{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HXJ6MNLWRXYL737ZQPCXF6BZIZ","short_pith_number":"pith:HXJ6MNLW","schema_version":"1.0","canonical_sha256":"3dd3e635768df0bfeff983c572f8394674b55efa7565bb52efdac6457694bb5d","source":{"kind":"arxiv","id":"1402.7257","version":1},"attestation_state":"computed","paper":{"title":"Proof of Blum's conjecture on hexagonal dungeons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mihai Ciucu, Tri Lai","submitted_at":"2014-02-28T14:30:02Z","abstract_excerpt":"Matt Blum conjectured that the number of tilings of the Hexagonal Dungeon of sides $a,\\ 2a,\\ b,\\ a,\\ 2a,\\ b$ (where $b\\geq 2a$) is $13^{2a^2}14^{\\lfloor\\frac{a^2}{2}\\rfloor}$ (J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (E. Kuo, Applications of Graphical Condensation for Enumerating Matchings and Tilings, Theoretical Computer Science, 2004)."},"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":"1402.7257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-28T14:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"dd7a2ebf9f36326644ae7e6b7caf604705ddb165e876f8aad48c1a24c56d8efd","abstract_canon_sha256":"bad1b8f3f5acc2b940b2cbd0aed55ee15d5881097dec3531a40fa183405b947c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:34.532346Z","signature_b64":"Cy9ps21Wa3htznGQoiS/M2gUQM5wy8VAOgI2pYl2+PSVC/HTwcLKzpI/Wu1vAKe9kEOw7rlYwMy+zFRr6Z51Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dd3e635768df0bfeff983c572f8394674b55efa7565bb52efdac6457694bb5d","last_reissued_at":"2026-05-18T02:57:34.531724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:34.531724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of Blum's conjecture on hexagonal dungeons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mihai Ciucu, Tri Lai","submitted_at":"2014-02-28T14:30:02Z","abstract_excerpt":"Matt Blum conjectured that the number of tilings of the Hexagonal Dungeon of sides $a,\\ 2a,\\ b,\\ a,\\ 2a,\\ b$ (where $b\\geq 2a$) is $13^{2a^2}14^{\\lfloor\\frac{a^2}{2}\\rfloor}$ (J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (E. Kuo, Applications of Graphical Condensation for Enumerating Matchings and Tilings, Theoretical Computer Science, 2004)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7257","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":""},"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":"1402.7257","created_at":"2026-05-18T02:57:34.531823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.7257v1","created_at":"2026-05-18T02:57:34.531823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.7257","created_at":"2026-05-18T02:57:34.531823+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXJ6MNLWRXYL","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXJ6MNLWRXYL737Z","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXJ6MNLW","created_at":"2026-05-18T12:28:30.664211+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/HXJ6MNLWRXYL737ZQPCXF6BZIZ","json":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ.json","graph_json":"https://pith.science/api/pith-number/HXJ6MNLWRXYL737ZQPCXF6BZIZ/graph.json","events_json":"https://pith.science/api/pith-number/HXJ6MNLWRXYL737ZQPCXF6BZIZ/events.json","paper":"https://pith.science/paper/HXJ6MNLW"},"agent_actions":{"view_html":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ","download_json":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ.json","view_paper":"https://pith.science/paper/HXJ6MNLW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.7257&json=true","fetch_graph":"https://pith.science/api/pith-number/HXJ6MNLWRXYL737ZQPCXF6BZIZ/graph.json","fetch_events":"https://pith.science/api/pith-number/HXJ6MNLWRXYL737ZQPCXF6BZIZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ/action/storage_attestation","attest_author":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ/action/author_attestation","sign_citation":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ/action/citation_signature","submit_replication":"https://pith.science/pith/HXJ6MNLWRXYL737ZQPCXF6BZIZ/action/replication_record"}},"created_at":"2026-05-18T02:57:34.531823+00:00","updated_at":"2026-05-18T02:57:34.531823+00:00"}