{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XS3QI4FDSFCKMX6UNT537QTJWJ","short_pith_number":"pith:XS3QI4FD","canonical_record":{"source":{"id":"1701.03213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-12T02:24:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"eb7ffc644bd32f04a8f189eff42e38840fe1fc26faf8e026b2759fc05588df2e","abstract_canon_sha256":"7566a412097d92deaf792a856b095b1a33acede7f3c9355f7fff711c523af186"},"schema_version":"1.0"},"canonical_sha256":"bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736","source":{"kind":"arxiv","id":"1701.03213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03213","created_at":"2026-05-18T00:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03213v1","created_at":"2026-05-18T00:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03213","created_at":"2026-05-18T00:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"XS3QI4FDSFCK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XS3QI4FDSFCKMX6U","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XS3QI4FD","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XS3QI4FDSFCKMX6UNT537QTJWJ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.03213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-12T02:24:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"eb7ffc644bd32f04a8f189eff42e38840fe1fc26faf8e026b2759fc05588df2e","abstract_canon_sha256":"7566a412097d92deaf792a856b095b1a33acede7f3c9355f7fff711c523af186"},"schema_version":"1.0"},"canonical_sha256":"bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:16.274494Z","signature_b64":"dAuA6JCz5znFfdhlL3za+t5uxz1i/nC8n42tdh9q7t30jJFiWOVisxKDziKISwQ8mC+eRaD09TEX7k+wfZpnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736","last_reissued_at":"2026-05-18T00:28:16.273689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:16.273689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.03213","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uv+PH7hG1spCnopjgb9vgxaiLYqXkpcDbz6vww1ff9s7HZ5uR6v0bcoGcYPKv0HlV8+w5F/gyTOc5xK061zABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:46:39.613713Z"},"content_sha256":"be081ff07694e2fdb9bf1427317f8246c30c697c9477ed0618945fa39b201a1f","schema_version":"1.0","event_id":"sha256:be081ff07694e2fdb9bf1427317f8246c30c697c9477ed0618945fa39b201a1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XS3QI4FDSFCKMX6UNT537QTJWJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorem for the Horton-Strahler bifurcation ratio of general branch order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Ken Yamamoto","submitted_at":"2017-01-12T02:24:31Z","abstract_excerpt":"The Horton-Strahler ordering method, originating in hydrology, formulates the hierarchical structure of branching patterns using a quantity called the bifurcation ratio. The main result of this paper is the central limit theorem for bifurcation ratio of general branch order. This is a generalized form of the central limit theorem for the lowest bifurcation ratio, which was previously proved. Some useful relations are also derived in the proofs of the main theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03213","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0SnXaYP7IXF6V64srms90M6eF7/fWbo+5+b/B6lPpEXymvb12BlpdSpZN517xISXjMQKrYYibjh8PZ1EJi9lCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:46:39.614193Z"},"content_sha256":"9b3966885eef60b90360c4f6ef8dd2a1ace096a098d2bf37fa43a03c89d5117e","schema_version":"1.0","event_id":"sha256:9b3966885eef60b90360c4f6ef8dd2a1ace096a098d2bf37fa43a03c89d5117e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XS3QI4FDSFCKMX6UNT537QTJWJ/bundle.json","state_url":"https://pith.science/pith/XS3QI4FDSFCKMX6UNT537QTJWJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XS3QI4FDSFCKMX6UNT537QTJWJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T20:46:39Z","links":{"resolver":"https://pith.science/pith/XS3QI4FDSFCKMX6UNT537QTJWJ","bundle":"https://pith.science/pith/XS3QI4FDSFCKMX6UNT537QTJWJ/bundle.json","state":"https://pith.science/pith/XS3QI4FDSFCKMX6UNT537QTJWJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XS3QI4FDSFCKMX6UNT537QTJWJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XS3QI4FDSFCKMX6UNT537QTJWJ","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":"7566a412097d92deaf792a856b095b1a33acede7f3c9355f7fff711c523af186","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-12T02:24:31Z","title_canon_sha256":"eb7ffc644bd32f04a8f189eff42e38840fe1fc26faf8e026b2759fc05588df2e"},"schema_version":"1.0","source":{"id":"1701.03213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03213","created_at":"2026-05-18T00:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03213v1","created_at":"2026-05-18T00:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03213","created_at":"2026-05-18T00:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"XS3QI4FDSFCK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XS3QI4FDSFCKMX6U","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XS3QI4FD","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:9b3966885eef60b90360c4f6ef8dd2a1ace096a098d2bf37fa43a03c89d5117e","target":"graph","created_at":"2026-05-18T00:28:16Z","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-Strahler ordering method, originating in hydrology, formulates the hierarchical structure of branching patterns using a quantity called the bifurcation ratio. The main result of this paper is the central limit theorem for bifurcation ratio of general branch order. This is a generalized form of the central limit theorem for the lowest bifurcation ratio, which was previously proved. Some useful relations are also derived in the proofs of the main theorems.","authors_text":"Ken Yamamoto","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-12T02:24:31Z","title":"Central limit theorem for the Horton-Strahler bifurcation ratio of general branch order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03213","kind":"arxiv","version":1},"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:be081ff07694e2fdb9bf1427317f8246c30c697c9477ed0618945fa39b201a1f","target":"record","created_at":"2026-05-18T00:28:16Z","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":"7566a412097d92deaf792a856b095b1a33acede7f3c9355f7fff711c523af186","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-12T02:24:31Z","title_canon_sha256":"eb7ffc644bd32f04a8f189eff42e38840fe1fc26faf8e026b2759fc05588df2e"},"schema_version":"1.0","source":{"id":"1701.03213","kind":"arxiv","version":1}},"canonical_sha256":"bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736","first_computed_at":"2026-05-18T00:28:16.273689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:16.273689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dAuA6JCz5znFfdhlL3za+t5uxz1i/nC8n42tdh9q7t30jJFiWOVisxKDziKISwQ8mC+eRaD09TEX7k+wfZpnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:16.274494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be081ff07694e2fdb9bf1427317f8246c30c697c9477ed0618945fa39b201a1f","sha256:9b3966885eef60b90360c4f6ef8dd2a1ace096a098d2bf37fa43a03c89d5117e"],"state_sha256":"2dc23c628caa68406376039b776da4bdc1bd55a925e58fbbb471bde4618551f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hH0vppRSQj5rX4PhLKudT2UL7aqHXrsapvRFwD2GEJieVatDfgaTDd5btYzwXLa1U4MnHCvKjVQDKz+YZ52uAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:46:39.617825Z","bundle_sha256":"056283cd699fff093c3fb54e0ddd93c4c25d54b466b82d2c64b200947e353cb3"}}