{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2BHAQ2KNGD2AHZSTJQGBFGJ2CP","short_pith_number":"pith:2BHAQ2KN","schema_version":"1.0","canonical_sha256":"d04e08694d30f403e6534c0c12993a13f26045452bd0c17afcba93b991df2c60","source":{"kind":"arxiv","id":"1409.7449","version":1},"attestation_state":"computed","paper":{"title":"Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Alberto Robledo, Alvaro Diaz-Ruelas, Miguel Angel Fuentes","submitted_at":"2014-09-26T00:46:30Z","abstract_excerpt":"The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of chaos and a Gaussian trivial fixed-point distribution for all chaotic attractors. Here we describe in detail the crossover distributions that can be generated at chaotic band-splitting points that mediate between the aforementioned fixed-point distributions. Self affinity in the chaotic region imprints scaling features to the crossover distribution"},"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":"1409.7449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-09-26T00:46:30Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"a230b62cfe2c0d912317c0b6d219a0b647270d855707ccee10373a29d52c00ce","abstract_canon_sha256":"fc9a64b3d3fe6597c1562fc2f7171497810deb057f8213f9999e06ff40e12417"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:56.685160Z","signature_b64":"q4TOsCxRCRL5jeiThX9nt1FcTQeH5HnRnHg4/aJZr90n1QBM8jcIgj9BDPeqjD0kd5vRW6OfBxtMKEEZcN19CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d04e08694d30f403e6534c0c12993a13f26045452bd0c17afcba93b991df2c60","last_reissued_at":"2026-05-18T01:41:56.684595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:56.684595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Alberto Robledo, Alvaro Diaz-Ruelas, Miguel Angel Fuentes","submitted_at":"2014-09-26T00:46:30Z","abstract_excerpt":"The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of chaos and a Gaussian trivial fixed-point distribution for all chaotic attractors. Here we describe in detail the crossover distributions that can be generated at chaotic band-splitting points that mediate between the aforementioned fixed-point distributions. Self affinity in the chaotic region imprints scaling features to the crossover distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7449","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":"1409.7449","created_at":"2026-05-18T01:41:56.684675+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.7449v1","created_at":"2026-05-18T01:41:56.684675+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7449","created_at":"2026-05-18T01:41:56.684675+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BHAQ2KNGD2A","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BHAQ2KNGD2AHZST","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BHAQ2KN","created_at":"2026-05-18T12:28:09.283467+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/2BHAQ2KNGD2AHZSTJQGBFGJ2CP","json":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP.json","graph_json":"https://pith.science/api/pith-number/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/graph.json","events_json":"https://pith.science/api/pith-number/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/events.json","paper":"https://pith.science/paper/2BHAQ2KN"},"agent_actions":{"view_html":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP","download_json":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP.json","view_paper":"https://pith.science/paper/2BHAQ2KN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.7449&json=true","fetch_graph":"https://pith.science/api/pith-number/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/graph.json","fetch_events":"https://pith.science/api/pith-number/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/action/storage_attestation","attest_author":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/action/author_attestation","sign_citation":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/action/citation_signature","submit_replication":"https://pith.science/pith/2BHAQ2KNGD2AHZSTJQGBFGJ2CP/action/replication_record"}},"created_at":"2026-05-18T01:41:56.684675+00:00","updated_at":"2026-05-18T01:41:56.684675+00:00"}