{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MGA5YVJVZGL7PFC3DQ2J4W6YGG","short_pith_number":"pith:MGA5YVJV","schema_version":"1.0","canonical_sha256":"6181dc5535c997f7945b1c349e5bd831a18179590ce50346c741e83b54f7b285","source":{"kind":"arxiv","id":"2607.05567","version":1},"attestation_state":"computed","paper":{"title":"One construction for the Miura-ori flip-graph degree sequence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Chakshu Gupta","submitted_at":"2026-07-06T19:09:19Z","abstract_excerpt":"The flip graph of an origami crease pattern has the flat-foldable mountain-valley assignments as vertices, and an edge joins two of them that differ by a single face flip. A basic invariant of this graph is the degree sequence, which counts the vertices of each degree. On the $m\\times n$ Miura-ori, this sequence is known as a bivariate polynomial only for small degrees, each count obtained by a separate argument whose casework grows with the degree. This paper gives one uniform construction that expresses, for every degree $d$, the number of degree-$d$ vertices as a single symmetric polynomial"},"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":"2607.05567","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-06T19:09:19Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"5470b1aadc2059a1e944dce5e5a3c97f6562a2ee7ade6d03d50cc8db65e4d978","abstract_canon_sha256":"01f79e819c6f771f61be78bca217f44e5ce9ffb80ad6efe5baed70797e007bfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:37.410516Z","signature_b64":"LunTfeliADubhNsIJjPjkv6QzJV1jd5K8Omvwojath3fOPYWXSx+8HfSu0rvyMktn5+nDrvDCSukl0wvV718Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6181dc5535c997f7945b1c349e5bd831a18179590ce50346c741e83b54f7b285","last_reissued_at":"2026-07-08T01:18:37.410034Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:37.410034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One construction for the Miura-ori flip-graph degree sequence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Chakshu Gupta","submitted_at":"2026-07-06T19:09:19Z","abstract_excerpt":"The flip graph of an origami crease pattern has the flat-foldable mountain-valley assignments as vertices, and an edge joins two of them that differ by a single face flip. A basic invariant of this graph is the degree sequence, which counts the vertices of each degree. On the $m\\times n$ Miura-ori, this sequence is known as a bivariate polynomial only for small degrees, each count obtained by a separate argument whose casework grows with the degree. This paper gives one uniform construction that expresses, for every degree $d$, the number of degree-$d$ vertices as a single symmetric polynomial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05567","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.05567/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.05567","created_at":"2026-07-08T01:18:37.410105+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.05567v1","created_at":"2026-07-08T01:18:37.410105+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05567","created_at":"2026-07-08T01:18:37.410105+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGA5YVJVZGL7","created_at":"2026-07-08T01:18:37.410105+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGA5YVJVZGL7PFC3","created_at":"2026-07-08T01:18:37.410105+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGA5YVJV","created_at":"2026-07-08T01:18:37.410105+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG","json":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG.json","graph_json":"https://pith.science/api/pith-number/MGA5YVJVZGL7PFC3DQ2J4W6YGG/graph.json","events_json":"https://pith.science/api/pith-number/MGA5YVJVZGL7PFC3DQ2J4W6YGG/events.json","paper":"https://pith.science/paper/MGA5YVJV"},"agent_actions":{"view_html":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG","download_json":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG.json","view_paper":"https://pith.science/paper/MGA5YVJV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.05567&json=true","fetch_graph":"https://pith.science/api/pith-number/MGA5YVJVZGL7PFC3DQ2J4W6YGG/graph.json","fetch_events":"https://pith.science/api/pith-number/MGA5YVJVZGL7PFC3DQ2J4W6YGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG/action/storage_attestation","attest_author":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG/action/author_attestation","sign_citation":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG/action/citation_signature","submit_replication":"https://pith.science/pith/MGA5YVJVZGL7PFC3DQ2J4W6YGG/action/replication_record"}},"created_at":"2026-07-08T01:18:37.410105+00:00","updated_at":"2026-07-08T01:18:37.410105+00:00"}