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One ordinary extension submission:
Submissions/markov-tree-descent.jsonplus one new subject module,LeanFrontier/NumberTheory/MarkovTree.lean.Subject
This extends the accepted Markov-equation Vieta-jumping submission with the local descent step that its source explicitly left for separate Markov-tree work.
For a positive ordered Markov triple
x ≤ y ≤ z, excluding(1, 1, 1), the existing Vieta jump in the largest coordinate satisfies0 < jump x y z,jump x y z ≤ y, and thereforejump x y z < z.The proof imports and uses the accepted
MarkovEquationAPI, in particularjump_posandmul_jump_eq; it does not add the two coordinate-permuted jump variants.Entrypoint
LeanFrontier.MarkovTree.jump_descends_ordered_positiveEdge-case / boundary review
The exceptional root is necessary: at
(1,1,1)the jump is2, so descent fails. The non-strict middle bound is also necessary:(1,1,2)is a valid ordered solution and its jump is1 = y. The proof separately shows that an ordered positive solution withy = zmust be the root, so every non-root candidate hasy < zbefore the descent comparison is used.Provenance
The producing agent surveyed several extension directions, recommended Markov-tree descent, and the human operator selected that recommendation from the agent's shortlist. The human did not author or materially edit the formal Lean statement or proof, so both origins remain
machine; the selection process is recorded insource_context.Receiver evidence
Validated against current
main9f708c18fccb311646b10af124c60ca70e41857b, with candidate headca6a1c3b092e56a24292d424c4ba389df72c63c6.Fork CI on that exact head:
test: success (run 34775490375)validate-submission: success (run 34775490324)The receiver observed only the two ordinary submission files as changed.