Use dimension-30 geometry for conditional kappa = 1.2649e-7

[rohanarun]

This follow-up supports the unreviewed conditional witness kappa = 12649/100000000000 = 1.2649e-7, about 2.84% above PR #10's 1.2299998e-7, in T(n) = O(n (log n)^(1-kappa)).

The change uses the five-subset bit network at dimension 30, the selected star rules of #9, and the bank-matching extension of #11. That dimension was weaker under uniform recursion but is stronger under icekylinx's controlled batching model. The dimension-28 complex network, its 7e-7 saving, path-depth guard, and Gaussian correction remain unchanged. The exact bit saving becomes 253/10^9.

This branch is based on PR #10 at 62691e395a0458ce089a1c7b5d89e74291e95e29, with its contribution retained unchanged except for the additional follow-up entry points and documentation. Dependencies from #9 and #11 are included. The incremental mathematical argument, certificate and integration generator are in research/batched-followup/; the full independent manuscript patch is patches/batched-dimension30.patch.

Validation completed:

• Rebuilt the complete h30 producer twice: 16,089,992 additions, 1,425,495 output uses, 17,515,487 roles. Independently checked all 27,405 star boundaries and all 456 selected templates.
• Checked every one of the 142,506 neighbor-permutation images and 164,002 scalar basis directions per orientation across the templates, including arbitrary dirty scratch and compiled frame-support paths.
• Exact rational logarithm/moment inequalities, all 29 parameter constraints and seven final margins pass. Bit moment gap exceeds 9e-12; final absorption gap exceeds 9.98e-12. Negative controls reject exaggerated exponents and inflated producer counts.
• The inherited PR Batch recursive networks for a conditional kappa > 2^-23 bound #10 baseline passed 166 tests and all 18 patch checks locally. The new integrated patch applies cleanly to the pinned manuscript and has no duplicate or unresolved source labels. make verify now also runs the new producer and follow-up checks.

The integrated patch retains the h28 baseline proofs, adds the h30 bit lemma, updates the layer interface and its downstream consumers, and includes the new integer rounding comparison for epsilon. Bundled upstream/ is unchanged. PDF compilation of the newly materialized manuscript is a separate check and is not claimed by the source-integration checks above.

The contribution remains conditional on the retained upstream framework and the written proofs in #7 and #10; finite checks are not formal verification of the full theorem. The scoped review found no blocking defect in the examined batching arguments. Original attribution and licenses remain intact, including Zhihao Chen's ternary construction and icekylinx's batching work. The dimension-30 continuation was prepared with substantial OpenAI Codex assistance at Rohan Arun's request. No worldwide priority or practical runtime improvement is claimed.

[Mister-Meeseeks]

Integrated and retained on main in 377e2bd. Thank you @rohanarun for this contribution.

The complete original source tree at 35d31e30f28bc5da0ae6a88e7b03d75ebc855534 is preserved in the historical source package, with original notices and predecessor credit. It can be extracted and replayed independently. Historical release wrappers do not overwrite current pinned suppliers.

Reviewed scope: Dimension-30 mixed-width composition: six complete native dimension screens and scoped prime-power exclusions; all seven matching enumerations; h30 full producer replay and 456 template dirty-state controls, exact moment, 29 assembly constraints and patch. Unchanged #10 dependencies remain inherited; not a new full theorem audit.

The batch review and per-file dispositions cover every original changed path. Local focused checks passed; regenerated artifacts match the submitted sources. Attribution is also recorded in CONTRIBUTORS.md. This is integration of historical research and finite evidence, not a new selected κ or full formal verification of inherited tape/analytic interfaces. Linux replay jobs are tracked separately.