{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NB3UOFCVGMPLGBXUGPVIGQDZVO","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":"58a026a2bbf7985369e1ff6cf20d4055e0305e9b85a023a885c2368bb8f4a0ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-23T20:58:48Z","title_canon_sha256":"3481c3f86ce2a7f94173422dd117aee023b5cdca629aa335abc16770913d1b3e"},"schema_version":"1.0","source":{"id":"1103.4629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4629","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4629v1","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4629","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"NB3UOFCVGMPL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NB3UOFCVGMPLGBXU","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NB3UOFCV","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:79483216984a4ca5d00beb8e5da4a99532fddaee384a889cfab32750514e63a2","target":"graph","created_at":"2026-05-18T04:26:01Z","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":"We obtain new bounds for the Laplacian spectral radius of a signed graph. Most of these new bounds have a dependence on edge sign, unlike previously known bounds, which only depend on the underlying structure of the graph. We then use some of these bounds to obtain new bounds for the Laplacian and signless Laplacian spectral radius of an unsigned graph by signing the edges all positive and all negative, respectively.","authors_text":"Nathan Reff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-23T20:58:48Z","title":"New Bounds for the Laplacian Spectral Radius of a Signed Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4629","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":"sha256:9cb5c0eaa5f5d3ea600e73c1df656e2354c1ad9a7d9c02d5d0f869081c9c36a6","target":"record","created_at":"2026-05-18T04:26:01Z","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":"58a026a2bbf7985369e1ff6cf20d4055e0305e9b85a023a885c2368bb8f4a0ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-23T20:58:48Z","title_canon_sha256":"3481c3f86ce2a7f94173422dd117aee023b5cdca629aa335abc16770913d1b3e"},"schema_version":"1.0","source":{"id":"1103.4629","kind":"arxiv","version":1}},"canonical_sha256":"6877471455331eb306f433ea834079aba4ddbe46fc27513dd4f96a604650b2e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6877471455331eb306f433ea834079aba4ddbe46fc27513dd4f96a604650b2e1","first_computed_at":"2026-05-18T04:26:01.201711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:01.201711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vg0Aq15WLOqvfFTAQaFJdUPqROkultNq3qg/7RzLmdT5mb+XR2sWROQdlwvssXd0eQXkdIZSuFcr5EcXBHuJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:01.202650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cb5c0eaa5f5d3ea600e73c1df656e2354c1ad9a7d9c02d5d0f869081c9c36a6","sha256:79483216984a4ca5d00beb8e5da4a99532fddaee384a889cfab32750514e63a2"],"state_sha256":"44fa698174ab993c75c3aa4aeb876f47f9a5edb0cf42d3d969090d2f2b8c9130"}