Repository navigation
Conversation
Prove all 5,114,417 costly-first paths are losses or attained ties using exact native-route floors. Include independent exceptional-path review and the bounded third neighborhood of five ties. No new kappa. Prepared for @CubeJerry with substantial OpenAI Codex assistance.
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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
No new κ. Close #6324's costly-first gap: 5,114,417 ordered forward-A2 paths with fixed correction frames give 5,114,412 losses and five attained ties for all 0<t<1. Exact non-edge route floors resolve 30 misleading collapsed invoices. With #6324, all 5,164,282 paths in this directed two-step domain are covered. The five new ties also have 11,363 third neighbours without saving.
Task and sources
Base 7c49fe3. #5708: 829d01f; #6324: 8bf1882. Distinct from #6664.
Validation
python3 -B scripts/research_package.py --package research/g20-costly-first-compensationExpected: PASS_REGISTERED_RESEARCH_PACKAGE. Seven registered checks, exact shard aggregation, independent domain enumeration and 35-path chronological review passed. Optimized read-only export passed. Controls cover 32,941 words including seed12, four code mutants and corrupt inputs. Remote tree matches tested files.
Limitations and credit
Fixed 645-frame catalogue; separately charged routes. Exact census, no sampling/early stop. No general depth-three, inverse-insertion or arbitrary-depth exclusion. All five assumptions remain; no supplier/caller admission. Full-history preflight unrun. @CubeJerry with substantial OpenAI assistance and separate review; credit Ali Romman, unpaidmoon, Nick Petalas and #6324.
Proofs, exact byte pins, receipts and remaining questions.