{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HWIIUGYZTE4MQG75FVC5KZFZEE","short_pith_number":"pith:HWIIUGYZ","canonical_record":{"source":{"id":"1202.0182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-01T14:57:32Z","cross_cats_sorted":[],"title_canon_sha256":"b26f1729ce0fc07472fcb4556b55ef3c5773cf08687ce952a1b06ae61863a0af","abstract_canon_sha256":"9b5e49608151ad66938dd457d82e05d96e4153e3c03eff3e990d2776547526b5"},"schema_version":"1.0"},"canonical_sha256":"3d908a1b199938c81bfd2d45d564b921380747bfe5c26e69a714b5e9a2060ac9","source":{"kind":"arxiv","id":"1202.0182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0182","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0182v1","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0182","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"HWIIUGYZTE4M","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HWIIUGYZTE4MQG75","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HWIIUGYZ","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HWIIUGYZTE4MQG75FVC5KZFZEE","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-01T14:57:32Z","cross_cats_sorted":[],"title_canon_sha256":"b26f1729ce0fc07472fcb4556b55ef3c5773cf08687ce952a1b06ae61863a0af","abstract_canon_sha256":"9b5e49608151ad66938dd457d82e05d96e4153e3c03eff3e990d2776547526b5"},"schema_version":"1.0"},"canonical_sha256":"3d908a1b199938c81bfd2d45d564b921380747bfe5c26e69a714b5e9a2060ac9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:49.005058Z","signature_b64":"B9KQ2GAt45NnCz1K/2GTdPzx4qDaNvatj5vVcTPvzYlr8SFVKADHERI0rm8zOjYKzEwx+K84kfjrQjVgWkXFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d908a1b199938c81bfd2d45d564b921380747bfe5c26e69a714b5e9a2060ac9","last_reissued_at":"2026-05-18T04:00:49.004132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:49.004132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0182","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":"2026-05-18T04:00:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"793YZHKaFr6wASnub9DMNWDQavVJLt9VFZJSxRL274FoImhA7U3VlOAr8bkuFEmFAIz4P1YxMiACiK3epO/BBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:19:50.532343Z"},"content_sha256":"5a043367665de35a97651fdbe23fa83a3b2f0ef00cd062cd7f6f4a634522c82f","schema_version":"1.0","event_id":"sha256:5a043367665de35a97651fdbe23fa83a3b2f0ef00cd062cd7f6f4a634522c82f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HWIIUGYZTE4MQG75FVC5KZFZEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Anton Winkler, Erwin Frey","submitted_at":"2012-02-01T14:57:32Z","abstract_excerpt":"Diffusion limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long wavelength fluctuations and is a universal function of the macroscopic decay rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0182","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":"2026-05-18T04:00:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"859zhJuLK/8xaIsTiIKPRtkayG6HtPs98Au34xlzrm9Wu4CvaAlYPPul76+QxvakTQUF/Hd7I11FBUEk+JFoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:19:50.532733Z"},"content_sha256":"ebd1821f9a6b724c15475cadc2e786f8a19835853fecf72fb994cdbb1122cd93","schema_version":"1.0","event_id":"sha256:ebd1821f9a6b724c15475cadc2e786f8a19835853fecf72fb994cdbb1122cd93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWIIUGYZTE4MQG75FVC5KZFZEE/bundle.json","state_url":"https://pith.science/pith/HWIIUGYZTE4MQG75FVC5KZFZEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWIIUGYZTE4MQG75FVC5KZFZEE/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":"2026-06-12T04:19:50Z","links":{"resolver":"https://pith.science/pith/HWIIUGYZTE4MQG75FVC5KZFZEE","bundle":"https://pith.science/pith/HWIIUGYZTE4MQG75FVC5KZFZEE/bundle.json","state":"https://pith.science/pith/HWIIUGYZTE4MQG75FVC5KZFZEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWIIUGYZTE4MQG75FVC5KZFZEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HWIIUGYZTE4MQG75FVC5KZFZEE","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":"9b5e49608151ad66938dd457d82e05d96e4153e3c03eff3e990d2776547526b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-01T14:57:32Z","title_canon_sha256":"b26f1729ce0fc07472fcb4556b55ef3c5773cf08687ce952a1b06ae61863a0af"},"schema_version":"1.0","source":{"id":"1202.0182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0182","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0182v1","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0182","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"HWIIUGYZTE4M","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HWIIUGYZTE4MQG75","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HWIIUGYZ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ebd1821f9a6b724c15475cadc2e786f8a19835853fecf72fb994cdbb1122cd93","target":"graph","created_at":"2026-05-18T04:00:49Z","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":"Diffusion limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long wavelength fluctuations and is a universal function of the macroscopic decay rate.","authors_text":"Anton Winkler, Erwin Frey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-01T14:57:32Z","title":"On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0182","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":"sha256:5a043367665de35a97651fdbe23fa83a3b2f0ef00cd062cd7f6f4a634522c82f","target":"record","created_at":"2026-05-18T04:00:49Z","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":"9b5e49608151ad66938dd457d82e05d96e4153e3c03eff3e990d2776547526b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-02-01T14:57:32Z","title_canon_sha256":"b26f1729ce0fc07472fcb4556b55ef3c5773cf08687ce952a1b06ae61863a0af"},"schema_version":"1.0","source":{"id":"1202.0182","kind":"arxiv","version":1}},"canonical_sha256":"3d908a1b199938c81bfd2d45d564b921380747bfe5c26e69a714b5e9a2060ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d908a1b199938c81bfd2d45d564b921380747bfe5c26e69a714b5e9a2060ac9","first_computed_at":"2026-05-18T04:00:49.004132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:49.004132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B9KQ2GAt45NnCz1K/2GTdPzx4qDaNvatj5vVcTPvzYlr8SFVKADHERI0rm8zOjYKzEwx+K84kfjrQjVgWkXFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:49.005058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a043367665de35a97651fdbe23fa83a3b2f0ef00cd062cd7f6f4a634522c82f","sha256:ebd1821f9a6b724c15475cadc2e786f8a19835853fecf72fb994cdbb1122cd93"],"state_sha256":"9ea69e432027f2fcea13ce0cfd0fcf3848bc348458d7ab767b92d245af0313a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zFfdReZo6zuPqYTy+VYFi8dkNgujPldtxoczafaelx9z09RomzPsuvD0+sEtiO3j6+Sbe5ayY116fxwO8qreBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:19:50.534698Z","bundle_sha256":"8b6c06fd551c89bb7d35acd5fd91660028a611bcd167c364896092a3613ccef8"}}