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)

1. Local propagation core
   First-active source s + adjacent support-preserving propagation
   ⟹ no first exact cancellation outside Cone(s)
   ⟹ nearest-source visibility
   ⟹ local trivial kernel.

2. Two-sided transport and residue production
   Local 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.

3. Residue to variance floor
   Rₗ ≠ 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.

4. Finite dyadic routing
   Packet 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.

5. Engine matching and lower-floor capture
   Qᵦ 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.

6. Bump-window stabilization
   Finite 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.

7. Geometric branch
   Positive-density good neighborhoods
   ⟹ complement deficit
   ⟹ nested-complement extraction
   ⟹ bounded-width carrier
   ⟹ incidence lower bound

   Inc(C, Good) ≥ δGood / M(w₀)

   ⟹ persistent bad geometry impossible.

8. Global localization
   Any 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.

9. Final contradiction
   Bad 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.