{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:P3OP4NX6PLNEWK5JOO7RPCFVCN","short_pith_number":"pith:P3OP4NX6","canonical_record":{"source":{"id":"1601.07012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T13:23:40Z","cross_cats_sorted":[],"title_canon_sha256":"d916e1899b5a083b6e38a9dc19e037a4031d4a531c08ac0ee97a49085c6c148d","abstract_canon_sha256":"013d9c7dc6c4a59fa3713bf0091af11a20c892261dee4c0edeed459d61b39d0a"},"schema_version":"1.0"},"canonical_sha256":"7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292","source":{"kind":"arxiv","id":"1601.07012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07012","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07012v1","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07012","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"P3OP4NX6PLNE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P3OP4NX6PLNEWK5J","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P3OP4NX6","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:P3OP4NX6PLNEWK5JOO7RPCFVCN","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T13:23:40Z","cross_cats_sorted":[],"title_canon_sha256":"d916e1899b5a083b6e38a9dc19e037a4031d4a531c08ac0ee97a49085c6c148d","abstract_canon_sha256":"013d9c7dc6c4a59fa3713bf0091af11a20c892261dee4c0edeed459d61b39d0a"},"schema_version":"1.0"},"canonical_sha256":"7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:59.293291Z","signature_b64":"iZhnhG0hRn07B8B+x+mUD5jZZMvtP4/nnbB6Ce9tV2ihKyA/B+/hXRgpFjlpJ6EF4USbdMk7Ung37/wQf5X4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292","last_reissued_at":"2026-05-18T01:21:59.292867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:59.292867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07012","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ce810Kkc/qykHNI7ucFM2cWRviaJyKi0zpUkkkKxAWH5m5uo0BJJTMwSRqk3mQTyQfiNg7GVYfjm9L3p19E7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:32:38.847756Z"},"content_sha256":"8c18bbd261182e0e18c22958743e3a435c94248b9e0ead3ecdefb8ca8735f20b","schema_version":"1.0","event_id":"sha256:8c18bbd261182e0e18c22958743e3a435c94248b9e0ead3ecdefb8ca8735f20b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:P3OP4NX6PLNEWK5JOO7RPCFVCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral characterizations of two families of nearly complete bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chia-an Liu, Chih-wen Weng","submitted_at":"2016-01-26T13:23:40Z","abstract_excerpt":"It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph is determined by its spectrum. We provide some graphs, each of which is obtained from a complete bipartite graph by adding a vertex and an edge incident on the new vertex and an original vertex, which are not determined by their spectra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07012","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4QcvAuxUQPHVj4jlZUHhjyHsIwKoYFfMmc2HeQl3SknxQyg4/E+XTpGc5eVWTE6RU2T/PlKJ28bKqaCm0rzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:32:38.848509Z"},"content_sha256":"b92acb3727ededcffc1ffdb3b374710b317e9240d5c346f9e075234394e5ef44","schema_version":"1.0","event_id":"sha256:b92acb3727ededcffc1ffdb3b374710b317e9240d5c346f9e075234394e5ef44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN/bundle.json","state_url":"https://pith.science/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T06:32:38Z","links":{"resolver":"https://pith.science/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN","bundle":"https://pith.science/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN/bundle.json","state":"https://pith.science/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3OP4NX6PLNEWK5JOO7RPCFVCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P3OP4NX6PLNEWK5JOO7RPCFVCN","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":"013d9c7dc6c4a59fa3713bf0091af11a20c892261dee4c0edeed459d61b39d0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T13:23:40Z","title_canon_sha256":"d916e1899b5a083b6e38a9dc19e037a4031d4a531c08ac0ee97a49085c6c148d"},"schema_version":"1.0","source":{"id":"1601.07012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07012","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07012v1","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07012","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"P3OP4NX6PLNE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P3OP4NX6PLNEWK5J","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P3OP4NX6","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:b92acb3727ededcffc1ffdb3b374710b317e9240d5c346f9e075234394e5ef44","target":"graph","created_at":"2026-05-18T01:21:59Z","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":"It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph is determined by its spectrum. We provide some graphs, each of which is obtained from a complete bipartite graph by adding a vertex and an edge incident on the new vertex and an original vertex, which are not determined by their spectra.","authors_text":"Chia-an Liu, Chih-wen Weng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T13:23:40Z","title":"Spectral characterizations of two families of nearly complete bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07012","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":"sha256:8c18bbd261182e0e18c22958743e3a435c94248b9e0ead3ecdefb8ca8735f20b","target":"record","created_at":"2026-05-18T01:21:59Z","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":"013d9c7dc6c4a59fa3713bf0091af11a20c892261dee4c0edeed459d61b39d0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T13:23:40Z","title_canon_sha256":"d916e1899b5a083b6e38a9dc19e037a4031d4a531c08ac0ee97a49085c6c148d"},"schema_version":"1.0","source":{"id":"1601.07012","kind":"arxiv","version":1}},"canonical_sha256":"7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7edcfe36fe7ada4b2ba973bf1788b51362030d08db72b86223afa7fa6768e292","first_computed_at":"2026-05-18T01:21:59.292867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:59.292867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZhnhG0hRn07B8B+x+mUD5jZZMvtP4/nnbB6Ce9tV2ihKyA/B+/hXRgpFjlpJ6EF4USbdMk7Ung37/wQf5X4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:59.293291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c18bbd261182e0e18c22958743e3a435c94248b9e0ead3ecdefb8ca8735f20b","sha256:b92acb3727ededcffc1ffdb3b374710b317e9240d5c346f9e075234394e5ef44"],"state_sha256":"a32e39e26eb5ae7c6a0a2f187827621b658446e605503e19ab05fdae16d280da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6WSelZkQQfPSykib9MCpC398GrpS4OqYlgl7/J6KxkqiN6RLasv+1GjoCpkrRX4WjzAKVGAn4LhZ9OAnQQtUCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:32:38.852651Z","bundle_sha256":"aecbe1564a68d173e6e51beaa572df55d4aa2384d0a6df2f8ec7636783c9ae8f"}}