{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RAEZIHCVF6ZJDUCR6QM4XEID4J","short_pith_number":"pith:RAEZIHCV","schema_version":"1.0","canonical_sha256":"8809941c552fb291d051f419cb9103e269318cd6415759ada2709e2a0f847484","source":{"kind":"arxiv","id":"2403.14584","version":2},"attestation_state":"computed","paper":{"title":"Dynamical importance and network perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.AO","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Ethan Young, Mason A. Porter","submitted_at":"2024-03-21T17:40:28Z","abstract_excerpt":"The leading eigenvalue $\\lambda$ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of the importance (specifically, centrality measures) of network structures to $\\lambda$ and its associated eigenvector. We study a previously derived measure of edge importance known as ``dynamical importance'', which estimates how much $\\lambda$ changes when one removes an edge from a graph or adds an edge to it. We examine the accuracy of this estimate for different network structures and compare it to the true "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2403.14584","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2024-03-21T17:40:28Z","cross_cats_sorted":["math.DS","nlin.AO","physics.soc-ph"],"title_canon_sha256":"c28fa3f65484d4a0d04d6e1af0cbab85b9a2ba6ff4ec4137cc17145f382a7e26","abstract_canon_sha256":"483f3aae9ac5aa0713c9161fb39e60cfcef6022a8926902cb1bb78207a5b27ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:57:36.948163Z","signature_b64":"UdpbQJLsGNdVPG3H6kXAIXucGb8Vj76gM+RuH9HASln4y1EPIjXY3KRPsE9+zLOslF4ZUvXVO+BDAOFIA4AIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8809941c552fb291d051f419cb9103e269318cd6415759ada2709e2a0f847484","last_reissued_at":"2026-07-05T08:57:36.947764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:57:36.947764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical importance and network perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.AO","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Ethan Young, Mason A. Porter","submitted_at":"2024-03-21T17:40:28Z","abstract_excerpt":"The leading eigenvalue $\\lambda$ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of the importance (specifically, centrality measures) of network structures to $\\lambda$ and its associated eigenvector. We study a previously derived measure of edge importance known as ``dynamical importance'', which estimates how much $\\lambda$ changes when one removes an edge from a graph or adds an edge to it. We examine the accuracy of this estimate for different network structures and compare it to the true "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.14584","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.14584/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2403.14584","created_at":"2026-07-05T08:57:36.947812+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.14584v2","created_at":"2026-07-05T08:57:36.947812+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.14584","created_at":"2026-07-05T08:57:36.947812+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAEZIHCVF6ZJ","created_at":"2026-07-05T08:57:36.947812+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAEZIHCVF6ZJDUCR","created_at":"2026-07-05T08:57:36.947812+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAEZIHCV","created_at":"2026-07-05T08:57:36.947812+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J","json":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J.json","graph_json":"https://pith.science/api/pith-number/RAEZIHCVF6ZJDUCR6QM4XEID4J/graph.json","events_json":"https://pith.science/api/pith-number/RAEZIHCVF6ZJDUCR6QM4XEID4J/events.json","paper":"https://pith.science/paper/RAEZIHCV"},"agent_actions":{"view_html":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J","download_json":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J.json","view_paper":"https://pith.science/paper/RAEZIHCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.14584&json=true","fetch_graph":"https://pith.science/api/pith-number/RAEZIHCVF6ZJDUCR6QM4XEID4J/graph.json","fetch_events":"https://pith.science/api/pith-number/RAEZIHCVF6ZJDUCR6QM4XEID4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J/action/storage_attestation","attest_author":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J/action/author_attestation","sign_citation":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J/action/citation_signature","submit_replication":"https://pith.science/pith/RAEZIHCVF6ZJDUCR6QM4XEID4J/action/replication_record"}},"created_at":"2026-07-05T08:57:36.947812+00:00","updated_at":"2026-07-05T08:57:36.947812+00:00"}