{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VW5DS4MCFR65Q5QE43HVOVAMRD","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":"32e1e79621de4c942ce81e17def081629cd49f4ddf331d91da96e48e129890d6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-08T06:26:29Z","title_canon_sha256":"b5a18eab3139af0ad377ea7aef56cb9e2967cc0bfd803bd2484860a15d563bc3"},"schema_version":"1.0","source":{"id":"1106.1506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1506","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1506v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1506","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"VW5DS4MCFR65","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VW5DS4MCFR65Q5QE","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VW5DS4MC","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:a01a4f2f64785f84e11b8e18a288e4ec9814b0971b89c06ce056ce25e177fa31","target":"graph","created_at":"2026-05-18T03:28:43Z","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 present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each fragment in each stage of cascade ceases fracture with a certain probability. When the probability is constant, the exponent of the power-law cumulative distribution lies between -1 and 0, depending not only on the probability but the distribution of fracture points. Whereas, when the probability depends on the size of a fragment, the exponent is less than -1, ","authors_text":"Ken Yamamoto, Yoshihiro Yamazaki","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-08T06:26:29Z","title":"A solvable model of fracture with power-law distribution of fragment sizes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1506","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":"sha256:2245f3440e4f2896cc1a1ecc14d7b2c7e43f3a453399a46feda84a46e0458e50","target":"record","created_at":"2026-05-18T03:28:43Z","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":"32e1e79621de4c942ce81e17def081629cd49f4ddf331d91da96e48e129890d6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-08T06:26:29Z","title_canon_sha256":"b5a18eab3139af0ad377ea7aef56cb9e2967cc0bfd803bd2484860a15d563bc3"},"schema_version":"1.0","source":{"id":"1106.1506","kind":"arxiv","version":1}},"canonical_sha256":"adba3971822c7dd87604e6cf57540c88ecea686edb3a1088a9a94b87a63598d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adba3971822c7dd87604e6cf57540c88ecea686edb3a1088a9a94b87a63598d1","first_computed_at":"2026-05-18T03:28:43.103187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.103187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VwUSuxzUYV1IGMRPH2Soa8kvUeyzkBFTQrDZNuOqhM22BW+D7zQxBHp8eK0deTKg8D23EuLhYyVKL81cSDs0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.103823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2245f3440e4f2896cc1a1ecc14d7b2c7e43f3a453399a46feda84a46e0458e50","sha256:a01a4f2f64785f84e11b8e18a288e4ec9814b0971b89c06ce056ce25e177fa31"],"state_sha256":"32e3e9572183a12950d1f74bc6753dabeb35bb935a0dd2b938933649e6ada57b"}