{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:L6XGTBWDKU4QZUH6U477AX4T56","short_pith_number":"pith:L6XGTBWD","canonical_record":{"source":{"id":"1309.5816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-23T14:18:27Z","cross_cats_sorted":[],"title_canon_sha256":"488a908e64f456c694583b3c5ba82b3bbc29c8c8a77a3a1e82713e4a3833ffb2","abstract_canon_sha256":"e4052c7b880e34472666e1c4822608db042ac641ee6c84b6810fbd57ab37a94f"},"schema_version":"1.0"},"canonical_sha256":"5fae6986c355390cd0fea73ff05f93efa45bdaac06adb216c875a907a30ac922","source":{"kind":"arxiv","id":"1309.5816","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5816","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5816v2","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5816","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"L6XGTBWDKU4Q","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L6XGTBWDKU4QZUH6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L6XGTBWD","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:L6XGTBWDKU4QZUH6U477AX4T56","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-23T14:18:27Z","cross_cats_sorted":[],"title_canon_sha256":"488a908e64f456c694583b3c5ba82b3bbc29c8c8a77a3a1e82713e4a3833ffb2","abstract_canon_sha256":"e4052c7b880e34472666e1c4822608db042ac641ee6c84b6810fbd57ab37a94f"},"schema_version":"1.0"},"canonical_sha256":"5fae6986c355390cd0fea73ff05f93efa45bdaac06adb216c875a907a30ac922","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:32.545961Z","signature_b64":"qIWeVEnmbNVLUFBsDVvukw54rsXbkz8GuIQYNV/327hG9dR7ACG6oBmJ+x93wbKSDrlMTHuOC5d9RhoaqZB1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fae6986c355390cd0fea73ff05f93efa45bdaac06adb216c875a907a30ac922","last_reissued_at":"2026-05-18T01:09:32.545556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:32.545556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5816","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":"2026-05-18T01:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ARp47SGfTgoIXp/DW/exa5xz928Hr4YBcSZWPiF4eEruNOZro78mGO11UbdNSg+/P11ZQ158+KJLKE8ssVzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:08:39.818309Z"},"content_sha256":"13bb51d27dd0b0be769f01d9c7a1189c20518669660d3b10b8e86c7c91338e3f","schema_version":"1.0","event_id":"sha256:13bb51d27dd0b0be769f01d9c7a1189c20518669660d3b10b8e86c7c91338e3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:L6XGTBWDKU4QZUH6U477AX4T56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Behavior near the extinction time in self-similar fragmentations II: Finite dislocation measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"B\\'en\\'edicte Haas, Christina Goldschmidt","submitted_at":"2013-09-23T14:18:27Z","abstract_excerpt":"We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\\alpha$, independently of the other blocks. Every block then splits randomly into sub-blocks whose relative sizes are distributed according to the so-called dislocation measure. We focus here on the case where $\\alpha<0$. In this case, small blocks split intensively, and so the whole state is reduced to \"dust\" in a finite time, almost surely (we call this the extinction ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5816","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":"2026-05-18T01:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i4B95acpYjHLvHfpkG+YRYdasbAlUM6UpAOsOBPj35FpkcLUMw4vP1R3StjUemGZ1D8CmFq5C4SF2ougKkfUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:08:39.818864Z"},"content_sha256":"238dd2c3eb57b172d9c115cea20b987de386b35ae8d174a6de34a478e2dbf503","schema_version":"1.0","event_id":"sha256:238dd2c3eb57b172d9c115cea20b987de386b35ae8d174a6de34a478e2dbf503"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6XGTBWDKU4QZUH6U477AX4T56/bundle.json","state_url":"https://pith.science/pith/L6XGTBWDKU4QZUH6U477AX4T56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6XGTBWDKU4QZUH6U477AX4T56/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":"2026-06-12T06:08:39Z","links":{"resolver":"https://pith.science/pith/L6XGTBWDKU4QZUH6U477AX4T56","bundle":"https://pith.science/pith/L6XGTBWDKU4QZUH6U477AX4T56/bundle.json","state":"https://pith.science/pith/L6XGTBWDKU4QZUH6U477AX4T56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6XGTBWDKU4QZUH6U477AX4T56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L6XGTBWDKU4QZUH6U477AX4T56","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":"e4052c7b880e34472666e1c4822608db042ac641ee6c84b6810fbd57ab37a94f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-23T14:18:27Z","title_canon_sha256":"488a908e64f456c694583b3c5ba82b3bbc29c8c8a77a3a1e82713e4a3833ffb2"},"schema_version":"1.0","source":{"id":"1309.5816","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5816","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5816v2","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5816","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"L6XGTBWDKU4Q","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L6XGTBWDKU4QZUH6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L6XGTBWD","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:238dd2c3eb57b172d9c115cea20b987de386b35ae8d174a6de34a478e2dbf503","target":"graph","created_at":"2026-05-18T01:09:32Z","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 study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\\alpha$, independently of the other blocks. Every block then splits randomly into sub-blocks whose relative sizes are distributed according to the so-called dislocation measure. We focus here on the case where $\\alpha<0$. In this case, small blocks split intensively, and so the whole state is reduced to \"dust\" in a finite time, almost surely (we call this the extinction ti","authors_text":"B\\'en\\'edicte Haas, Christina Goldschmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-23T14:18:27Z","title":"Behavior near the extinction time in self-similar fragmentations II: Finite dislocation measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5816","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":"sha256:13bb51d27dd0b0be769f01d9c7a1189c20518669660d3b10b8e86c7c91338e3f","target":"record","created_at":"2026-05-18T01:09:32Z","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":"e4052c7b880e34472666e1c4822608db042ac641ee6c84b6810fbd57ab37a94f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-23T14:18:27Z","title_canon_sha256":"488a908e64f456c694583b3c5ba82b3bbc29c8c8a77a3a1e82713e4a3833ffb2"},"schema_version":"1.0","source":{"id":"1309.5816","kind":"arxiv","version":2}},"canonical_sha256":"5fae6986c355390cd0fea73ff05f93efa45bdaac06adb216c875a907a30ac922","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fae6986c355390cd0fea73ff05f93efa45bdaac06adb216c875a907a30ac922","first_computed_at":"2026-05-18T01:09:32.545556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:32.545556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qIWeVEnmbNVLUFBsDVvukw54rsXbkz8GuIQYNV/327hG9dR7ACG6oBmJ+x93wbKSDrlMTHuOC5d9RhoaqZB1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:32.545961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5816","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13bb51d27dd0b0be769f01d9c7a1189c20518669660d3b10b8e86c7c91338e3f","sha256:238dd2c3eb57b172d9c115cea20b987de386b35ae8d174a6de34a478e2dbf503"],"state_sha256":"580588761a31be73f8cab927f7ee5058e1df1d74d2ef87f6298e2926e430c0cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FkFXQnptcYkcfQNvzh4cwIsoHMysCOmzWuGVWmJr/VJe3HOVgXLr6jOFPKWEj0XqTdYepJ+s76QaBgfwlQPuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:08:39.821756Z","bundle_sha256":"d53ca836c315aec3432ab3c7248409121376635c464b0c7ddd15112e2a33c0ab"}}