Mission Dashboard

Current position live

✔ PHASE 0, 1, 3, 4 COMPLETE. PHASE 2 (Track B): mapped to exhaustion
at current technology (2.6–2.13, parked). PHASE 5: 5.3 ✔ 5.4 ✔ 5.2 ✔
(live). PHASE 5B (tier ii′): **COMPLETE (session 041)** — all
sub-stages ii′-0..ii′-7 done (see NGUYEN.md §5B for the full log).

**Theorem status (session 041 — the closed forms):**
- T-1 (R-004): [PROVED-CONDITIONAL(computational RH-to-T₀;
  computational finite verification)] — **FULLY MACHINE-PROVED in
  Lean 4**: `lambda_pos_finite_height_closed` (LiClosed.lean) —
  λ_n > 0 for ALL 1 ≤ n ≤ N₁ = (3×10¹²−1)² from EXACTLY SEVEN
  declared hypotheses: RHUpTo (Platt–Trudgian), LiVerifiedUpTo(10⁵)
  (finite Li verification: E-011/E-015 to 3000 + Johansson 2015 § 4.2
  rigorous ordinary-λ_n table to 10⁵), ZeroCountProp/ZeroCountProp2/
  ZeroCountGlobalProp (Trudgian N(T)/S(T) forms), NoLowZeros
  (Platt-class zero-location), MZeroProp (M₀ interval certificate).
  Axiom audit on the full chain: [propext, Classical.choice,
  Quot.sound] only, 0 sorryAx (AuditSession041, 29 decls).
  sorryAx remains ONLY on the 5 skeleton statements (1 Suzuki + 4
  valley) by design.
- T-2 (R-003 + D-041): factorization + (★) ⟺ (1.12) [PROVED modulo
  Phase-5 formalities]; (1.12) ⟹ spec(D) ⊂ ℝ [PROVED via Suzuki + D1];
  ⇐ [SKELETON L3/L4].
- T-3 (valley, D-049 + D-058): [PROVED-CONDITIONAL(RH)].

**Paper:** research/paper/paperA.tex — Paper A (finite-height Li +
machine-verified reduction), **REVISED PER EXPERT REVIEW and RE-FROZEN
at session 045: 15 pp, compiles clean, zero undefined refs, zero
overfull hboxes** (focused note: §1 intro [transfer-theorem pitch],
§2 theorem + proof, §2.1 dog-leg with the published-version check,
App. A numerics, App. B formal verification [seven-hypotheses table;
zeta-23-lean as imported library], **App. C zero-count derivations**
[NEW]; seven-hypotheses headline; B(n) display corrected + the
F-A/F-B/F-E correction-note footnote; verbatim Lean signature +
instantiation table + dependency-chain diagram; abstract
normalization-precise (Keiper vs Li); hedged novelty with Oesterlé's
unpublished precursor noted; zero-count attribution "Rosser and
Trudgian"). paperA.pdf committed. paperB.tex — spectral-line research
note (skeleton, standing items in §0), 6 pp — NOTE: the certificate-
method background and the obstruction analysis cut from Paper A are
Paper B material. draft.tex — FROZEN combined archive copy (12 pp).

**Lean:** research/lean/NguyenRH1/ — full build GREEN (8775 jobs);
all 26 modules root-imported incl. LiSideBounds (ii′-6-c..d) and
LiClosed (ii′-7). sorryAx remains ONLY on: R003_exact_factorization
(tier iv) + 4 valley statements (tier iii).

**Deprioritized / open threads:** a=13+ push; adversary-ceiling LP;
T4b; λ-channel (G-004); θ-channel (dead, E-024); Paper B Task 1
(R-003 tempered-FT bookkeeping trace, queued); user read-through of
paperA.pdf (NOW THE FRONT ITEM — nothing blocks it); repo-publication
prep; submission decision (cover-letter.md + referee-list.md exist
from session 013, target Experimental Mathematics); the c = 1.5
fallback branch wip/c-1.5-margin-redo (642d47a, preserved, unneeded);
the T = √n hidden-cancellation open question (D-073 §8 D4); the
Lagarias F-D correspondence package (user's own work-in-progress in
research/correspondence/lagarias-F-D-package/, uncommitted — NOT
mine to commit).

Next action live

**PAPER A REVISED PER EXPERT REVIEW AND RE-FROZEN (session 045 end;
15 pp, zero undefined refs, zero overfull hboxes; journal-045, D-075,
E-035). NEXT ACTION: user read-through of the revised paperA.pdf —
especially the new introduction, §2.1's published-version sentence,
the reframed Appendix B first paragraph, and the new Appendix C — then
the submission decision (cover-letter.md rewritten + referee-list.md
updated; Experimental Mathematics first, alternatives listed in the
letter header). Do not edit paperA.tex while frozen — any edit
re-opens the honesty audit for the edited lines (D-060 §5). Optional
tightening if a JNT copy becomes available: confirm Trudgian-II's
published Theorem-1 constants (0.112/0.278/2.510) against the journal
text. If told to continue research instead: Paper B Task 1 (R-003
tempered-FT bookkeeping trace) or the parked Track-B remainders per
the user's call. All session-045 work committed; the user's
correspondence package remains uncommitted by design (the AIF
published-version check in journal-045 is reusable there).**

Blockers

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