{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HVPUJITGYGT4TQ6HC36LFI72GL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a4a2fb193eae8f2b083c1f0b7d84d0b87a9b481de2a9ba913761ad1341f6b1de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T04:02:35Z","title_canon_sha256":"a71fca596a1b1aed656cc01c8c46512fd079ca656e0b0988047ed90aa1425926"},"schema_version":"1.0","source":{"id":"1310.7308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7308","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7308v1","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7308","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"HVPUJITGYGT4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HVPUJITGYGT4TQ6H","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HVPUJITG","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:33da0d72bffcae82a080a0836bfdb51dfc63e0c6455002ecf5542d001e750773","target":"graph","created_at":"2026-05-18T03:08:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we determine the maximal Laplacian and signless Laplacian spectral radii for graphs with fixed number of vertices and domination number, and characterize the extremal graphs respectively.","authors_text":"Bo Zhou, Rundan Xing","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T04:02:35Z","title":"Laplacian and signless Laplacian spectral radii of graphs with fixed domination number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7308","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2f295152398b8f3f62f00dd67b826b54b362442d516f89b4f26ced39a742d147","target":"record","created_at":"2026-05-18T03:08:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a4a2fb193eae8f2b083c1f0b7d84d0b87a9b481de2a9ba913761ad1341f6b1de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T04:02:35Z","title_canon_sha256":"a71fca596a1b1aed656cc01c8c46512fd079ca656e0b0988047ed90aa1425926"},"schema_version":"1.0","source":{"id":"1310.7308","kind":"arxiv","version":1}},"canonical_sha256":"3d5f44a266c1a7c9c3c716fcb2a3fa32db0b46064c4bacf95548f59829e3d54d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d5f44a266c1a7c9c3c716fcb2a3fa32db0b46064c4bacf95548f59829e3d54d","first_computed_at":"2026-05-18T03:08:45.712270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:45.712270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Inujg/qJ4lwYoeznJQw0vPXXsBUEEzMkgKQjv4DlVw1MT/3lBIAh5yMNr1HEmtjXLO+JJ+efBB6F6GCbzlRCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:45.712744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f295152398b8f3f62f00dd67b826b54b362442d516f89b4f26ced39a742d147","sha256:33da0d72bffcae82a080a0836bfdb51dfc63e0c6455002ecf5542d001e750773"],"state_sha256":"052f19603ff96517bb1ba6691865e261e2c9a63fa3166cae7c9f5f51fe8019ba"}