{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OUEVQ5JGYYOE37RCOBYWNCZU5V","short_pith_number":"pith:OUEVQ5JG","canonical_record":{"source":{"id":"1211.5814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-25T21:56:21Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"0582943d6bcb7a3c4921b7aabf35f9ddd40a02aaba82eae7fbb839961d52e1c7","abstract_canon_sha256":"863d80d73f775ffc5ba9e6b407557f6c2867852e4a5526c2daf1316e143fbe25"},"schema_version":"1.0"},"canonical_sha256":"7509587526c61c4dfe227071668b34ed4c751ed1117ebb14708676632ad58974","source":{"kind":"arxiv","id":"1211.5814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5814","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5814v1","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5814","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"OUEVQ5JGYYOE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OUEVQ5JGYYOE37RC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OUEVQ5JG","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OUEVQ5JGYYOE37RCOBYWNCZU5V","target":"record","payload":{"canonical_record":{"source":{"id":"1211.5814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-25T21:56:21Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"0582943d6bcb7a3c4921b7aabf35f9ddd40a02aaba82eae7fbb839961d52e1c7","abstract_canon_sha256":"863d80d73f775ffc5ba9e6b407557f6c2867852e4a5526c2daf1316e143fbe25"},"schema_version":"1.0"},"canonical_sha256":"7509587526c61c4dfe227071668b34ed4c751ed1117ebb14708676632ad58974","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:55.299902Z","signature_b64":"oQLKL3X3Rw0CIj31Kw5OZ8EiZzQZv6bZAQGya9g7NG+Zpi0BlsoyutdR36y2OU9gvP13pEkYE+OX0Q9OQzppAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7509587526c61c4dfe227071668b34ed4c751ed1117ebb14708676632ad58974","last_reissued_at":"2026-05-18T01:52:55.299134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:55.299134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.5814","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":"2026-05-18T01:52:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtzrYlSxMW7Sg8TzFdRVebG3O4w0uW9ie2BjqTe4JqWBWyejcABl/N9+mlgbxddBNTGNht/stGjjzQX+WVfGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:21.568523Z"},"content_sha256":"7084dfe9cb8f4506e9d26603378722c932905c2420207677249fafadfaf06cc8","schema_version":"1.0","event_id":"sha256:7084dfe9cb8f4506e9d26603378722c932905c2420207677249fafadfaf06cc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OUEVQ5JGYYOE37RCOBYWNCZU5V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact solutions of kinetic equations in an autocatalytic growth model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jakub J\\c{e}drak","submitted_at":"2012-11-25T21:56:21Z","abstract_excerpt":"Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, $\\xi_{k} = s_k(\\xi_{1})\\propto \\xi_{1}^{k}/k $ was obtained, while in the latter, the functional form of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5814","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":"2026-05-18T01:52:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxNE7geNrIYrJHOo/XCc0z5FbPpOnP4RHEPknpbxHJfIPyeHRWy4bSDDx3bvonYvWUFdMGIIY2623TOZgOVrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:21.568871Z"},"content_sha256":"7252a4b1c7be05d5342fdc93c954eaa7bc3a9a813ecd54f633ff63885646263b","schema_version":"1.0","event_id":"sha256:7252a4b1c7be05d5342fdc93c954eaa7bc3a9a813ecd54f633ff63885646263b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V/bundle.json","state_url":"https://pith.science/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V/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":"2026-06-24T22:25:21Z","links":{"resolver":"https://pith.science/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V","bundle":"https://pith.science/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V/bundle.json","state":"https://pith.science/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUEVQ5JGYYOE37RCOBYWNCZU5V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OUEVQ5JGYYOE37RCOBYWNCZU5V","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":"863d80d73f775ffc5ba9e6b407557f6c2867852e4a5526c2daf1316e143fbe25","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-25T21:56:21Z","title_canon_sha256":"0582943d6bcb7a3c4921b7aabf35f9ddd40a02aaba82eae7fbb839961d52e1c7"},"schema_version":"1.0","source":{"id":"1211.5814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5814","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5814v1","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5814","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"OUEVQ5JGYYOE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OUEVQ5JGYYOE37RC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OUEVQ5JG","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:7252a4b1c7be05d5342fdc93c954eaa7bc3a9a813ecd54f633ff63885646263b","target":"graph","created_at":"2026-05-18T01:52:55Z","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":"Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, $\\xi_{k} = s_k(\\xi_{1})\\propto \\xi_{1}^{k}/k $ was obtained, while in the latter, the functional form of","authors_text":"Jakub J\\c{e}drak","cross_cats":["physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-25T21:56:21Z","title":"Exact solutions of kinetic equations in an autocatalytic growth model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5814","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":"sha256:7084dfe9cb8f4506e9d26603378722c932905c2420207677249fafadfaf06cc8","target":"record","created_at":"2026-05-18T01:52:55Z","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":"863d80d73f775ffc5ba9e6b407557f6c2867852e4a5526c2daf1316e143fbe25","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-25T21:56:21Z","title_canon_sha256":"0582943d6bcb7a3c4921b7aabf35f9ddd40a02aaba82eae7fbb839961d52e1c7"},"schema_version":"1.0","source":{"id":"1211.5814","kind":"arxiv","version":1}},"canonical_sha256":"7509587526c61c4dfe227071668b34ed4c751ed1117ebb14708676632ad58974","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7509587526c61c4dfe227071668b34ed4c751ed1117ebb14708676632ad58974","first_computed_at":"2026-05-18T01:52:55.299134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:55.299134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oQLKL3X3Rw0CIj31Kw5OZ8EiZzQZv6bZAQGya9g7NG+Zpi0BlsoyutdR36y2OU9gvP13pEkYE+OX0Q9OQzppAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:55.299902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7084dfe9cb8f4506e9d26603378722c932905c2420207677249fafadfaf06cc8","sha256:7252a4b1c7be05d5342fdc93c954eaa7bc3a9a813ecd54f633ff63885646263b"],"state_sha256":"e0549a963817141f3717f5cbdefc9aeafb136e0f887fcae6b7d7334a672ddf3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6nrVPw2gvbvw31a8pc1ydMX8UoGBKoSQbAdohYayoGM5bpPpMRaLE8tOPsXT1tvtGlYmTTON3dS/PF7q9WlyDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:25:21.570858Z","bundle_sha256":"204db835026473c632ba497b77af815232155dc9878ee9028edd52094debf94b"}}