{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:74JE2XLLWECVYKTPKPPRQJWDBG","short_pith_number":"pith:74JE2XLL","schema_version":"1.0","canonical_sha256":"ff124d5d6bb1055c2a6f53df1826c309911c25e5eec20abf44fc275dfd23b256","source":{"kind":"arxiv","id":"2505.21299","version":2},"attestation_state":"computed","paper":{"title":"On Distinguishing Graphs and Cost Number using Automorphism Representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alexa Gopaulsingh, Amitayu Banerjee, Zal\\'an Moln\\'ar","submitted_at":"2025-05-27T15:02:20Z","abstract_excerpt":"A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which can be distinguished using 2 colors. The cost $\\rho(G)$ of a 2-distinguishable graph is the smallest size of a color set of a distinguishing coloring of $G$. The determining number of a graph, $Det(G)$, is the minimum number of nodes, which if fixed by a coloring, would ensure that the coloring distinguishes the entire graph.\n  Boutin (J. Combin. Math. Combin. Comput. 85: 161-171, 2013) posed an open problem which ask"},"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":"2505.21299","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-27T15:02:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d8d874be20b79acf1450e8a749a22bcb03b490c7a82026622074c4938fc6ede9","abstract_canon_sha256":"0adf841b3f3ba1ebcff75e64d56c4f3097537176ebf98318c3a2b749b60484a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:00.490282Z","signature_b64":"kCryHyPVptg02WOOXsT523Wvq+WbZi032slI1hAm4Yn/gN0jpv/YIM8XbmHSn7vz8MvnobZj9Y1e5NTLDM3KAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff124d5d6bb1055c2a6f53df1826c309911c25e5eec20abf44fc275dfd23b256","last_reissued_at":"2026-07-05T11:15:00.489803Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:00.489803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Distinguishing Graphs and Cost Number using Automorphism Representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alexa Gopaulsingh, Amitayu Banerjee, Zal\\'an Moln\\'ar","submitted_at":"2025-05-27T15:02:20Z","abstract_excerpt":"A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which can be distinguished using 2 colors. The cost $\\rho(G)$ of a 2-distinguishable graph is the smallest size of a color set of a distinguishing coloring of $G$. The determining number of a graph, $Det(G)$, is the minimum number of nodes, which if fixed by a coloring, would ensure that the coloring distinguishes the entire graph.\n  Boutin (J. Combin. Math. Combin. Comput. 85: 161-171, 2013) posed an open problem which ask"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21299","kind":"arxiv","version":2},"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/2505.21299/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":"2505.21299","created_at":"2026-07-05T11:15:00.489861+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.21299v2","created_at":"2026-07-05T11:15:00.489861+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21299","created_at":"2026-07-05T11:15:00.489861+00:00"},{"alias_kind":"pith_short_12","alias_value":"74JE2XLLWECV","created_at":"2026-07-05T11:15:00.489861+00:00"},{"alias_kind":"pith_short_16","alias_value":"74JE2XLLWECVYKTP","created_at":"2026-07-05T11:15:00.489861+00:00"},{"alias_kind":"pith_short_8","alias_value":"74JE2XLL","created_at":"2026-07-05T11:15:00.489861+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/74JE2XLLWECVYKTPKPPRQJWDBG","json":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG.json","graph_json":"https://pith.science/api/pith-number/74JE2XLLWECVYKTPKPPRQJWDBG/graph.json","events_json":"https://pith.science/api/pith-number/74JE2XLLWECVYKTPKPPRQJWDBG/events.json","paper":"https://pith.science/paper/74JE2XLL"},"agent_actions":{"view_html":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG","download_json":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG.json","view_paper":"https://pith.science/paper/74JE2XLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.21299&json=true","fetch_graph":"https://pith.science/api/pith-number/74JE2XLLWECVYKTPKPPRQJWDBG/graph.json","fetch_events":"https://pith.science/api/pith-number/74JE2XLLWECVYKTPKPPRQJWDBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG/action/storage_attestation","attest_author":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG/action/author_attestation","sign_citation":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG/action/citation_signature","submit_replication":"https://pith.science/pith/74JE2XLLWECVYKTPKPPRQJWDBG/action/replication_record"}},"created_at":"2026-07-05T11:15:00.489861+00:00","updated_at":"2026-07-05T11:15:00.489861+00:00"}