{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:Q3KZ7BSI2LQU2LSZBCQRJIFWEZ","short_pith_number":"pith:Q3KZ7BSI","schema_version":"1.0","canonical_sha256":"86d59f8648d2e14d2e5908a114a0b6266195f233b9dc06b6dd2e8bc03453683a","source":{"kind":"arxiv","id":"2305.04544","version":1},"attestation_state":"computed","paper":{"title":"Maximal Arrangement of Dominos in the Diamond","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dominique D\\'es\\'erable, Franciszek Seredy\\'nski, Rolf Hoffmann","submitted_at":"2023-05-08T08:38:49Z","abstract_excerpt":"\"Dominos\" are special entities consisting of a hard dimer-like kernel surrounded by a soft hull and governed by local interactions. \"Soft hull\" and \"hard kernel\" mean that the hulls can overlap while the kernel acts under a repulsive potential. Unlike the dimer problem in statistical physics, which lists the number of all possible configurations for a given n x n lattice, the more modest goal herein is to provide lower and upper bounds for the maximum allowed number of dominos in the diamond. In this NP problem, a deterministic construction rule is proposed and leads to a suboptimal solution {"},"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":"2305.04544","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-05-08T08:38:49Z","cross_cats_sorted":[],"title_canon_sha256":"9e5f209419fffcb85c285620b934373609515f04eea234d0424aa5d75e94dd7a","abstract_canon_sha256":"4ffe429929eef90e58b379eb6a2c6089139fd4c08da7c062b2a38d7bc6eb4acc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:07:51.097542Z","signature_b64":"C5vgW7QluS6sWEqziR6AORhfeOIFiJ4bKaeISCtrn1egCcoFvZ0tqZDEoZnmuFelty+3tvvlopWOz4Tl41p0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86d59f8648d2e14d2e5908a114a0b6266195f233b9dc06b6dd2e8bc03453683a","last_reissued_at":"2026-07-05T06:07:51.097094Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:07:51.097094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal Arrangement of Dominos in the Diamond","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dominique D\\'es\\'erable, Franciszek Seredy\\'nski, Rolf Hoffmann","submitted_at":"2023-05-08T08:38:49Z","abstract_excerpt":"\"Dominos\" are special entities consisting of a hard dimer-like kernel surrounded by a soft hull and governed by local interactions. \"Soft hull\" and \"hard kernel\" mean that the hulls can overlap while the kernel acts under a repulsive potential. Unlike the dimer problem in statistical physics, which lists the number of all possible configurations for a given n x n lattice, the more modest goal herein is to provide lower and upper bounds for the maximum allowed number of dominos in the diamond. In this NP problem, a deterministic construction rule is proposed and leads to a suboptimal solution {"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.04544","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/2305.04544/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":"2305.04544","created_at":"2026-07-05T06:07:51.097150+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.04544v1","created_at":"2026-07-05T06:07:51.097150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.04544","created_at":"2026-07-05T06:07:51.097150+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q3KZ7BSI2LQU","created_at":"2026-07-05T06:07:51.097150+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q3KZ7BSI2LQU2LSZ","created_at":"2026-07-05T06:07:51.097150+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q3KZ7BSI","created_at":"2026-07-05T06:07:51.097150+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.05246","citing_title":"Optimizing Wealth by a Game within Cellular Automata","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ","json":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ.json","graph_json":"https://pith.science/api/pith-number/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/graph.json","events_json":"https://pith.science/api/pith-number/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/events.json","paper":"https://pith.science/paper/Q3KZ7BSI"},"agent_actions":{"view_html":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ","download_json":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ.json","view_paper":"https://pith.science/paper/Q3KZ7BSI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.04544&json=true","fetch_graph":"https://pith.science/api/pith-number/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/action/storage_attestation","attest_author":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/action/author_attestation","sign_citation":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/action/citation_signature","submit_replication":"https://pith.science/pith/Q3KZ7BSI2LQU2LSZBCQRJIFWEZ/action/replication_record"}},"created_at":"2026-07-05T06:07:51.097150+00:00","updated_at":"2026-07-05T06:07:51.097150+00:00"}