{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:U33DKOR6FO27FWZSARNMBL7YX7","short_pith_number":"pith:U33DKOR6","canonical_record":{"source":{"id":"1609.06078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-20T10:06:37Z","cross_cats_sorted":[],"title_canon_sha256":"f224cda5087b59103ae88088835c5d6f4b05fe913e100ca0f2bad5fadb52ecdf","abstract_canon_sha256":"37d2b928ca523efaa2dece678772e67a1c02f48ab377c936ffe404b8c8869582"},"schema_version":"1.0"},"canonical_sha256":"a6f6353a3e2bb5f2db32045ac0aff8bfda1b5f5f11ca86ef9be122d5fe386bd7","source":{"kind":"arxiv","id":"1609.06078","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06078","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06078v2","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06078","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"U33DKOR6FO27","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U33DKOR6FO27FWZS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U33DKOR6","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:U33DKOR6FO27FWZSARNMBL7YX7","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-20T10:06:37Z","cross_cats_sorted":[],"title_canon_sha256":"f224cda5087b59103ae88088835c5d6f4b05fe913e100ca0f2bad5fadb52ecdf","abstract_canon_sha256":"37d2b928ca523efaa2dece678772e67a1c02f48ab377c936ffe404b8c8869582"},"schema_version":"1.0"},"canonical_sha256":"a6f6353a3e2bb5f2db32045ac0aff8bfda1b5f5f11ca86ef9be122d5fe386bd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:01.512741Z","signature_b64":"4//A1kFwnz7b9phXiaxlDwdixAdyu2yPcMc4w0F6MGqCNe2N7WpgAs5viYz+o6kjU99jctAMXM1ptNgrWq+wDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6f6353a3e2bb5f2db32045ac0aff8bfda1b5f5f11ca86ef9be122d5fe386bd7","last_reissued_at":"2026-05-18T00:45:01.512205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:01.512205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06078","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":"2026-05-18T00:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pdLv3wMlPGLBk9BIzjhH29q6Q9Kk4LValKcYDaOx+YzyVebCegBgRsRcaicdywGjD7461dAv1iHAnQdERtSiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:55:18.181991Z"},"content_sha256":"1cfd17b1637e5022305137a3de211ad65aa9b8ee2581d8692620ae55bf227382","schema_version":"1.0","event_id":"sha256:1cfd17b1637e5022305137a3de211ad65aa9b8ee2581d8692620ae55bf227382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:U33DKOR6FO27FWZSARNMBL7YX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Renormalization group calculation of dynamic exponent in the models E and F with hydrodynamic fluctuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. Dan\\v{c}o, M. Hnati\\v{c}, M. V. Komarova, M. Yu. Nalimov, T. Lu\\v{c}ivjansk\\'y","submitted_at":"2016-09-20T10:06:37Z","abstract_excerpt":"The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation for the anomalous dimension $\\gamma_\\lambda$ and fixed-points' structure. The dynamic exponent $z$ is calculated in the turbulent regime and stability of the fixed points for the standard model E is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06078","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":"2026-05-18T00:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5w/STXA4X+AO4rW2uNSOjWoapIDcemuIUg2emPiuBZT5HdcNitxNZlznRVhDRlQBhb8/Ul/7ArQU252OPbdYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:55:18.182343Z"},"content_sha256":"44e708ec26616dbf168fd17a4923b3e275dd43c75158cbb8860e0f5e154ce4fd","schema_version":"1.0","event_id":"sha256:44e708ec26616dbf168fd17a4923b3e275dd43c75158cbb8860e0f5e154ce4fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U33DKOR6FO27FWZSARNMBL7YX7/bundle.json","state_url":"https://pith.science/pith/U33DKOR6FO27FWZSARNMBL7YX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U33DKOR6FO27FWZSARNMBL7YX7/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":"2026-06-02T19:55:18Z","links":{"resolver":"https://pith.science/pith/U33DKOR6FO27FWZSARNMBL7YX7","bundle":"https://pith.science/pith/U33DKOR6FO27FWZSARNMBL7YX7/bundle.json","state":"https://pith.science/pith/U33DKOR6FO27FWZSARNMBL7YX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U33DKOR6FO27FWZSARNMBL7YX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U33DKOR6FO27FWZSARNMBL7YX7","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":"37d2b928ca523efaa2dece678772e67a1c02f48ab377c936ffe404b8c8869582","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-20T10:06:37Z","title_canon_sha256":"f224cda5087b59103ae88088835c5d6f4b05fe913e100ca0f2bad5fadb52ecdf"},"schema_version":"1.0","source":{"id":"1609.06078","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06078","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06078v2","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06078","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"U33DKOR6FO27","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U33DKOR6FO27FWZS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U33DKOR6","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:44e708ec26616dbf168fd17a4923b3e275dd43c75158cbb8860e0f5e154ce4fd","target":"graph","created_at":"2026-05-18T00:45:01Z","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":"The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation for the anomalous dimension $\\gamma_\\lambda$ and fixed-points' structure. The dynamic exponent $z$ is calculated in the turbulent regime and stability of the fixed points for the standard model E is discussed.","authors_text":"M. Dan\\v{c}o, M. Hnati\\v{c}, M. V. Komarova, M. Yu. Nalimov, T. Lu\\v{c}ivjansk\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-20T10:06:37Z","title":"Renormalization group calculation of dynamic exponent in the models E and F with hydrodynamic fluctuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06078","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":"sha256:1cfd17b1637e5022305137a3de211ad65aa9b8ee2581d8692620ae55bf227382","target":"record","created_at":"2026-05-18T00:45:01Z","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":"37d2b928ca523efaa2dece678772e67a1c02f48ab377c936ffe404b8c8869582","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-09-20T10:06:37Z","title_canon_sha256":"f224cda5087b59103ae88088835c5d6f4b05fe913e100ca0f2bad5fadb52ecdf"},"schema_version":"1.0","source":{"id":"1609.06078","kind":"arxiv","version":2}},"canonical_sha256":"a6f6353a3e2bb5f2db32045ac0aff8bfda1b5f5f11ca86ef9be122d5fe386bd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6f6353a3e2bb5f2db32045ac0aff8bfda1b5f5f11ca86ef9be122d5fe386bd7","first_computed_at":"2026-05-18T00:45:01.512205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:01.512205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4//A1kFwnz7b9phXiaxlDwdixAdyu2yPcMc4w0F6MGqCNe2N7WpgAs5viYz+o6kjU99jctAMXM1ptNgrWq+wDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:01.512741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06078","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cfd17b1637e5022305137a3de211ad65aa9b8ee2581d8692620ae55bf227382","sha256:44e708ec26616dbf168fd17a4923b3e275dd43c75158cbb8860e0f5e154ce4fd"],"state_sha256":"d24f7b6a43d44f4c8e8bb2b3b3397d21146b5d31f4308037275b0e5f814fe1c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"22CA2yF3e/UKH6jPsTwC9t1gAWc6vqBX2+V8M6seGjaloKiomntzREQCPVe8q++/KEtClEqa6D2c6ct48fOFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:55:18.184431Z","bundle_sha256":"39e8174973cac0cd016132568fa222ab703355898e34ecc774dc10d8da524e99"}}