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If $D\\subseteq\\{2,\\ldots,r\\}$ and $|\\mathcal G|\\ge n+|D|$, then the hyperedges can be reassigned to the adjacent pairs of the same cyclic order so that, for each $d\\in D$, a distinct unused hyperedge realizes cyclic distance $d$. Consequently, the odd-order case of the one-extra-edge question of Bailey, Hollars, Li and Luo has an affirmative answ"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.12230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T15:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"af8fc9e160c61363c185fb7c5bc345d3d96ee1be2712fe5cd26a1c7e20911169","abstract_canon_sha256":"6c1a2e500a7bd32854c6480841ef60b507059657018a2c4825a8eb91e7726d58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:55.637960Z","signature_b64":"AaJiVsnwh5R1y9CmctCsdIA0sh+oxWB0wTqpek2t5MAj6Tg6zEAxB+fxFXl1EYyjtjN6Nx0ViYZxZrpOO9DuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f1847c7736773f1732ea8b055606da349651b54250bf507f04a291d02871efb","last_reissued_at":"2026-06-11T01:10:55.637134Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:55.637134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prescribed leftover chords and one-extra-edge Berge pancyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henry Shin","submitted_at":"2026-06-10T15:39:33Z","abstract_excerpt":"We prove a prescribed-leftover-chord theorem for Hamiltonian Berge cycles of odd order. Let $C$ be a Hamiltonian Berge cycle on $n=2r+1$ vertices, and let $\\mathcal G$ be a set of hyperedges, all of size at least $r$, containing the hyperedges of $C$. If $D\\subseteq\\{2,\\ldots,r\\}$ and $|\\mathcal G|\\ge n+|D|$, then the hyperedges can be reassigned to the adjacent pairs of the same cyclic order so that, for each $d\\in D$, a distinct unused hyperedge realizes cyclic distance $d$. 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