{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:V4JULZ2YZLEJYBYCXQ4PWG4FGA","short_pith_number":"pith:V4JULZ2Y","schema_version":"1.0","canonical_sha256":"af1345e758cac89c0702bc38fb1b853018381aeed2bfd7792c44d548972afde8","source":{"kind":"arxiv","id":"2507.13777","version":1},"attestation_state":"computed","paper":{"title":"Intertwining local (adjacency) metric dimension with the clique number of a graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Ghalavand, Sandi Klav\\v{z}ar, Xueliang Li","submitted_at":"2025-07-18T09:36:29Z","abstract_excerpt":"Let $G$ be a simple connected graph with order $ n(G)$, local metric dimension $ {\\rm dim}_l(G)$, local adjacency metric dimension $ {\\rm dim}_{A,l}(G)$, and clique number $ \\omega(G)$, where $G\\not\\cong K_{n(G)}$ and $\\omega(G)\\geq3$. It is proved that $ {\\rm dim}_{A,l}(G) \\leq \\left\\lfloor \\left(\\frac{\\omega(G) - 2}{\\omega(G) - 1}\\right)n(G)\\right\\rfloor$. Consequently, the conjecture asserting that the latter expression is an upper bound for ${\\rm dim}_l(G)$ is confirmed. It is important to note that there are infinitely many graphs that satisfy the equalities."},"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":"2507.13777","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-18T09:36:29Z","cross_cats_sorted":[],"title_canon_sha256":"91309cf58f688461357180c94e618f5ebac4e865977e0f104b7a29bf5106eed6","abstract_canon_sha256":"94b9428f4650a103a8c967fdf5fd65662d30351eafc28b42f826c587cf62e99f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:22.832299Z","signature_b64":"ozVcGe5J45GgvhqLObWilC2UCXjLeIpJYOPWgcGTOoul3DcvniS5EEyWMvzFsXw1JDuo8vZI2MBDWuvKOOWsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af1345e758cac89c0702bc38fb1b853018381aeed2bfd7792c44d548972afde8","last_reissued_at":"2026-07-05T11:39:22.831816Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:22.831816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intertwining local (adjacency) metric dimension with the clique number of a graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Ghalavand, Sandi Klav\\v{z}ar, Xueliang Li","submitted_at":"2025-07-18T09:36:29Z","abstract_excerpt":"Let $G$ be a simple connected graph with order $ n(G)$, local metric dimension $ {\\rm dim}_l(G)$, local adjacency metric dimension $ {\\rm dim}_{A,l}(G)$, and clique number $ \\omega(G)$, where $G\\not\\cong K_{n(G)}$ and $\\omega(G)\\geq3$. It is proved that $ {\\rm dim}_{A,l}(G) \\leq \\left\\lfloor \\left(\\frac{\\omega(G) - 2}{\\omega(G) - 1}\\right)n(G)\\right\\rfloor$. Consequently, the conjecture asserting that the latter expression is an upper bound for ${\\rm dim}_l(G)$ is confirmed. It is important to note that there are infinitely many graphs that satisfy the equalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13777","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/2507.13777/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":"2507.13777","created_at":"2026-07-05T11:39:22.831872+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.13777v1","created_at":"2026-07-05T11:39:22.831872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13777","created_at":"2026-07-05T11:39:22.831872+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4JULZ2YZLEJ","created_at":"2026-07-05T11:39:22.831872+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4JULZ2YZLEJYBYC","created_at":"2026-07-05T11:39:22.831872+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4JULZ2Y","created_at":"2026-07-05T11:39:22.831872+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/V4JULZ2YZLEJYBYCXQ4PWG4FGA","json":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA.json","graph_json":"https://pith.science/api/pith-number/V4JULZ2YZLEJYBYCXQ4PWG4FGA/graph.json","events_json":"https://pith.science/api/pith-number/V4JULZ2YZLEJYBYCXQ4PWG4FGA/events.json","paper":"https://pith.science/paper/V4JULZ2Y"},"agent_actions":{"view_html":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA","download_json":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA.json","view_paper":"https://pith.science/paper/V4JULZ2Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.13777&json=true","fetch_graph":"https://pith.science/api/pith-number/V4JULZ2YZLEJYBYCXQ4PWG4FGA/graph.json","fetch_events":"https://pith.science/api/pith-number/V4JULZ2YZLEJYBYCXQ4PWG4FGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA/action/storage_attestation","attest_author":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA/action/author_attestation","sign_citation":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA/action/citation_signature","submit_replication":"https://pith.science/pith/V4JULZ2YZLEJYBYCXQ4PWG4FGA/action/replication_record"}},"created_at":"2026-07-05T11:39:22.831872+00:00","updated_at":"2026-07-05T11:39:22.831872+00:00"}