{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ET3CMIZYUPJMWRRPKGWPWU6G2N","short_pith_number":"pith:ET3CMIZY","canonical_record":{"source":{"id":"1203.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-17T23:23:58Z","cross_cats_sorted":[],"title_canon_sha256":"d5ba92933bb03676924737d45a64d895f1a425a50159c43ee7a80d8c8464f086","abstract_canon_sha256":"738e2ad721c7e9c54349e396790a55fd28e01f23565db5b6deaf94fe9bca9607"},"schema_version":"1.0"},"canonical_sha256":"24f6262338a3d2cb462f51acfb53c6d35068f0c9140f66f19dcd18a011a9cab0","source":{"kind":"arxiv","id":"1203.3905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3905","created_at":"2026-05-18T01:58:06Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3905v1","created_at":"2026-05-18T01:58:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3905","created_at":"2026-05-18T01:58:06Z"},{"alias_kind":"pith_short_12","alias_value":"ET3CMIZYUPJM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ET3CMIZYUPJMWRRP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ET3CMIZY","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ET3CMIZYUPJMWRRPKGWPWU6G2N","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-17T23:23:58Z","cross_cats_sorted":[],"title_canon_sha256":"d5ba92933bb03676924737d45a64d895f1a425a50159c43ee7a80d8c8464f086","abstract_canon_sha256":"738e2ad721c7e9c54349e396790a55fd28e01f23565db5b6deaf94fe9bca9607"},"schema_version":"1.0"},"canonical_sha256":"24f6262338a3d2cb462f51acfb53c6d35068f0c9140f66f19dcd18a011a9cab0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:06.411523Z","signature_b64":"+QuxBP3S3RbR1LrDPADjZkMmQx9zO0yx4rZWp12svN2CNHj/hmpT2z7UYYXG+lbexzraQmlpwsjXfu633cnSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24f6262338a3d2cb462f51acfb53c6d35068f0c9140f66f19dcd18a011a9cab0","last_reissued_at":"2026-05-18T01:58:06.411113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:06.411113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3905","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/T6RVA6eZIZn5zWoblO/Nz7js1EzAaFNtVJUASHlgC0yXBy6ykKqsFHoz8aQoHZADS5w8bpBEejxO9f8nGnsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:52.762490Z"},"content_sha256":"46c0d7abd924c35691089fdb7ac827403f9fdd616d6cfaa6d2797f1f000dd4f8","schema_version":"1.0","event_id":"sha256:46c0d7abd924c35691089fdb7ac827403f9fdd616d6cfaa6d2797f1f000dd4f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ET3CMIZYUPJMWRRPKGWPWU6G2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Driven Brownian coagulation of polymers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Colm Connaughton, P. L. Krapivsky","submitted_at":"2012-03-17T23:23:58Z","abstract_excerpt":"We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, $a$, of the aggregates. We find that two types of long time behavior are possible. For $0\\leq a < 1/2$ the size distribution reaches a stationary state with a power law distribution of cluster sizes having exponent 3/2. The amplitude of this stationary state is determined exactly as a function of $a$. For $1/2 < a \\leq 1$, the cluster size "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3905","kind":"arxiv","version":1},"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":"2026-05-18T01:58:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0jeiQPb8QKi8/xj6Ptigni3EuS1t6qfw5AXI/YPzexw8+XB/amMD15VKcvUyvBTnOmEuL4i7RGPBbEl1DSYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:52.762867Z"},"content_sha256":"a8df12094ceda641ee77fd60d5f0c290d97f7587ba27415134179e25a4775be4","schema_version":"1.0","event_id":"sha256:a8df12094ceda641ee77fd60d5f0c290d97f7587ba27415134179e25a4775be4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N/bundle.json","state_url":"https://pith.science/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N/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":"2026-06-09T19:36:52Z","links":{"resolver":"https://pith.science/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N","bundle":"https://pith.science/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N/bundle.json","state":"https://pith.science/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ET3CMIZYUPJMWRRPKGWPWU6G2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ET3CMIZYUPJMWRRPKGWPWU6G2N","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":"738e2ad721c7e9c54349e396790a55fd28e01f23565db5b6deaf94fe9bca9607","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-17T23:23:58Z","title_canon_sha256":"d5ba92933bb03676924737d45a64d895f1a425a50159c43ee7a80d8c8464f086"},"schema_version":"1.0","source":{"id":"1203.3905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3905","created_at":"2026-05-18T01:58:06Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3905v1","created_at":"2026-05-18T01:58:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3905","created_at":"2026-05-18T01:58:06Z"},{"alias_kind":"pith_short_12","alias_value":"ET3CMIZYUPJM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ET3CMIZYUPJMWRRP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ET3CMIZY","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:a8df12094ceda641ee77fd60d5f0c290d97f7587ba27415134179e25a4775be4","target":"graph","created_at":"2026-05-18T01:58:06Z","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 present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, $a$, of the aggregates. We find that two types of long time behavior are possible. For $0\\leq a < 1/2$ the size distribution reaches a stationary state with a power law distribution of cluster sizes having exponent 3/2. The amplitude of this stationary state is determined exactly as a function of $a$. For $1/2 < a \\leq 1$, the cluster size ","authors_text":"Colm Connaughton, P. L. Krapivsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-17T23:23:58Z","title":"Driven Brownian coagulation of polymers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3905","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":"sha256:46c0d7abd924c35691089fdb7ac827403f9fdd616d6cfaa6d2797f1f000dd4f8","target":"record","created_at":"2026-05-18T01:58:06Z","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":"738e2ad721c7e9c54349e396790a55fd28e01f23565db5b6deaf94fe9bca9607","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-03-17T23:23:58Z","title_canon_sha256":"d5ba92933bb03676924737d45a64d895f1a425a50159c43ee7a80d8c8464f086"},"schema_version":"1.0","source":{"id":"1203.3905","kind":"arxiv","version":1}},"canonical_sha256":"24f6262338a3d2cb462f51acfb53c6d35068f0c9140f66f19dcd18a011a9cab0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24f6262338a3d2cb462f51acfb53c6d35068f0c9140f66f19dcd18a011a9cab0","first_computed_at":"2026-05-18T01:58:06.411113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:06.411113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+QuxBP3S3RbR1LrDPADjZkMmQx9zO0yx4rZWp12svN2CNHj/hmpT2z7UYYXG+lbexzraQmlpwsjXfu633cnSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:06.411523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46c0d7abd924c35691089fdb7ac827403f9fdd616d6cfaa6d2797f1f000dd4f8","sha256:a8df12094ceda641ee77fd60d5f0c290d97f7587ba27415134179e25a4775be4"],"state_sha256":"b8ae2fe744cebb8715643f64cc4fcef1952486fe251ce41d86265623c3f41994"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IlhMJ1GYpzSOLoQsFKes2KzkjjIpVMkcUK7xitdj/t2k4gq3A1GHD7Q68iW0E9qTCXQbvLKWJfYNucMCCwFlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:36:52.765273Z","bundle_sha256":"f849294be632245e9c13277cc20c4de7fb413b5b5427790582d2778298188047"}}