{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZMTOVDSJ2SR2LZSRBJXLL4THR7","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":"92400d5d924c05696519da72ca04a6fcaf465cef5b058fb8c586dd6ec05f372b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-27T06:55:10Z","title_canon_sha256":"ef66755ce82c99a75eb1801100dfe076716e82fe2f6d52d8511463a666bdeeb2"},"schema_version":"1.0","source":{"id":"1705.10611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10611","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10611v1","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10611","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZMTOVDSJ2SR2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZMTOVDSJ2SR2LZSR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZMTOVDSJ","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:3969fbb524ba1a126ae79ec71eba3d25112aadbf6ca1a8aa3b5f6b4013609fcc","target":"graph","created_at":"2026-05-18T00:43:24Z","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 compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups.","authors_text":"Parama Dutta, Rajat Kanti Nath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-27T06:55:10Z","title":"On Laplacian energy of non-commuting graphs of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10611","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":"sha256:2b71b78a3bdc49f433d663a39e289b1f30960b48df5a6fbe4dbe555841f24e3f","target":"record","created_at":"2026-05-18T00:43:24Z","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":"92400d5d924c05696519da72ca04a6fcaf465cef5b058fb8c586dd6ec05f372b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-27T06:55:10Z","title_canon_sha256":"ef66755ce82c99a75eb1801100dfe076716e82fe2f6d52d8511463a666bdeeb2"},"schema_version":"1.0","source":{"id":"1705.10611","kind":"arxiv","version":1}},"canonical_sha256":"cb26ea8e49d4a3a5e6510a6eb5f2678ff13b109d145f533ab5db9d4b54983bb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb26ea8e49d4a3a5e6510a6eb5f2678ff13b109d145f533ab5db9d4b54983bb7","first_computed_at":"2026-05-18T00:43:24.051490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:24.051490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OFpD0I9lwJ/3c65Vzg2jZMdqtl8jiM/+96fvEGljAZtWWZvuUBkCI+nJRP2ETWcPeT+wSAxsCefjRBvKzBciCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:24.052225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b71b78a3bdc49f433d663a39e289b1f30960b48df5a6fbe4dbe555841f24e3f","sha256:3969fbb524ba1a126ae79ec71eba3d25112aadbf6ca1a8aa3b5f6b4013609fcc"],"state_sha256":"c588b5e04680dfaf37aa2312c739e7a2f12d3c36e90ea5e857de1ebbb4b2a09d"}