Repository navigation
Certify all-source first-crossing descent through horizon 14186 - #31
Merged
Merged
Conversation
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
1 participant
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
Every source greater than one descends at its first coefficient crossing whenever that crossing occurs by horizon 14186. The inherited bounded stopping certificate supplies the exceptional sources; the localized Beatty accumulator barrier and banked coefficient certificate supply the remaining sources. The change also proves equality with first actual descent, heavy-prefix survival, a lower bound on any discrepancy horizon, and the inherited first-crossing record witness. The endpoint route separately certifies horizon 10000.
Crossing existence remains a hypothesis. This does not prove Collatz or establish frontier priority.
Validation: both CI runs passed full Lean compilation and the audit. Twelve theorem axiom footprints allow only the standard logical axioms; 3,998,718 sources independently checked with latest first crossing 224; three deliberately false controls rejected. The prior conditional-only proof of the final deduction also compiled locally. The interrupted local cold rebuild was not counted as a completed check.