{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PDB7XFCDQEURBAEBWVR4HBYVOV","short_pith_number":"pith:PDB7XFCD","schema_version":"1.0","canonical_sha256":"78c3fb94438129108081b563c387157575410646d3dd87d7a71544f8bfb5d581","source":{"kind":"arxiv","id":"1803.03741","version":2},"attestation_state":"computed","paper":{"title":"Tokunaga self-similarity arises naturally from time invariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","nlin.AO","nlin.CD"],"primary_cat":"math.DS","authors_text":"Ilya Zaliapin, Yevgeniy Kovchegov","submitted_at":"2018-03-10T02:18:43Z","abstract_excerpt":"The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching processes $\\mathcal{G}(s)$ that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of $\\mathcal{G}(s)$ with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region w"},"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":"1803.03741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-10T02:18:43Z","cross_cats_sorted":["math.PR","nlin.AO","nlin.CD"],"title_canon_sha256":"727d44d329b46438ab9e1fc30f15a3be4414f9998dc03cf52b96d148e77c9fd5","abstract_canon_sha256":"82d9ef0f336d00664ba068a2da8c10b6aa5b44b5617d8c44d351b1804b3e3c1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:25.329542Z","signature_b64":"UkNdfcQQiKQX28MG4rVwajbXvCw4hDfimFIGdnVCmBlLeUu4ANBAfoD+wmDy7aFTUN8kvjEHw8715mX0QUV/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78c3fb94438129108081b563c387157575410646d3dd87d7a71544f8bfb5d581","last_reissued_at":"2026-05-18T00:16:25.328836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:25.328836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tokunaga self-similarity arises naturally from time invariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","nlin.AO","nlin.CD"],"primary_cat":"math.DS","authors_text":"Ilya Zaliapin, Yevgeniy Kovchegov","submitted_at":"2018-03-10T02:18:43Z","abstract_excerpt":"The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching processes $\\mathcal{G}(s)$ that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of $\\mathcal{G}(s)$ with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03741","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.03741","created_at":"2026-05-18T00:16:25.328947+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03741v2","created_at":"2026-05-18T00:16:25.328947+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03741","created_at":"2026-05-18T00:16:25.328947+00:00"},{"alias_kind":"pith_short_12","alias_value":"PDB7XFCDQEUR","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"PDB7XFCDQEURBAEB","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"PDB7XFCD","created_at":"2026-05-18T12:32:43.782077+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/PDB7XFCDQEURBAEBWVR4HBYVOV","json":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV.json","graph_json":"https://pith.science/api/pith-number/PDB7XFCDQEURBAEBWVR4HBYVOV/graph.json","events_json":"https://pith.science/api/pith-number/PDB7XFCDQEURBAEBWVR4HBYVOV/events.json","paper":"https://pith.science/paper/PDB7XFCD"},"agent_actions":{"view_html":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV","download_json":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV.json","view_paper":"https://pith.science/paper/PDB7XFCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03741&json=true","fetch_graph":"https://pith.science/api/pith-number/PDB7XFCDQEURBAEBWVR4HBYVOV/graph.json","fetch_events":"https://pith.science/api/pith-number/PDB7XFCDQEURBAEBWVR4HBYVOV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV/action/storage_attestation","attest_author":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV/action/author_attestation","sign_citation":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV/action/citation_signature","submit_replication":"https://pith.science/pith/PDB7XFCDQEURBAEBWVR4HBYVOV/action/replication_record"}},"created_at":"2026-05-18T00:16:25.328947+00:00","updated_at":"2026-05-18T00:16:25.328947+00:00"}