{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZAPY26FLK2IXYZ3ETIET7HAYGN","short_pith_number":"pith:ZAPY26FL","canonical_record":{"source":{"id":"1301.2728","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-01-12T22:57:32Z","cross_cats_sorted":["physics.data-an","q-fin.GN","stat.AP"],"title_canon_sha256":"45ce854b2ebbeadb0bb358a34bd0a8a04facebfc48ac90c4660f17b7f1449b45","abstract_canon_sha256":"bde3cb6a0a8728138f0e3b9e34fac796da8f78763adb656784b479652c52467b"},"schema_version":"1.0"},"canonical_sha256":"c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490","source":{"kind":"arxiv","id":"1301.2728","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2728","created_at":"2026-05-18T01:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2728v4","created_at":"2026-05-18T01:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2728","created_at":"2026-05-18T01:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZAPY26FLK2IX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZAPY26FLK2IXYZ3E","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZAPY26FL","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZAPY26FLK2IXYZ3ETIET7HAYGN","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2728","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-01-12T22:57:32Z","cross_cats_sorted":["physics.data-an","q-fin.GN","stat.AP"],"title_canon_sha256":"45ce854b2ebbeadb0bb358a34bd0a8a04facebfc48ac90c4660f17b7f1449b45","abstract_canon_sha256":"bde3cb6a0a8728138f0e3b9e34fac796da8f78763adb656784b479652c52467b"},"schema_version":"1.0"},"canonical_sha256":"c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:12.977902Z","signature_b64":"j1Wiywx0uFkQzyZI/K18GPLm14hpRwDE1gMDtrz4otFMrRhjy1W7tUL1Z2ZTIVn5hUM4lcaPnCQHXKykSO+dAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490","last_reissued_at":"2026-05-18T01:52:12.977196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:12.977196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2728","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":"2026-05-18T01:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkwVOMbdVO4veAIkgiLDXT/AUYHFDMDINTi3EPDvJD8x6a/MPhgjVzwLIsTrJogCFSVakdZyjxi9WsS+bODWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:42:52.431983Z"},"content_sha256":"aacabbbb3b9c3abff2883035baeaf05c0f1ec2fd0853d03370d32cd5c2949def","schema_version":"1.0","event_id":"sha256:aacabbbb3b9c3abff2883035baeaf05c0f1ec2fd0853d03370d32cd5c2949def"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZAPY26FLK2IXYZ3ETIET7HAYGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised central limit theorems for growth rate distribution of complex systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an","q-fin.GN","stat.AP"],"primary_cat":"physics.soc-ph","authors_text":"Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu","submitted_at":"2013-01-12T22:57:32Z","abstract_excerpt":"We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the ent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2728","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":"2026-05-18T01:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHfhRWGteHbleyCV8wemg0n/kupjyLaxl5vquGBkK9Uat8RUrdI5sEyBYtZB9yBQ+mQRFodLOaDOxPmZ93UGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:42:52.432346Z"},"content_sha256":"54d4f6b8135df5c0c5fd48c6a7617b8f981552e6fe183062cbe295c578292571","schema_version":"1.0","event_id":"sha256:54d4f6b8135df5c0c5fd48c6a7617b8f981552e6fe183062cbe295c578292571"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN/bundle.json","state_url":"https://pith.science/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN/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":"2026-06-21T21:42:52Z","links":{"resolver":"https://pith.science/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN","bundle":"https://pith.science/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN/bundle.json","state":"https://pith.science/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAPY26FLK2IXYZ3ETIET7HAYGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZAPY26FLK2IXYZ3ETIET7HAYGN","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":"bde3cb6a0a8728138f0e3b9e34fac796da8f78763adb656784b479652c52467b","cross_cats_sorted":["physics.data-an","q-fin.GN","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-01-12T22:57:32Z","title_canon_sha256":"45ce854b2ebbeadb0bb358a34bd0a8a04facebfc48ac90c4660f17b7f1449b45"},"schema_version":"1.0","source":{"id":"1301.2728","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2728","created_at":"2026-05-18T01:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2728v4","created_at":"2026-05-18T01:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2728","created_at":"2026-05-18T01:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZAPY26FLK2IX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZAPY26FLK2IXYZ3E","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZAPY26FL","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:54d4f6b8135df5c0c5fd48c6a7617b8f981552e6fe183062cbe295c578292571","target":"graph","created_at":"2026-05-18T01:52:12Z","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":"We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the ent","authors_text":"Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu","cross_cats":["physics.data-an","q-fin.GN","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-01-12T22:57:32Z","title":"Generalised central limit theorems for growth rate distribution of complex systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2728","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:aacabbbb3b9c3abff2883035baeaf05c0f1ec2fd0853d03370d32cd5c2949def","target":"record","created_at":"2026-05-18T01:52:12Z","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":"bde3cb6a0a8728138f0e3b9e34fac796da8f78763adb656784b479652c52467b","cross_cats_sorted":["physics.data-an","q-fin.GN","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-01-12T22:57:32Z","title_canon_sha256":"45ce854b2ebbeadb0bb358a34bd0a8a04facebfc48ac90c4660f17b7f1449b45"},"schema_version":"1.0","source":{"id":"1301.2728","kind":"arxiv","version":4}},"canonical_sha256":"c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490","first_computed_at":"2026-05-18T01:52:12.977196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:12.977196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1Wiywx0uFkQzyZI/K18GPLm14hpRwDE1gMDtrz4otFMrRhjy1W7tUL1Z2ZTIVn5hUM4lcaPnCQHXKykSO+dAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:12.977902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2728","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aacabbbb3b9c3abff2883035baeaf05c0f1ec2fd0853d03370d32cd5c2949def","sha256:54d4f6b8135df5c0c5fd48c6a7617b8f981552e6fe183062cbe295c578292571"],"state_sha256":"1d4d3e5e76573e1820bc4e9cbe83dce57e40eb1bb30d5b434b24b387c0d0ec80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fk2DoK5OdWUFzlWA4VLgzibNAtRQGo6RNdwK0fb56GGfp31atJ7Yj74FTUK7WH8O8jD8vjAjVCswZwrfdVOyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:42:52.434301Z","bundle_sha256":"318b15cd27454ef389ffe33b07d2887b17b63ad8124bf55b6ab557b177f25c2a"}}