{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JFDUPLEBH4ILWVHMWXR3EY4B7X","short_pith_number":"pith:JFDUPLEB","schema_version":"1.0","canonical_sha256":"494747ac813f10bb54ecb5e3b26381fdcaa6a0e09c5657187d4cde52555258a7","source":{"kind":"arxiv","id":"2606.22614","version":1},"attestation_state":"computed","paper":{"title":"Height functions on the $m \\times n$ Miura-ori flip graph: degree sequence and diameter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Chakshu Gupta","submitted_at":"2026-06-21T17:40:19Z","abstract_excerpt":"The state space of an origami crease pattern forms a flip graph, whose vertices are the flat-foldable mountain-valley assignments and whose edges join assignments differing by a single face flip. For the $m \\times n$ Miura-ori, the degree sequence and diameter of this graph are known only for two rows. Each assignment maps to an integer height function on the grid, under which a vertex's degree equals its number of local extrema. In this model the vertices of each degree up to five are counted by an explicit polynomial in $m$ and $n$, valid once both exceed a bound that grows with the degree, "},"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":"2606.22614","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-21T17:40:19Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0bca4ea873d10238819b56dc4b8654d23a84095b94542063b32a7f02f5ce3e54","abstract_canon_sha256":"0def3f39e5ebefe84d1175d1352b4065b04378658ef9ad845155a3f528841894"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:43.009276Z","signature_b64":"c1Ry+WAMluIhT0kDG2rjXx92xFuT1OPNtjvqd+4i4adr29v6bCK4oRb6aTt1rlp9kkgoLYMy2e45ryRK75PFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"494747ac813f10bb54ecb5e3b26381fdcaa6a0e09c5657187d4cde52555258a7","last_reissued_at":"2026-06-23T02:13:43.008854Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:43.008854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Height functions on the $m \\times n$ Miura-ori flip graph: degree sequence and diameter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Chakshu Gupta","submitted_at":"2026-06-21T17:40:19Z","abstract_excerpt":"The state space of an origami crease pattern forms a flip graph, whose vertices are the flat-foldable mountain-valley assignments and whose edges join assignments differing by a single face flip. For the $m \\times n$ Miura-ori, the degree sequence and diameter of this graph are known only for two rows. Each assignment maps to an integer height function on the grid, under which a vertex's degree equals its number of local extrema. In this model the vertices of each degree up to five are counted by an explicit polynomial in $m$ and $n$, valid once both exceed a bound that grows with the degree, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22614","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/2606.22614/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":"2606.22614","created_at":"2026-06-23T02:13:43.008916+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22614v1","created_at":"2026-06-23T02:13:43.008916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22614","created_at":"2026-06-23T02:13:43.008916+00:00"},{"alias_kind":"pith_short_12","alias_value":"JFDUPLEBH4IL","created_at":"2026-06-23T02:13:43.008916+00:00"},{"alias_kind":"pith_short_16","alias_value":"JFDUPLEBH4ILWVHM","created_at":"2026-06-23T02:13:43.008916+00:00"},{"alias_kind":"pith_short_8","alias_value":"JFDUPLEB","created_at":"2026-06-23T02:13:43.008916+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/JFDUPLEBH4ILWVHMWXR3EY4B7X","json":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X.json","graph_json":"https://pith.science/api/pith-number/JFDUPLEBH4ILWVHMWXR3EY4B7X/graph.json","events_json":"https://pith.science/api/pith-number/JFDUPLEBH4ILWVHMWXR3EY4B7X/events.json","paper":"https://pith.science/paper/JFDUPLEB"},"agent_actions":{"view_html":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X","download_json":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X.json","view_paper":"https://pith.science/paper/JFDUPLEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22614&json=true","fetch_graph":"https://pith.science/api/pith-number/JFDUPLEBH4ILWVHMWXR3EY4B7X/graph.json","fetch_events":"https://pith.science/api/pith-number/JFDUPLEBH4ILWVHMWXR3EY4B7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X/action/storage_attestation","attest_author":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X/action/author_attestation","sign_citation":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X/action/citation_signature","submit_replication":"https://pith.science/pith/JFDUPLEBH4ILWVHMWXR3EY4B7X/action/replication_record"}},"created_at":"2026-06-23T02:13:43.008916+00:00","updated_at":"2026-06-23T02:13:43.008916+00:00"}