{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:27GMD46BKYUJZ4RSBXSXOB3LYC","short_pith_number":"pith:27GMD46B","canonical_record":{"source":{"id":"1301.2369","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-11T01:17:45Z","cross_cats_sorted":["cs.DM","cs.SI","math-ph","math.MP","nlin.AO"],"title_canon_sha256":"34797fa621938bb29624ad9d7d51cbb6490c1312d2957ae381d0ca2b2d456270","abstract_canon_sha256":"3c0990b0ef85ee17c4b00a30a7a4dae1c57208cf167fa6b4e732f1a2e45d47df"},"schema_version":"1.0"},"canonical_sha256":"d7ccc1f3c156289cf2320de577076bc0995dbe460ac12779f15c9130bc96bffb","source":{"kind":"arxiv","id":"1301.2369","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2369","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2369v2","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2369","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"27GMD46BKYUJ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"27GMD46BKYUJZ4RS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"27GMD46B","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:27GMD46BKYUJZ4RSBXSXOB3LYC","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2369","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-11T01:17:45Z","cross_cats_sorted":["cs.DM","cs.SI","math-ph","math.MP","nlin.AO"],"title_canon_sha256":"34797fa621938bb29624ad9d7d51cbb6490c1312d2957ae381d0ca2b2d456270","abstract_canon_sha256":"3c0990b0ef85ee17c4b00a30a7a4dae1c57208cf167fa6b4e732f1a2e45d47df"},"schema_version":"1.0"},"canonical_sha256":"d7ccc1f3c156289cf2320de577076bc0995dbe460ac12779f15c9130bc96bffb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:13.608907Z","signature_b64":"4hrd1c9ALwv3pLLYaMGXacQGidSRrnXX36IwgCK1zHExvTHR8PLRI8r4uWaAptK9o/L6soCUPXQwIer2sLjdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7ccc1f3c156289cf2320de577076bc0995dbe460ac12779f15c9130bc96bffb","last_reissued_at":"2026-05-18T01:52:13.608364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:13.608364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2369","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PAVG1fiVo/Oic6kX8B/h8tYIV3Sra6w1FoVeuTB/YbDmMrX7HxXXjmkO2kmGAWj2kLYLr1WeqfmcvJO/X5X6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:07:15.271902Z"},"content_sha256":"a015a48b673847fc00a65d2e6f5f4915367c7bd021334853edad486d80d6cd64","schema_version":"1.0","event_id":"sha256:a015a48b673847fc00a65d2e6f5f4915367c7bd021334853edad486d80d6cd64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:27GMD46BKYUJZ4RSBXSXOB3LYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial and approximative analyses in a spatially random division process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI","math-ph","math.MP","nlin.AO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Norio Konno, Takayuki Komaki, Takuya Machida, Yukio Hayashi, Yusuke Ide","submitted_at":"2013-01-11T01:17:45Z","abstract_excerpt":"For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2369","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7D/d3UVDBOqjOEMMf+mq4JdRGd357alh8cCSBo5xZ0iot9GZIinCTIQtPLTCgtvB5VfVngW1/F147BPCFzrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:07:15.272255Z"},"content_sha256":"1f3ee0a00d48241cb399daa668c61809db47f70647fb1c3f71100e860dcd8260","schema_version":"1.0","event_id":"sha256:1f3ee0a00d48241cb399daa668c61809db47f70647fb1c3f71100e860dcd8260"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27GMD46BKYUJZ4RSBXSXOB3LYC/bundle.json","state_url":"https://pith.science/pith/27GMD46BKYUJZ4RSBXSXOB3LYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27GMD46BKYUJZ4RSBXSXOB3LYC/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":"2026-06-23T19:07:15Z","links":{"resolver":"https://pith.science/pith/27GMD46BKYUJZ4RSBXSXOB3LYC","bundle":"https://pith.science/pith/27GMD46BKYUJZ4RSBXSXOB3LYC/bundle.json","state":"https://pith.science/pith/27GMD46BKYUJZ4RSBXSXOB3LYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27GMD46BKYUJZ4RSBXSXOB3LYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:27GMD46BKYUJZ4RSBXSXOB3LYC","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":"3c0990b0ef85ee17c4b00a30a7a4dae1c57208cf167fa6b4e732f1a2e45d47df","cross_cats_sorted":["cs.DM","cs.SI","math-ph","math.MP","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-11T01:17:45Z","title_canon_sha256":"34797fa621938bb29624ad9d7d51cbb6490c1312d2957ae381d0ca2b2d456270"},"schema_version":"1.0","source":{"id":"1301.2369","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2369","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2369v2","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2369","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"27GMD46BKYUJ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"27GMD46BKYUJZ4RS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"27GMD46B","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:1f3ee0a00d48241cb399daa668c61809db47f70647fb1c3f71100e860dcd8260","target":"graph","created_at":"2026-05-18T01:52:13Z","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":"For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution o","authors_text":"Norio Konno, Takayuki Komaki, Takuya Machida, Yukio Hayashi, Yusuke Ide","cross_cats":["cs.DM","cs.SI","math-ph","math.MP","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-11T01:17:45Z","title":"Combinatorial and approximative analyses in a spatially random division process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2369","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:a015a48b673847fc00a65d2e6f5f4915367c7bd021334853edad486d80d6cd64","target":"record","created_at":"2026-05-18T01:52:13Z","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":"3c0990b0ef85ee17c4b00a30a7a4dae1c57208cf167fa6b4e732f1a2e45d47df","cross_cats_sorted":["cs.DM","cs.SI","math-ph","math.MP","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-11T01:17:45Z","title_canon_sha256":"34797fa621938bb29624ad9d7d51cbb6490c1312d2957ae381d0ca2b2d456270"},"schema_version":"1.0","source":{"id":"1301.2369","kind":"arxiv","version":2}},"canonical_sha256":"d7ccc1f3c156289cf2320de577076bc0995dbe460ac12779f15c9130bc96bffb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7ccc1f3c156289cf2320de577076bc0995dbe460ac12779f15c9130bc96bffb","first_computed_at":"2026-05-18T01:52:13.608364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:13.608364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4hrd1c9ALwv3pLLYaMGXacQGidSRrnXX36IwgCK1zHExvTHR8PLRI8r4uWaAptK9o/L6soCUPXQwIer2sLjdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:13.608907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2369","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a015a48b673847fc00a65d2e6f5f4915367c7bd021334853edad486d80d6cd64","sha256:1f3ee0a00d48241cb399daa668c61809db47f70647fb1c3f71100e860dcd8260"],"state_sha256":"e8a0c3c4734349c32b921fe2653c81695583eb4da4ea519bc03e3d7635299a8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cWTbvbcgxVFqeLcqP6/sxgnPgesDtNTHb3KsTIKMONfzyPWezwL+jlqAWIN3rMtdvevMae7Dmml14FcOrJLiAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:07:15.274275Z","bundle_sha256":"1641262f9602355cd0c80d457b68e1a65ab23f0bd1e7c4e52a132e77dd9e3de5"}}