{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BZE2LMF6IH2MSTBDFFQLP2YCNC","short_pith_number":"pith:BZE2LMF6","schema_version":"1.0","canonical_sha256":"0e49a5b0be41f4c94c232960b7eb02689ac7b819fdbdbde4addac4ee25075696","source":{"kind":"arxiv","id":"1804.03711","version":1},"attestation_state":"computed","paper":{"title":"Finite-time scaling in local bifurcations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Alvaro Corral, Josep Sardanyes, Lluis Alseda","submitted_at":"2018-04-10T20:40:03Z","abstract_excerpt":"Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal. Our work"},"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":"1804.03711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2018-04-10T20:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"5ebc1c301ca3151dd608cf3b89e5e613e64af611df1c6a4aaa0d8c611759dabd","abstract_canon_sha256":"173cccea8efd8e1fed54da09108d06bad239c522ce0ade99f9a371500170b819"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:45.242818Z","signature_b64":"Ock240uznk2yFbXCXYsf5pKEq0hY5xkxU2025pxlgF/KljfJ44x0E2/9PgGU+DsmHBmdiCPOXjqyFLLtnGjmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e49a5b0be41f4c94c232960b7eb02689ac7b819fdbdbde4addac4ee25075696","last_reissued_at":"2026-05-18T00:18:45.242294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:45.242294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite-time scaling in local bifurcations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Alvaro Corral, Josep Sardanyes, Lluis Alseda","submitted_at":"2018-04-10T20:40:03Z","abstract_excerpt":"Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal. Our work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03711","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.03711","created_at":"2026-05-18T00:18:45.242390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03711v1","created_at":"2026-05-18T00:18:45.242390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03711","created_at":"2026-05-18T00:18:45.242390+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZE2LMF6IH2M","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZE2LMF6IH2MSTBD","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZE2LMF6","created_at":"2026-05-18T12:32:16.446611+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/BZE2LMF6IH2MSTBDFFQLP2YCNC","json":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC.json","graph_json":"https://pith.science/api/pith-number/BZE2LMF6IH2MSTBDFFQLP2YCNC/graph.json","events_json":"https://pith.science/api/pith-number/BZE2LMF6IH2MSTBDFFQLP2YCNC/events.json","paper":"https://pith.science/paper/BZE2LMF6"},"agent_actions":{"view_html":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC","download_json":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC.json","view_paper":"https://pith.science/paper/BZE2LMF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03711&json=true","fetch_graph":"https://pith.science/api/pith-number/BZE2LMF6IH2MSTBDFFQLP2YCNC/graph.json","fetch_events":"https://pith.science/api/pith-number/BZE2LMF6IH2MSTBDFFQLP2YCNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC/action/storage_attestation","attest_author":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC/action/author_attestation","sign_citation":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC/action/citation_signature","submit_replication":"https://pith.science/pith/BZE2LMF6IH2MSTBDFFQLP2YCNC/action/replication_record"}},"created_at":"2026-05-18T00:18:45.242390+00:00","updated_at":"2026-05-18T00:18:45.242390+00:00"}