Repository navigation
Construct a connected 18-stage root and bound its native completion (no new κ) - #7002
Merged
Mister-Meeseeks merged 1 commit intoNov 10, 2026
Conversation
This was referenced Nov 10, 2026
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Change and mathematical scope
Construct the connected L=18, rho=1 extension left open in #6937: 38 independent roles, 39 rank-one units, commuting stage masks and a 2,370-event dyadic caller. Its exact action is Q times the diagonal product of the 18 independent body variables. L3 and L9 instances supply source-bound controls.
No new κ. The caller invokes 18 specified HOST(t=-1) macros whose native implementation remains unbuilt. It explicitly retains 181 idle jobs, three queries and 2,168 ordinary events. The per-stage native price must be below 17.13134090285433 at the pending benchmark.
The package also proves why two proposed shortcuts fail. Same-frame main-plane remix cannot extract an autonomous resonant HOST. For the pinned F+H1 repair, an exact eligibility-compression argument bounds even free coordinate-role idle merging: saving 9.707289925177 versus required 10.081828034876 per port. A complete-profile interval proof keeps this repair's moment negative throughout κ in [0.00362701882, 0.01].
Sources and verification
Base:
7c49fe32c55de02c2c873655c804b16e4c3fef0a. Extends #6937's mask pattern, not its literal vectors; credits #6842's normalization and #6936's root/grammar. The F profile is #6824 through #6833; all exported heads, paths and byte pins are in INPUT-PINS.json.All seven registered checks pass read-only: deterministic construction, exact four-character replay, complete census, independently implemented root/sector checks, reverse formal Q4 replay of all 1,444 coefficients, exact coalescing optimum and uniform interval bound. Repeated body-variable powers are preserved. Controls reject omitted/wrong operations, malformed host/incidence assignments, omitted paid adapters and reversed intervals. Assertion-based entry points reject optimized mode; the explicit-exception coalescing check also passes optimized replay.
Limits and credit
The negative results concern this fixed native profile and coordinate-role merging. Noncoordinate idle directions, changed roots, helper mixing and genuinely new native words remain open. Native realization, ordinary/physical tariffs, compiler and all five framework assumptions remain unresolved; no selected-frontier change or unconditional theorem.
Prepared for @CubeJerry (Jerry Chen) with substantial OpenAI Codex assistance, including separate implementations for independent checks. Credit DreamingOfClouds, #6912's caller precedent and all retained native/root authors. The complete-sign header is prior; the connected mask geometry, emitted caller and scoped completion analysis are new.
Research package and evidence
Construction, proof, independent receipts and validation