{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KSWFEB7XYKNIUQZRLKERBPB2B3","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":"d46fda95712d3605b3af9ef7cb887871b71badcb63f13b03ad38057b28714e4a","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-04T15:02:06Z","title_canon_sha256":"70b0780307ea08751216e11ebfa480cf4f29fee176a4df3e0b5d7d11ea0f09ad"},"schema_version":"1.0","source":{"id":"1303.0718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0718","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0718v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0718","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"KSWFEB7XYKNI","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KSWFEB7XYKNIUQZR","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KSWFEB7X","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:10c7bf7fa7dbb8f98678479ec6b31b39455576b504a3fb5530a139d68749be24","target":"graph","created_at":"2026-05-18T03:31:55Z","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":"There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;, the behavior of groups, or cliques, in social networks; the study of optimal convergence for consensus algorithm; and many other examples. Frequently the problems involve computing the index of a matrix, i.e. the number of positive and negative eigenvalues, and the dimension of the kernel. In this paper we consider one of the most common examples, where the ma","authors_text":"Jared C. Bronski, Lee DeVille","cross_cats":["cond-mat.dis-nn","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-04T15:02:06Z","title":"Spectral Theory for Networks with Attractive and Repulsive Interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0718","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:f4b201ddc62a9f6798ea8248bc80009536016ad065286c51386012fbe498a8d0","target":"record","created_at":"2026-05-18T03:31:55Z","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":"d46fda95712d3605b3af9ef7cb887871b71badcb63f13b03ad38057b28714e4a","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-04T15:02:06Z","title_canon_sha256":"70b0780307ea08751216e11ebfa480cf4f29fee176a4df3e0b5d7d11ea0f09ad"},"schema_version":"1.0","source":{"id":"1303.0718","kind":"arxiv","version":1}},"canonical_sha256":"54ac5207f7c29a8a43315a8910bc3a0ec7a67f84c5c5d91326f392d867a83af2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54ac5207f7c29a8a43315a8910bc3a0ec7a67f84c5c5d91326f392d867a83af2","first_computed_at":"2026-05-18T03:31:55.135103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:55.135103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S4qsxwQW8RphunFZP+R/9j8idGuVLfgQD+D4u3eZNorP7UvvO7jmkhDYFHPY7lf2K8PYXWK20wQwo2IlG7pRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:55.135726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4b201ddc62a9f6798ea8248bc80009536016ad065286c51386012fbe498a8d0","sha256:10c7bf7fa7dbb8f98678479ec6b31b39455576b504a3fb5530a139d68749be24"],"state_sha256":"2d408a1ba64d26acbc8a6ad52183473b271ff20160bb5fac3b636906a29ddfcf"}