{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:45GMAKHTDK5JOYQUD5BV3GFPQC","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":"931df8774be2ad463c615300b36baccd51857926dbc3f6bcd08c0bfe6f6e03c0","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-07T14:57:55Z","title_canon_sha256":"40dd6817f405c1f37805d48e2c93e2395bf1170e86c7b030429b571e88695062"},"schema_version":"1.0","source":{"id":"1905.02629","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02629","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02629v2","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02629","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"45GMAKHTDK5J","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"45GMAKHTDK5JOYQU","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"45GMAKHT","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:538e7f58a1e8e6e0f36c1376564628ae2533907574320a502fe91e48667941d3","target":"graph","created_at":"2026-05-17T23:45:51Z","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":"The Horton laws originated in hydrology with a 1945 paper by Robert E. Horton, and for a long time remained a purely empirical finding. Ubiquitous in hierarchical branching systems, the Horton laws have been rediscovered in many disciplines ranging from geomorphology to genetics to computer science. Attempts to build a mathematical foundation behind the Horton laws during the 1990s revealed their close connection to the operation of pruning -- erasing a tree from the leaves down to the root. This survey synthesizes recent results on invariances and self-similarities of tree measures under vari","authors_text":"Ilya Zaliapin, Yevgeniy Kovchegov","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-07T14:57:55Z","title":"Random Self-Similar Trees: A mathematical theory of Horton laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02629","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:a5545a69b474831d07fe503aba13be70f294ea89b1f5979fff84231adfab53ea","target":"record","created_at":"2026-05-17T23:45:51Z","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":"931df8774be2ad463c615300b36baccd51857926dbc3f6bcd08c0bfe6f6e03c0","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-07T14:57:55Z","title_canon_sha256":"40dd6817f405c1f37805d48e2c93e2395bf1170e86c7b030429b571e88695062"},"schema_version":"1.0","source":{"id":"1905.02629","kind":"arxiv","version":2}},"canonical_sha256":"e74cc028f31aba9762141f435d98af809ccf9f657662687840a546cadb1a66a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e74cc028f31aba9762141f435d98af809ccf9f657662687840a546cadb1a66a9","first_computed_at":"2026-05-17T23:45:51.584854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:51.584854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GtNWEQTwqub6Vh9lzrrxGLuD6LwGnez6gG5VKxfoa5wdZ4xQhtWM8MOcLALDv7B7+ORQs610nh4cQka0qf3aCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:51.585231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02629","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5545a69b474831d07fe503aba13be70f294ea89b1f5979fff84231adfab53ea","sha256:538e7f58a1e8e6e0f36c1376564628ae2533907574320a502fe91e48667941d3"],"state_sha256":"1ed2baef2aa727ebcf2c086630a45248ac74b405759dc16e39a9e8646e842e2d"}