{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:E2BRPMVTJUMNKXJBWDW445KEK3","short_pith_number":"pith:E2BRPMVT","schema_version":"1.0","canonical_sha256":"268317b2b34d18d55d21b0edce754456f96c558965e88759776f1544a1e7b7f7","source":{"kind":"arxiv","id":"1008.2557","version":2},"attestation_state":"computed","paper":{"title":"A Note on the Critical Group of a Line Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Perkinson, Nicholas Salter, Tianyuan Xu","submitted_at":"2010-08-15T23:20:03Z","abstract_excerpt":"This note answers a question posed by Levine in arkiv:math.CO/0906.2809. The main result is Theorem 1 which shows that under certain circumstances a critical group of a directed graph is the quotient of a critical group of its directed line graph."},"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":"1008.2557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-15T23:20:03Z","cross_cats_sorted":[],"title_canon_sha256":"26cb26bf9a27e6db2bce927b7477d76986dac0a27c3b20cca4b2a335223174b1","abstract_canon_sha256":"4d133ba183a0dd02c6b5436e6084f65fa2c0cc9810d361548829af0f96248bb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:55.178189Z","signature_b64":"gmoBMei4FUzl8aYzE+K+Qz4rMqD9Ub1N1q6naZgmMPyCRgtoh/EpgZwhyKXFMnbdzqUrAbenIDCcESH6QQNEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"268317b2b34d18d55d21b0edce754456f96c558965e88759776f1544a1e7b7f7","last_reissued_at":"2026-05-18T04:34:55.177846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:55.177846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on the Critical Group of a Line Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Perkinson, Nicholas Salter, Tianyuan Xu","submitted_at":"2010-08-15T23:20:03Z","abstract_excerpt":"This note answers a question posed by Levine in arkiv:math.CO/0906.2809. The main result is Theorem 1 which shows that under certain circumstances a critical group of a directed graph is the quotient of a critical group of its directed line graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2557","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":""},"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":"1008.2557","created_at":"2026-05-18T04:34:55.177900+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.2557v2","created_at":"2026-05-18T04:34:55.177900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2557","created_at":"2026-05-18T04:34:55.177900+00:00"},{"alias_kind":"pith_short_12","alias_value":"E2BRPMVTJUMN","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"E2BRPMVTJUMNKXJB","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"E2BRPMVT","created_at":"2026-05-18T12:26:06.534383+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/E2BRPMVTJUMNKXJBWDW445KEK3","json":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3.json","graph_json":"https://pith.science/api/pith-number/E2BRPMVTJUMNKXJBWDW445KEK3/graph.json","events_json":"https://pith.science/api/pith-number/E2BRPMVTJUMNKXJBWDW445KEK3/events.json","paper":"https://pith.science/paper/E2BRPMVT"},"agent_actions":{"view_html":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3","download_json":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3.json","view_paper":"https://pith.science/paper/E2BRPMVT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.2557&json=true","fetch_graph":"https://pith.science/api/pith-number/E2BRPMVTJUMNKXJBWDW445KEK3/graph.json","fetch_events":"https://pith.science/api/pith-number/E2BRPMVTJUMNKXJBWDW445KEK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3/action/storage_attestation","attest_author":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3/action/author_attestation","sign_citation":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3/action/citation_signature","submit_replication":"https://pith.science/pith/E2BRPMVTJUMNKXJBWDW445KEK3/action/replication_record"}},"created_at":"2026-05-18T04:34:55.177900+00:00","updated_at":"2026-05-18T04:34:55.177900+00:00"}