiemannZeta_eq_Gammaℝ_mul` (module Zeta23.RvM.CountByIntegral)
2. `completedRiemannZeta_one_sub` (Mathlib)
3. `completedRiemannZeta_eq_zero_iff` (Zeta23)
4. `RvM.logDeriv_Gammaℝ`
5. `digamma_apply_add_one` (Mathlib)
6. `StirlingVert.digamma_stirling` (Zeta23)
Let me plan the task. This is a Lean formalization task. Let me create a task list:
1. Read LiDisc.lean capstone (logDeriv_riemannZeta_sub_nearZeros_le) to see exact statement shape and nearZeros definition
2. Inventory the Zeta23/Mathlib seams live (grep the vendored repo)
3. Build ii′-5d part 1: FE logDeriv identity (ζ′/ζ(s) = −ζ′/ζ(1−s) − [ΓR′/ΓR(1−s) + ΓR′/ΓR(s)])
4. Part 2: zero-sum cancellation (reflection finset map + mult_reflect)
5. Part 3: ΓR-bracket bound via digamma shift + digamma_stirling
6. Part 4: left-plane uniform digamma bound |ψ(w) − log w| ≤ C away from poles
7. Assembly: the left-half R-bound
8. Optionally: zeroMult(−2n) = 1 for all n (can slip)
9. Build green + axiom audit
10. Session closure (journal, STATE, NGUYEN, db, commit)
Let me start by reading the LiDisc.lean file to see the capstone and nearZeros definition. The file is probably large (~1000+ lines added in session 024). Let me search for key definitions first.
Design loaded. Let me set up the task list and inspect the current Lean state.
tool: TodoWrite
input
{
"todos": [
{
"content": "Survey seams: LiDisc capstone, nearZeros def, Zeta23 RvM/StirlingVert APIs",
"status": "in_progress",
"activeForm": "Surveying seams and APIs"
},
{
"content": "Build FE logDeriv identity: \u03b6\u2032/\u03b6(s) = \u2212\u03b6\u2032/\u03b6(1\u2212s) \u2212 [\u0393R\u2032/\u0393R(1\u2212s) + \u0393R\u2032/\u0393R(s)]",
"status": "pending",
"activeForm": "Building FE logDeriv identity"
},
{
"content": "Prove zero-sum cancellation under s \u21a6 1\u2212s reflection (finset map + mult match)",
"status": "pending",
"activeForm": "Proving zero-sum cancellation"
},
{
"content": "Bound \u0393R-bracket: digamma shift +2 then StirlingVert.digamma_stirling",
"status": "pending",
"activeForm": "Bounding \u0393R-bracket"
},
{
"content": "Left-plane uniform digamma bound |\u03c8(w) \u2212 log w| \u2264 C away from poles",
"status": "pending",
"activeForm": "Proving left-plane digamma bound"
},
{
"content": "Assemble left-half R-bound theorem + build green",
"status": "pending",
"activeForm": "Assembling left-half R-bound"
},
{
"content": "Axiom audit new decls",
"status": "pending",
"activeForm": "Auditing axioms"
},
{
"content": "Session closure: journal, STATE, NGUYEN, db, commit",
"status": "pending",
"activeForm": "Closing session"
}
]
}
raw content_json (database row)
[{"type":"thinking","thinking":"Now I have the design. Let me look at the current LiDisc.lean capstone and relevant parts, plus check what exists in LiContour.lean (zeroMult_neg_two) and the Zeta23 seams I'll need:\n\n1. `RvM.completedRiemannZeta_eq_Gammaℝ_mul` (module Zeta23.RvM.CountByIntegral)\n2. `completedRiemannZeta_one_sub` (Mathlib)\n3. `completedRiemannZeta_eq_zero_iff` (Zeta23)\n4. `RvM.logDeriv_Gammaℝ`\n5. `digamma_apply_add_one` (Mathlib)\n6. `StirlingVert.digamma_stirling` (Zeta23)\n\nLet me plan the task. This is a Lean formalization task. Let me create a task list:\n\n1. Read LiDisc.lean capstone (logDeriv_riemannZeta_sub_nearZeros_le) to see exact statement shape and nearZeros definition\n2. Inventory the Zeta23/Mathlib seams live (grep the vendored repo)\n3. Build ii′-5d part 1: FE logDeriv identity (ζ′/ζ(s) = −ζ′/ζ(1−s) − [ΓR′/ΓR(1−s) + ΓR′/ΓR(s)])\n4. Part 2: zero-sum cancellation (reflection finset map + mult_reflect)\n5. Part 3: ΓR-bracket bound via digamma shift + digamma_stirling\n6. Part 4: left-plane uniform digamma bound |ψ(w) − log w| ≤ C away from poles\n7. Assembly: the left-half R-bound\n8. Optionally: zeroMult(−2n) = 1 for all n (can slip)\n9. Build green + axiom audit\n10. Session closure (journal, STATE, NGUYEN, db, commit)\n\nLet me start by reading the LiDisc.lean file to see the capstone and nearZeros definition. The file is probably large (~1000+ lines added in session 024). Let me search for key definitions first.","signature":""},{"type":"text","text":"Design loaded. Let me set up the task list and inspect the current Lean state."},{"type":"tool_use","id":"TodoWrite_4","name":"TodoWrite","input":{"todos":[{"content":"Survey seams: LiDisc capstone, nearZeros def, Zeta23 RvM/StirlingVert APIs","status":"in_progress","activeForm":"Surveying seams and APIs"},{"content":"Build FE logDeriv identity: ζ′/ζ(s) = −ζ′/ζ(1−s) − [ΓR′/ΓR(1−s) + ΓR′/ΓR(s)]","status":"pending","activeForm":"Building FE logDeriv identity"},{"content":"Prove zero-sum cancellation under s ↦ 1−s reflection (finset map + mult match)","status":"pending","activeForm":"Proving zero-sum cancellation"},{"content":"Bound ΓR-bracket: digamma shift +2 then StirlingVert.digamma_stirling","status":"pending","activeForm":"Bounding ΓR-bracket"},{"content":"Left-plane uniform digamma bound |ψ(w) − log w| ≤ C away from poles","status":"pending","activeForm":"Proving left-plane digamma bound"},{"content":"Assemble left-half R-bound theorem + build green","status":"pending","activeForm":"Assembling left-half R-bound"},{"content":"Axiom audit new decls","status":"pending","activeForm":"Auditing axioms"},{"content":"Session closure: journal, STATE, NGUYEN, db, commit","status":"pending","activeForm":"Closing session"}]},"extra_content":null}]