Goldbach's conjecture - Proof Program

This record contains a compact proof manuscript for Goldbach’s conjecture, organized as an explicit dependency-DAG with fixed interfaces between local propagation, residue production, dyadic routing, bump-window stabilization, geometric extraction, and final contradiction against certified upper-corridor inputs. The manuscript is written so that each major block exports a single downstream statement, while routing, purification, and geometric extraction mechanics are isolated in appendices. The presentation is intentionally compact and corridor-certified: a short target statement, a node-aligned Unicode proof-line, and explicit acceptance/firewall discipline. Target statement Every sufficiently large even integer N admits a representation N = p + q with primes p and q. Combined with finite verification below the fixed threshold, this yields Goldbach’s conjecture in full. Core proof-line (Unicode, condensed, manuscript-level) Local propagation coreFirst-active source s + adjacent support-preserving propagation⟹ no first exact cancellation outside Cone(s)⟹ nearest-source visibility⟹ local trivial kernel. Two-sided transport and residue productionLocal trivial kernel⟹ inward memory survives step-by-step from both ends⟹ two inward cones overlap on a bounded adjacent path⟹ first bad layer L carries a compatibility obstruction⟹ residue Rₗ ≠ 0. Residue to variance floorRₗ ≠ 0⟹ finite residue-to-fan transport⟹ positive normalized L¹-deviation on a bounded fan⟹ positive L²-variance floor⟹ packet variance PV(N; W) ≥ c₀ · N · (log N)⁻ᴮ⁰. Finite dyadic routingPacket grammar + quadratic normal form + mixed-term purification⟹ finite routed template family J(W)⟹ PV(N; W) ≤ ∑β∈J(W) cᵦ · Qᵦ(N), where each Qᵦ is canonically of Type II or Type III. Engine matching and lower-floor captureQᵦ matched to certified dyadic energies E₂, E₃⟹ PV(N; W) ≤ C · ∑j∈J(W) Eⱼ(N) ⟹ some routed block captures a nontrivial lower floor⟹ quantitative routed lower bound. Bump-window stabilizationFinite signature on I = [N, N + H(N)] threshold-crossing control constant-signature nondegeneracy⟹ routed lower floor survives on a positive subfamily of the bump window⟹ averaged lower floor. Geometric branchPositive-density good neighborhoods⟹ complement deficit⟹ nested-complement extraction⟹ bounded-width carrier⟹ incidence lower bound Inc(C, Good) ≥ δGood / M(w₀) ⟹ persistent bad geometry impossible. Global localizationAny durable carrier surviving through the comparison horizon⟹ nonzero statistic in the finite exhaustion vector Obs = (Obsarith, Obsgeom) ⟹ either arithmetic routed visibility or geometric persistence⟹ no third durable mode. Final contradictionBad obstruction⟹ arithmetic lower-floor corridor or geometric incidence corridor;geometric corridor is impossible by extraction/incidence;arithmetic corridor is incompatible with the certified upper dyadic regime;hence no bad obstruction survives. Therefore all sufficiently large even N are Goldbach, and finite verification closes the remaining range. Corridor discipline The manuscript is intentionally written as a compact proof machine with: fixed local propagation objects, fixed dyadic routing dictionary, fixed bump-window signature grammar, fixed finite geometric template model, fixed exhaustion vector for durable obstruction statistics. Firewalls exclude regime-jumping, post hoc threshold retuning, pointwise-from-mean leaps, and off-dictionary routed templates. Appendices supply: the local propagation mechanics, the routing / purification / classification machinery, the finite geometric extraction / incidence model. What the files contain PDF manuscript: compact main proof with appendices. TeX source: fully editable source matching the PDF structure.