Expert Review Request -- Paste Ready

Subject:

Review request: Depth-3 Buchstab minorant map for binary Goldbach

Message:

I am looking for expert review of a Goldbach research-map packet.

This is not a proof of Goldbach and not an almost-proof. The package is an obstruction map for a depth-3 Buchstab minorant route.

The route reduces the relevant positivity problem to a Type-III shifted-prime surface

    N = p + r s t.

The current sharp wall is the one-R-match layer. At the top Type-III edge

    R = N^(5/16),  S = P = N^(3/8),

the local model reduces to the ratio relation

    r4/r2 == s1/s2 mod p.

The documented standard L2 expansion, signed-weight split, minorant-geometry adjustment, and ratio-large-sieve pivot all return to the same saturated nonnegative variance object:

    (1/(p-1)) sum_{chi != chi0} |A_p(chi)|^2 |B_p(chi)|^2.

The intended theorem is averaged over the auxiliary prime moduli p ~ P. Writing

    pi_P = #{ prime p : p ~ P },

the notes define

    AvgShear = (1 / pi_P) * Shear.

At the top edge, the intended averaged scale is R^2 S = N. The equivalent unaveraged aggregate statement carries the corresponding pi_P factor.

The review question is:

    Is this one-R-match variance wall a real structural obstruction in this depth-3 Buchstab architecture, or is there a pre-Cauchy / sign-preserving Type-III identity that avoids the saturated nonnegative variance object?

The canonical packet is here:

    research/goldbach/notes/EXPERT_REVIEW_PACKET.md

Suggested reading order:

    0. REVIEWER_FIRST_PAGE.md
    1. TYPEIII_RESIDUAL_SHEAR_OPEN_PROBLEM.md
    2. FORMAL_DYADIC_MODEL.md
    3. EXPONENT_BUDGET.md
    4. GOLDBACH_NORMALIZATION_AUDIT.md
    5. ONE_R_MATCH_LOCAL_MODEL.md
    6. POST_SATURATION_BRANCH_DECISION.md
    7. PUBLIC_MAP_STOP_DECISION.md
    8. DEPTH3_BUCHSTAB_MINORANT_REDUCTION.md

The ideal answer is one of:

    - this follows from theorem X after these normalizations;
    - this is false because of obstruction Y;
    - the exact dispersion identity supplies signed kernel Z;
    - no signed kernel exists in this formulation;
    - the ranges are misstated and should be reformulated as ...

The goal is not announcement language. The goal is to find whether the named wall is genuine or whether the architecture is missing a known sign-preserving identity.

Use Conditions

Send only with the explicit non-proof framing intact.

Do not shorten the request into:

Can you check our Goldbach proof?

That would misrepresent the packet.

EXPERT REVIEW REQUEST PASTE READY

Expert Review Request -- Paste Ready

Use Conditions