{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JKIVEWB7GD4OUYPWOH22CCN4AX","short_pith_number":"pith:JKIVEWB7","canonical_record":{"source":{"id":"1109.6431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-09-29T08:18:42Z","cross_cats_sorted":[],"title_canon_sha256":"278c854b1fbb639334b77255a6aec0f73869153378e88427a55a64668f340ca8","abstract_canon_sha256":"8c82c88b9e93476c8f78cef47cda26f4591c19228e0bb160308902eec89ef77d"},"schema_version":"1.0"},"canonical_sha256":"4a9152583f30f8ea61f671f5a109bc05de82ea839d6aa3e27a8784505216a679","source":{"kind":"arxiv","id":"1109.6431","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6431","created_at":"2026-05-18T02:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6431v1","created_at":"2026-05-18T02:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6431","created_at":"2026-05-18T02:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"JKIVEWB7GD4O","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JKIVEWB7GD4OUYPW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JKIVEWB7","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JKIVEWB7GD4OUYPWOH22CCN4AX","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-09-29T08:18:42Z","cross_cats_sorted":[],"title_canon_sha256":"278c854b1fbb639334b77255a6aec0f73869153378e88427a55a64668f340ca8","abstract_canon_sha256":"8c82c88b9e93476c8f78cef47cda26f4591c19228e0bb160308902eec89ef77d"},"schema_version":"1.0"},"canonical_sha256":"4a9152583f30f8ea61f671f5a109bc05de82ea839d6aa3e27a8784505216a679","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:21.697738Z","signature_b64":"VXMq/y07axWQ5xpJe4FzHnFK/cc/F4w93TPrJZ8nwil8jXc6JJnUqdtd0nbO4XvXkkX/i7h/2QdTDVgQ4IIPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a9152583f30f8ea61f671f5a109bc05de82ea839d6aa3e27a8784505216a679","last_reissued_at":"2026-05-18T02:00:21.697256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:21.697256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6431","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":"2026-05-18T02:00:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EjHzCK/ntBRElBljwDTIM2VOs447I8yZyQsLg9Ax0IMRTa5ciUBQNY6l8Uhi8NGdzwBQ5fJqsbwvG2oCqNoLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:20:19.168792Z"},"content_sha256":"0695d371da2678253ff2484750b1a441115736537d51e42795cf393b0e177894","schema_version":"1.0","event_id":"sha256:0695d371da2678253ff2484750b1a441115736537d51e42795cf393b0e177894"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JKIVEWB7GD4OUYPWOH22CCN4AX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Study of Anomalous Kinetics of The Annihilation Reaction A+A->0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"J. Honkonen, M. Hnatich, T. Lu\\v{c}ivjansk\\'y","submitted_at":"2011-09-29T08:18:42Z","abstract_excerpt":"Using the perturbative renormalization group, we study the influence of a random velocity field on the kinetics of the single-species annihilation reaction A+A->0 at and below its critical dimension d_c=2. We use the second-quantization formalism of Doi to bring the stochastic problem to a field-theoretic form. We investigate the reaction in the vicinity of the space dimension d=2 using a two-parameter expansion in $\\epsilon$ and $\\Delta$, where $\\epsilon$ is the deviation from the Kolmogorov scaling parameter and $\\Delta$ is the deviation from the space dimension d=2. We evaluate all the nece"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6431","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":"2026-05-18T02:00:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XkiU7NNVlDYyvbFH0Ec16IeV1/uA+W2J4T3WJ8PJ281Ho2ntPRv9UvvXA7emfcJ7KmpjlBrDmrmkV1I/3JDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:20:19.169144Z"},"content_sha256":"3886f10627c72179de38a272d43736e20bea89158694adbee443ad0b6f3a43aa","schema_version":"1.0","event_id":"sha256:3886f10627c72179de38a272d43736e20bea89158694adbee443ad0b6f3a43aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKIVEWB7GD4OUYPWOH22CCN4AX/bundle.json","state_url":"https://pith.science/pith/