{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YTCTYG4RUBZ6G7VTBA4ILGENCL","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":"132f47cfe56670d959b9e4b32ebd300477969a36452cb85232ae050b64bb39a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-18T14:23:34Z","title_canon_sha256":"4664c4af878dbb9ab1caf8eeff6accb7caaf298315ce3818bdd5975ef0c7bb8d"},"schema_version":"1.0","source":{"id":"1411.4850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4850","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4850v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4850","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"YTCTYG4RUBZ6","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YTCTYG4RUBZ6G7VT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YTCTYG4R","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:55ae55b03a7ae51e99e097a30af73a64d908e8c9fe51559802e0efb0dd321b0c","target":"graph","created_at":"2026-05-18T02:34:51Z","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":"For a simple graph $G$ and a real number $\\alpha $ $\\left(\\alpha \\neq 0,1\\right) $ the graph invariant $s_{\\alpha}\\left(G\\right) $ is equal to the sum of powers of signless Laplacian eigenvalues of $G$. In this note, we present some new bounds on $s_{\\alpha}\\left(G\\right) $. As a result of these bounds, we also give some results on incidence energy.","authors_text":"\\c{S}. Burcu Bozkurt Alt{\\i}nda\\u{g}, Durmu\\c{s} Bozkurt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-18T14:23:34Z","title":"Note on the Sum of Powers of Signless Laplacian Eigenvalues of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4850","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:d377f8373ab162b6f65d39e61ee14812f2c6b35f52fff9531f1efe9fd43dadf4","target":"record","created_at":"2026-05-18T02:34:51Z","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":"132f47cfe56670d959b9e4b32ebd300477969a36452cb85232ae050b64bb39a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-18T14:23:34Z","title_canon_sha256":"4664c4af878dbb9ab1caf8eeff6accb7caaf298315ce3818bdd5975ef0c7bb8d"},"schema_version":"1.0","source":{"id":"1411.4850","kind":"arxiv","version":1}},"canonical_sha256":"c4c53c1b91a073e37eb3083885988d12fc8e594c36da30cdfaa8a142d74ba1ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4c53c1b91a073e37eb3083885988d12fc8e594c36da30cdfaa8a142d74ba1ff","first_computed_at":"2026-05-18T02:34:51.122592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:51.122592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3yad8m5A3d3RV2APf0ELOMVhwRslf6id4EGHwAZm8LkEHCeYyR3H6qb6ryuSsq9+OqnUz2Jj9mAHfeyXJUPbCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:51.122944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d377f8373ab162b6f65d39e61ee14812f2c6b35f52fff9531f1efe9fd43dadf4","sha256:55ae55b03a7ae51e99e097a30af73a64d908e8c9fe51559802e0efb0dd321b0c"],"state_sha256":"1c411fe5366f8b0dae8ed57df006dff16450cbe0a9f3d56cab7d0bedfc981682"}