{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:K55VI34MGBF4LJJVL4SPFAOMJ2","short_pith_number":"pith:K55VI34M","canonical_record":{"source":{"id":"1503.01069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-03T19:20:21Z","cross_cats_sorted":[],"title_canon_sha256":"18864bb06cd5ced813d7ebe2f5a0af64a7546b3b35246bcd3827c9cd069e2d5c","abstract_canon_sha256":"9ccb8e9c95147fcac1d2e10956b3027aa86e4477c4b08bcef89f824803814983"},"schema_version":"1.0"},"canonical_sha256":"577b546f8c304bc5a5355f24f281cc4eb24b49490614f3b92e8df5144790eba2","source":{"kind":"arxiv","id":"1503.01069","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01069","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01069v2","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01069","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"pith_short_12","alias_value":"K55VI34MGBF4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K55VI34MGBF4LJJV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K55VI34M","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:K55VI34MGBF4LJJVL4SPFAOMJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-03T19:20:21Z","cross_cats_sorted":[],"title_canon_sha256":"18864bb06cd5ced813d7ebe2f5a0af64a7546b3b35246bcd3827c9cd069e2d5c","abstract_canon_sha256":"9ccb8e9c95147fcac1d2e10956b3027aa86e4477c4b08bcef89f824803814983"},"schema_version":"1.0"},"canonical_sha256":"577b546f8c304bc5a5355f24f281cc4eb24b49490614f3b92e8df5144790eba2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:25.956323Z","signature_b64":"rtdRNVcDszqEwnaEri4KwUfHond8wsYsr+s4OOGcthGlyBmjNk1w47AoVRmTkcJAAGVgtnuJfUcH8DD+3tcvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"577b546f8c304bc5a5355f24f281cc4eb24b49490614f3b92e8df5144790eba2","last_reissued_at":"2026-05-18T02:23:25.955681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:25.955681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01069","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TJvmPu0FLlie1stqnm4Pv1PFks+KhWPnpxNWp+9i2fcXOlrazI1sh6rPUD2LdxjRdQXPreAJT2LIE9zQDikCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:40:35.738016Z"},"content_sha256":"5d311e1a0079e75e07e9927999b39cbf11f2894ef483f0fb1474d0b7b74bcb20","schema_version":"1.0","event_id":"sha256:5d311e1a0079e75e07e9927999b39cbf11f2894ef483f0fb1474d0b7b74bcb20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:K55VI34MGBF4LJJVL4SPFAOMJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spectral index of signed Laplacians and their structural stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jared Bronski, K. Paolina Koutsaki, Lee DeVille","submitted_at":"2015-03-03T19:20:21Z","abstract_excerpt":"Given a graph Laplacian with positively and negatively weighted edges we are interested in characterizing the set of weights that give a particular spectral index, i.e.~give a prescribed number of positive, zero, and negative eigenvalues. One of the main results of this paper is that the set of signed Laplacians that exhibit multiple zero eigenvalues is \"small\", and that eigenvalue crossings are nongeneric --- specifically, eigenvalues repel each other near zero in a sense that can be made precise. We exhibit an algebraic discriminant that measures the level of repulsion, and show that this di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01069","kind":"arxiv","version":2},"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":"2026-05-18T02:23:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UsaU9j3rYUq90JaFtftSA2GDelIoQH9PLNNfprr1/KrRKy9ptCu4npbzmAIaPib6OVLLrcR4wbya9FTSaYjcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:40:35.738787Z"},"content_sha256":"3c6a7ca628cd828fd60c9c99bbde2d015c2e15b05c51655ccee011a834581c35","schema_version":"1.0","event_id":"sha256:3c6a7ca628cd828fd60c9c99bbde2d015c2e15b05c51655ccee011a834581c35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K55VI34MGBF4LJJVL4SPFAOMJ2/bundle.json","state_url":"https://pith.science/pith/K55VI34MGBF4LJJVL4SPFAOMJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K55VI34MGBF4LJJVL4SPFAOMJ2/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":"2026-05-28T17:40:35Z","links":{"resolver":"https://pith.science/pith/K55VI34MGBF4LJJVL4SPFAOMJ2","bundle":"https://pith.science/pith/K55VI34MGBF4LJJVL4SPFAOMJ2/bundle.json","state":"https://pith.science/pith/K55VI34MGBF4LJJVL4SPFAOMJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K55VI34MGBF4LJJVL4SPFAOMJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K55VI34MGBF4LJJVL4SPFAOMJ2","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":"9ccb8e9c95147fcac1d2e10956b3027aa86e4477c4b08bcef89f824803814983","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-03T19:20:21Z","title_canon_sha256":"18864bb06cd5ced813d7ebe2f5a0af64a7546b3b35246bcd3827c9cd069e2d5c"},"schema_version":"1.0","source":{"id":"1503.01069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01069","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01069v2","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01069","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"pith_short_12","alias_value":"K55VI34MGBF4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K55VI34MGBF4LJJV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K55VI34M","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:3c6a7ca628cd828fd60c9c99bbde2d015c2e15b05c51655ccee011a834581c35","target":"graph","created_at":"2026-05-18T02:23:25Z","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":"Given a graph Laplacian with positively and negatively weighted edges we are interested in characterizing the set of weights that give a particular spectral index, i.e.~give a prescribed number of positive, zero, and negative eigenvalues. One of the main results of this paper is that the set of signed Laplacians that exhibit multiple zero eigenvalues is \"small\", and that eigenvalue crossings are nongeneric --- specifically, eigenvalues repel each other near zero in a sense that can be made precise. We exhibit an algebraic discriminant that measures the level of repulsion, and show that this di","authors_text":"Jared Bronski, K. Paolina Koutsaki, Lee DeVille","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-03T19:20:21Z","title":"The spectral index of signed Laplacians and their structural stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01069","kind":"arxiv","version":2},"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":"sha256:5d311e1a0079e75e07e9927999b39cbf11f2894ef483f0fb1474d0b7b74bcb20","target":"record","created_at":"2026-05-18T02:23:25Z","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":"9ccb8e9c95147fcac1d2e10956b3027aa86e4477c4b08bcef89f824803814983","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-03T19:20:21Z","title_canon_sha256":"18864bb06cd5ced813d7ebe2f5a0af64a7546b3b35246bcd3827c9cd069e2d5c"},"schema_version":"1.0","source":{"id":"1503.01069","kind":"arxiv","version":2}},"canonical_sha256":"577b546f8c304bc5a5355f24f281cc4eb24b49490614f3b92e8df5144790eba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"577b546f8c304bc5a5355f24f281cc4eb24b49490614f3b92e8df5144790eba2","first_computed_at":"2026-05-18T02:23:25.955681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:25.955681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rtdRNVcDszqEwnaEri4KwUfHond8wsYsr+s4OOGcthGlyBmjNk1w47AoVRmTkcJAAGVgtnuJfUcH8DD+3tcvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:25.956323Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d311e1a0079e75e07e9927999b39cbf11f2894ef483f0fb1474d0b7b74bcb20","sha256:3c6a7ca628cd828fd60c9c99bbde2d015c2e15b05c51655ccee011a834581c35"],"state_sha256":"2c23794987978ac975d230a1b84b9c45e7f57baef9d989278ef7778f0abcd71d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6yui/Y8+tOaebEPU0fudNZLWFsJqb5uCZtMJG11G/dQvv+Zom++5Lx9nv2WWSHwnqGfiqYBgjoFPm05E8HzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:40:35.742670Z","bundle_sha256":"bc7a8a6b768fee04e4dd1d5b002e1b3042644ae4746203168603daceb0b21af1"}}