JKIVEWB7GD4OUYPWOH22CCN4AX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKIVEWB7GD4OUYPWOH22CCN4AX/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":"2026-06-24T21:20:19Z","links":{"resolver":"https://pith.science/pith/JKIVEWB7GD4OUYPWOH22CCN4AX","bundle":"https://pith.science/pith/JKIVEWB7GD4OUYPWOH22CCN4AX/bundle.json","state":"https://pith.science/pith/JKIVEWB7GD4OUYPWOH22CCN4AX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKIVEWB7GD4OUYPWOH22CCN4AX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JKIVEWB7GD4OUYPWOH22CCN4AX","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":"8c82c88b9e93476c8f78cef47cda26f4591c19228e0bb160308902eec89ef77d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-09-29T08:18:42Z","title_canon_sha256":"278c854b1fbb639334b77255a6aec0f73869153378e88427a55a64668f340ca8"},"schema_version":"1.0","source":{"id":"1109.6431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6431","created_at":"2026-05-18T02:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6431v1","created_at":"2026-05-18T02:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6431","created_at":"2026-05-18T02:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"JKIVEWB7GD4O","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JKIVEWB7GD4OUYPW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JKIVEWB7","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:3886f10627c72179de38a272d43736e20bea89158694adbee443ad0b6f3a43aa","target":"graph","created_at":"2026-05-18T02:00:21Z","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":"Using the perturbative renormalization group, we study the influence of a random velocity field on the kinetics of the single-species annihilation reaction A+A->0 at and below its critical dimension d_c=2. We use the second-quantization formalism of Doi to bring the stochastic problem to a field-theoretic form. We investigate the reaction in the vicinity of the space dimension d=2 using a two-parameter expansion in $\\epsilon$ and $\\Delta$, where $\\epsilon$ is the deviation from the Kolmogorov scaling parameter and $\\Delta$ is the deviation from the space dimension d=2. We evaluate all the nece","authors_text":"J. Honkonen, M. Hnatich, T. Lu\\v{c}ivjansk\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-09-29T08:18:42Z","title":"Study of Anomalous Kinetics of The Annihilation Reaction A+A->0"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6431","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":"sha256:0695d371da2678253ff2484750b1a441115736537d51e42795cf393b0e177894","target":"record","created_at":"2026-05-18T02:00:21Z","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":"8c82c88b9e93476c8f78cef47cda26f4591c19228e0bb160308902eec89ef77d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-09-29T08:18:42Z","title_canon_sha256":"278c854b1fbb639334b77255a6aec0f73869153378e88427a55a64668f340ca8"},"schema_version":"1.0","source":{"id":"1109.6431","kind":"arxiv","version":1}},"canonical_sha256":"4a9152583f30f8ea61f671f5a109bc05de82ea839d6aa3e27a8784505216a679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a9152583f30f8ea61f671f5a109bc05de82ea839d6aa3e27a8784505216a679","first_computed_at":"2026-05-18T02:00:21.697256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:21.697256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VXMq/y07axWQ5xpJe4FzHnFK/cc/F4w93TPrJZ8nwil8jXc6JJnUqdtd0nbO4XvXkkX/i7h/2QdTDVgQ4IIPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:21.697738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0695d371da2678253ff2484750b1a441115736537d51e42795cf393b0e177894","sha256:3886f10627c72179de38a272d43736e20bea89158694adbee443ad0b6f3a43aa"],"state_sha256":"f85107a931d715f81a197ff0572b02ac44ce98664a96e202009905f7965bb00e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yG9q5FkzyoGcdoKDYZhjni+ilxE+g62EdJDHFmZECHVmS0+tOIEDQTVtoi/5G3oGVl3pzFMCZsIY8dDge4uCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:20:19.171166Z","bundle_sha256":"6b69f370adabe9aa6b395a88db4b237b4075350d1788e25c2552845391e49252"}}