Public Map Stop Decision

Status

Stop decision for the current Goldbach architecture.

This is not a proof of Goldbach.

This is not an almost-proof of Goldbach.

It is a structural reduction and obstruction map.

Current Architecture

The route is:

depth-3 Buchstab minorant
-> pointwise rough prime minorant
-> Type-III shifted-prime surface N = p + r s t
-> local product-cloud / prime-ratio shearing problem
-> one-R-match corridor
-> nonnegative variance wall

The combinatorial reduction remains useful because it names the load-bearing analytic surface.

The current analytic architecture does not close the wall.

Tested Local Pivots

Standard L2 dispersion

Recorded in:

SIGNED_KERNEL_DERIVATION_ATTEMPT_L2.md

Result:

W_p(chi) = 1

The route collapses to the saturated positive variance object.

Signed-weight pivot

Recorded in:

SIGNED_WEIGHT_PIVOT_STRUCTURAL_RESULT.md

Result:

Signed splitting of the triple rebate is not useful unless the signed pieces remain coupled before L2/Cauchy. No such coupled identity is present in the documented method.

Minorant-geometry pivot

Recorded in:

MINORANT_GEOMETRY_PIVOT_TEST.md

Result:

Inside the current P <= S range, pushing the one-R-match layer below the wall would require

pi > rho + sigma,

but the geometry gives

pi <= sigma.

So this local geometry cannot remove the wall.

Ratio-large-sieve pivot

Recorded in:

RATIO_LARGE_SIEVE_PIVOT_TEST.md

Result:

A direct ratio-large-sieve closure would need to beat the natural positive variance scale:

average_p Err_p(R,S) = o(RS).

Standard large-sieve technology controls variance at natural size; it does not supply this saving in the positive formulation.

Named Wall

The current named wall is:

one-R-match variance wall

It is sharper than the earlier broad phrase "Type-III residual shearing."

The public phrasing should say:

The map isolates a one-R-match variance wall inside the Type-III shifted-prime surface. The documented local pivots do not remove it.

What Would Reopen The Analytic Push

Only reopen this route if a new idea changes one of the following:

• a pre-L2 identity produces a genuinely signed or oscillatory one-R-match kernel;
• a new minorant/dispersion geometry moves the relevant moduli beyond the product scale R S;
• the positive variance object is replaced by a phase-sensitive expression before absolute squares appear;
• a new theorem specifically proves depletion below the natural variance scale for the actual prime/sieve ratio measures.

Current Public Action

Freeze the Goldbach package as a public-review obstruction map.

The useful outside review question is no longer:

Can someone import a routine estimate to finish this?

It is:

Is the one-R-match variance wall a real structural obstruction in this depth-3 Buchstab architecture,
or is there a pre-L2 identity that keeps sign and removes it?