{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SUBZ3AUQQF7MSGBURK7RLLY6VA","short_pith_number":"pith:SUBZ3AUQ","canonical_record":{"source":{"id":"1501.01382","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-07T07:43:58Z","cross_cats_sorted":[],"title_canon_sha256":"76e760e9ada118a96b2d77edd9eda771bacc22a876451d9c41374375ac8df1dd","abstract_canon_sha256":"e629ec9608996e4a9654125351b1107bd050ecfe5f4d352beb36a8ca8fd05993"},"schema_version":"1.0"},"canonical_sha256":"95039d8290817ec918348abf15af1ea82f28d13b95c0835cccc0381222420e0a","source":{"kind":"arxiv","id":"1501.01382","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01382","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01382v4","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01382","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"SUBZ3AUQQF7M","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUBZ3AUQQF7MSGBU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUBZ3AUQ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SUBZ3AUQQF7MSGBURK7RLLY6VA","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01382","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-07T07:43:58Z","cross_cats_sorted":[],"title_canon_sha256":"76e760e9ada118a96b2d77edd9eda771bacc22a876451d9c41374375ac8df1dd","abstract_canon_sha256":"e629ec9608996e4a9654125351b1107bd050ecfe5f4d352beb36a8ca8fd05993"},"schema_version":"1.0"},"canonical_sha256":"95039d8290817ec918348abf15af1ea82f28d13b95c0835cccc0381222420e0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:51.812752Z","signature_b64":"Ro+Kq+s14Zm7MylK0dVXqIcbJJs54KE8Xzm8nG1okfn7Xt01JgyfWoCF1RITGozUbSPnXtcCmRcZpvterDcQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95039d8290817ec918348abf15af1ea82f28d13b95c0835cccc0381222420e0a","last_reissued_at":"2026-05-18T01:11:51.812420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:51.812420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01382","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/7VcmCo2ZmppRgeBU/AIhqZcL1O7cNx6qn61NgvcE7EX+o4Z9k/0mcVV5yXZUEVkroD2qz30RIskbSVD/45/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:22:21.842371Z"},"content_sha256":"10baceefb4c67cbe7664db9f6abc463d3886014d10713a5f2a3c1399f5081b02","schema_version":"1.0","event_id":"sha256:10baceefb4c67cbe7664db9f6abc463d3886014d10713a5f2a3c1399f5081b02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SUBZ3AUQQF7MSGBURK7RLLY6VA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hack's law in a drainage network model: A Brownian web approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anish Sarkar, Kumarjit Saha, Rahul Roy","submitted_at":"2015-01-07T07:43:58Z","abstract_excerpt":"Hack [Studies of longitudinal stream profiles in Virginia and Maryland (1957). Report], while studying the drainage system in the Shenandoah valley and the adjacent mountains of Virginia, observed a power law relation $l\\sim a^{0.6}$ between the length $l$ of a stream from its source to a divide and the area $a$ of the basin that collects the precipitation contributing to the stream as tributaries. We study the tributary structure of Howard's drainage network model of headward growth and branching studied by Gangopadhyay, Roy and Sarkar [Ann. Appl. Probab. 14 (2004) 1242-1266]. We show that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01382","kind":"arxiv","version":4},"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":"2026-05-18T01:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFfHIRX4nvpzSy1FWYj2M/OHZfMJ/YRYNG5Z8YLzf7Cw5BL/C3mUQlh2CNso3ew7husAFgHheNrvg7mCr5ueDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:22:21.842996Z"},"content_sha256":"2b4ed6212a404906bb9129cdc67d4dc70a00951da361f10ac62714f9410044dd","schema_version":"1.0","event_id":"sha256:2b4ed6212a404906bb9129cdc67d4dc70a00951da361f10ac62714f9410044dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA/bundle.json","state_url":"https://pith.science/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA/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":"2026-06-11T16:22:21Z","links":{"resolver":"https://pith.science/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA","bundle":"https://pith.science/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA/bundle.json","state":"https://pith.science/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUBZ3AUQQF7MSGBURK7RLLY6VA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SUBZ3AUQQF7MSGBURK7RLLY6VA","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":"e629ec9608996e4a9654125351b1107bd050ecfe5f4d352beb36a8ca8fd05993","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-07T07:43:58Z","title_canon_sha256":"76e760e9ada118a96b2d77edd9eda771bacc22a876451d9c41374375ac8df1dd"},"schema_version":"1.0","source":{"id":"1501.01382","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01382","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01382v4","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01382","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"SUBZ3AUQQF7M","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUBZ3AUQQF7MSGBU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUBZ3AUQ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:2b4ed6212a404906bb9129cdc67d4dc70a00951da361f10ac62714f9410044dd","target":"graph","created_at":"2026-05-18T01:11:51Z","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":"Hack [Studies of longitudinal stream profiles in Virginia and Maryland (1957). Report], while studying the drainage system in the Shenandoah valley and the adjacent mountains of Virginia, observed a power law relation $l\\sim a^{0.6}$ between the length $l$ of a stream from its source to a divide and the area $a$ of the basin that collects the precipitation contributing to the stream as tributaries. We study the tributary structure of Howard's drainage network model of headward growth and branching studied by Gangopadhyay, Roy and Sarkar [Ann. Appl. Probab. 14 (2004) 1242-1266]. We show that th","authors_text":"Anish Sarkar, Kumarjit Saha, Rahul Roy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-07T07:43:58Z","title":"Hack's law in a drainage network model: A Brownian web approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01382","kind":"arxiv","version":4},"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":"sha256:10baceefb4c67cbe7664db9f6abc463d3886014d10713a5f2a3c1399f5081b02","target":"record","created_at":"2026-05-18T01:11:51Z","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":"e629ec9608996e4a9654125351b1107bd050ecfe5f4d352beb36a8ca8fd05993","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-07T07:43:58Z","title_canon_sha256":"76e760e9ada118a96b2d77edd9eda771bacc22a876451d9c41374375ac8df1dd"},"schema_version":"1.0","source":{"id":"1501.01382","kind":"arxiv","version":4}},"canonical_sha256":"95039d8290817ec918348abf15af1ea82f28d13b95c0835cccc0381222420e0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95039d8290817ec918348abf15af1ea82f28d13b95c0835cccc0381222420e0a","first_computed_at":"2026-05-18T01:11:51.812420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:51.812420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ro+Kq+s14Zm7MylK0dVXqIcbJJs54KE8Xzm8nG1okfn7Xt01JgyfWoCF1RITGozUbSPnXtcCmRcZpvterDcQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:51.812752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01382","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10baceefb4c67cbe7664db9f6abc463d3886014d10713a5f2a3c1399f5081b02","sha256:2b4ed6212a404906bb9129cdc67d4dc70a00951da361f10ac62714f9410044dd"],"state_sha256":"d1ebc5056d200fd74e39a5a3da47fa1100c7afee01fddbe9c3b63cc92524e92c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ta7z2Ja/FcxXfR07OfgY2KnPQXX6bohreGe4xFba6WOQ/BLKrlnD5arjPOKgOvDLTMWszAdafsVuBz05+BOEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:22:21.846588Z","bundle_sha256":"feede01e1dad0f912f20c0957d0e0d02fa84e64ef688033c30fff26b0be62267"}}