{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WTC3TV2C6W6CDOZG73WOM3SBGZ","short_pith_number":"pith:WTC3TV2C","canonical_record":{"source":{"id":"1107.3227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-16T12:57:25Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d4f324631dd75f4999d6692edd7bdf055375c50efab7aa8510afe9a8d6ca8b55","abstract_canon_sha256":"733235403808534e6b0138df2e18db9e8798868b3176bf947ec4ffaf92d13f30"},"schema_version":"1.0"},"canonical_sha256":"b4c5b9d742f5bc21bb26feece66e41367be4a25d0b81a570132adce7dc586070","source":{"kind":"arxiv","id":"1107.3227","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3227","created_at":"2026-05-18T03:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3227v2","created_at":"2026-05-18T03:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3227","created_at":"2026-05-18T03:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"WTC3TV2C6W6C","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WTC3TV2C6W6CDOZG","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WTC3TV2C","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WTC3TV2C6W6CDOZG73WOM3SBGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-16T12:57:25Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d4f324631dd75f4999d6692edd7bdf055375c50efab7aa8510afe9a8d6ca8b55","abstract_canon_sha256":"733235403808534e6b0138df2e18db9e8798868b3176bf947ec4ffaf92d13f30"},"schema_version":"1.0"},"canonical_sha256":"b4c5b9d742f5bc21bb26feece66e41367be4a25d0b81a570132adce7dc586070","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:13.886918Z","signature_b64":"LKIHTYZf/pBAlAPwz1h/u7+c53jJn332JectZsSZEamP4SPcoFUecUvbmwhStwlJLAFpsvhnU80GZDbexWbkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4c5b9d742f5bc21bb26feece66e41367be4a25d0b81a570132adce7dc586070","last_reissued_at":"2026-05-18T03:06:13.886179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:13.886179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3227","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":"2026-05-18T03:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HA4c/7OEjEUu/OhOCo/TUFVrhpupYZ9QGpriig2ZySd3GNvhKS0TlBYzZnuNrQcvBw7O8eqXUI7HyYoYPs6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:35:00.639901Z"},"content_sha256":"80432d3e9a7c04679b9e2eaa4e1d4df1238197ae740566df5ee37666b7eec8eb","schema_version":"1.0","event_id":"sha256:80432d3e9a7c04679b9e2eaa4e1d4df1238197ae740566df5ee37666b7eec8eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WTC3TV2C6W6CDOZG73WOM3SBGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A one-dimensional coagulation-fragmentation process with a dynamical phase transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Cedric Bernardin (UMPA-ENSL), Fabio Lucio Toninelli (Phys-ENS)","submitted_at":"2011-07-16T12:57:25Z","abstract_excerpt":"We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\\{1,\\ldots,L\\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be seen as the Gibbs measure for a homogeneous pinning model \\cite{cf:GBbook}. Depending on a parameter $\\lambda$, the typical configuration can be either dominated by a single big interval (delocalized phase), or be composed of many intervals of order $1$ (localized phase), or the interval length can have a power law distribution (critical regime). In the thre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3227","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":"2026-05-18T03:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1jhWvyi1D0mWNScknVy5hH1QYGa/GHnuCxsOd86O8NimJx+/lNhg6Z3mfNAUOHc2fZ4mIEwjHMN+oC0ZhD5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:35:00.640255Z"},"content_sha256":"3d64b501e0092990afaf67ee5f800989dc0a35f3090639d49aaa0cc0b5b4c34a","schema_version":"1.0","event_id":"sha256:3d64b501e0092990afaf67ee5f800989dc0a35f3090639d49aaa0cc0b5b4c34a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ/bundle.json","state_url":"https://pith.science/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ/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":"2026-06-10T20:35:00Z","links":{"resolver":"https://pith.science/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ","bundle":"https://pith.science/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ/bundle.json","state":"https://pith.science/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTC3TV2C6W6CDOZG73WOM3SBGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WTC3TV2C6W6CDOZG73WOM3SBGZ","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":"733235403808534e6b0138df2e18db9e8798868b3176bf947ec4ffaf92d13f30","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-16T12:57:25Z","title_canon_sha256":"d4f324631dd75f4999d6692edd7bdf055375c50efab7aa8510afe9a8d6ca8b55"},"schema_version":"1.0","source":{"id":"1107.3227","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3227","created_at":"2026-05-18T03:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3227v2","created_at":"2026-05-18T03:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3227","created_at":"2026-05-18T03:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"WTC3TV2C6W6C","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WTC3TV2C6W6CDOZG","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WTC3TV2C","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:3d64b501e0092990afaf67ee5f800989dc0a35f3090639d49aaa0cc0b5b4c34a","target":"graph","created_at":"2026-05-18T03:06:13Z","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":"We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\\{1,\\ldots,L\\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be seen as the Gibbs measure for a homogeneous pinning model \\cite{cf:GBbook}. Depending on a parameter $\\lambda$, the typical configuration can be either dominated by a single big interval (delocalized phase), or be composed of many intervals of order $1$ (localized phase), or the interval length can have a power law distribution (critical regime). In the thre","authors_text":"Cedric Bernardin (UMPA-ENSL), Fabio Lucio Toninelli (Phys-ENS)","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-16T12:57:25Z","title":"A one-dimensional coagulation-fragmentation process with a dynamical phase transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3227","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":"sha256:80432d3e9a7c04679b9e2eaa4e1d4df1238197ae740566df5ee37666b7eec8eb","target":"record","created_at":"2026-05-18T03:06:13Z","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":"733235403808534e6b0138df2e18db9e8798868b3176bf947ec4ffaf92d13f30","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-16T12:57:25Z","title_canon_sha256":"d4f324631dd75f4999d6692edd7bdf055375c50efab7aa8510afe9a8d6ca8b55"},"schema_version":"1.0","source":{"id":"1107.3227","kind":"arxiv","version":2}},"canonical_sha256":"b4c5b9d742f5bc21bb26feece66e41367be4a25d0b81a570132adce7dc586070","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4c5b9d742f5bc21bb26feece66e41367be4a25d0b81a570132adce7dc586070","first_computed_at":"2026-05-18T03:06:13.886179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:13.886179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKIHTYZf/pBAlAPwz1h/u7+c53jJn332JectZsSZEamP4SPcoFUecUvbmwhStwlJLAFpsvhnU80GZDbexWbkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:13.886918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3227","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80432d3e9a7c04679b9e2eaa4e1d4df1238197ae740566df5ee37666b7eec8eb","sha256:3d64b501e0092990afaf67ee5f800989dc0a35f3090639d49aaa0cc0b5b4c34a"],"state_sha256":"a691696fb3009f24bc463ee61017cf8adaeacacaa6830686f4ea3c678e321d65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cx5bBp7HB83f2py7RLgCECwSAmShNPJSt/CSMMfxD6UaqsJSgXC6JVAfyFX5Gn4oLTA0+272Oxit9hg5JLogCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:35:00.642226Z","bundle_sha256":"532c2004a8492c787b60bf0e57bbd9ae38b295c949f8b7ac35774d36bfa9e3dc"}}