{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SCNGNMGO52RL4TJBYI2T54A3CL","short_pith_number":"pith:SCNGNMGO","canonical_record":{"source":{"id":"1310.6128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-23T07:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"3ede0e98e4e9814164cc71ebb0f833e3ef898ae194c0761d50bcd9691defa2b4","abstract_canon_sha256":"54a7306821cf2432293d8129637419b2e9fcc80dea79f96154534b2b9f51dd46"},"schema_version":"1.0"},"canonical_sha256":"909a66b0ceeea2be4d21c2353ef01b12e97a3a8ceb3110ed2e3dd8b546569c01","source":{"kind":"arxiv","id":"1310.6128","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6128","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6128v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6128","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"SCNGNMGO52RL","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SCNGNMGO52RL4TJB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SCNGNMGO","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SCNGNMGO52RL4TJBYI2T54A3CL","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-23T07:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"3ede0e98e4e9814164cc71ebb0f833e3ef898ae194c0761d50bcd9691defa2b4","abstract_canon_sha256":"54a7306821cf2432293d8129637419b2e9fcc80dea79f96154534b2b9f51dd46"},"schema_version":"1.0"},"canonical_sha256":"909a66b0ceeea2be4d21c2353ef01b12e97a3a8ceb3110ed2e3dd8b546569c01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:54.185410Z","signature_b64":"1gJt0bfqySNUkqoULjf6W853U+IzO6nAJYsxsF4XpzOVEG08h+lE0lVX3pjTUVQ9UvKY/2jXZ0S6H15+8keTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"909a66b0ceeea2be4d21c2353ef01b12e97a3a8ceb3110ed2e3dd8b546569c01","last_reissued_at":"2026-05-18T02:40:54.184980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:54.184980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6128","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":"2026-05-18T02:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZoF8lr6gZpFRndo6lbZzFfuJOSC2K0DGwhFX75Yz5RlYYpKUkgHUgwFdLrYuwXOi+nlQn8fQjnCA68a5JkQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:34:24.331617Z"},"content_sha256":"62c37472d66cc7ec7addf02760c36a88520f9277a99691011bb7568f8844809b","schema_version":"1.0","event_id":"sha256:62c37472d66cc7ec7addf02760c36a88520f9277a99691011bb7568f8844809b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SCNGNMGO52RL4TJBYI2T54A3CL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential growth of the vorticity gradient for the Euler equation on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrej Zlatos","submitted_at":"2013-10-23T07:01:07Z","abstract_excerpt":"We prove that there are solutions to the Euler equation on the torus with $C^{1,\\alpha}$ vorticity and smooth except at one point such that the vorticity gradient grows in $L^\\infty$ at least exponentially as $t\\to\\infty$. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Sverak."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6128","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":"2026-05-18T02:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKP1Fk2lbxIgjXyTj1mA6P/e2GMKs8WJXjmYbWvLEEHrFXjENiAI3GkVwbli4VzxQtAeCdZIRnx4bUji+HJhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:34:24.331967Z"},"content_sha256":"2f979e8fb6c3ebb65529708a96cb05481b13529bd28aafe3f1663a8118b3c0b6","schema_version":"1.0","event_id":"sha256:2f979e8fb6c3ebb65529708a96cb05481b13529bd28aafe3f1663a8118b3c0b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCNGNMGO52RL4TJBYI2T54A3CL/bundle.json","state_url":"https://pith.science/pith/SCNGNMGO52RL4TJBYI2T54A3CL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCNGNMGO52RL4TJBYI2T54A3CL/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":"2026-06-02T17:34:24Z","links":{"resolver":"https://pith.science/pith/SCNGNMGO52RL4TJBYI2T54A3CL","bundle":"https://pith.science/pith/SCNGNMGO52RL4TJBYI2T54A3CL/bundle.json","state":"https://pith.science/pith/SCNGNMGO52RL4TJBYI2T54A3CL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCNGNMGO52RL4TJBYI2T54A3CL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SCNGNMGO52RL4TJBYI2T54A3CL","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":"54a7306821cf2432293d8129637419b2e9fcc80dea79f96154534b2b9f51dd46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-23T07:01:07Z","title_canon_sha256":"3ede0e98e4e9814164cc71ebb0f833e3ef898ae194c0761d50bcd9691defa2b4"},"schema_version":"1.0","source":{"id":"1310.6128","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6128","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6128v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6128","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"SCNGNMGO52RL","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SCNGNMGO52RL4TJB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SCNGNMGO","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:2f979e8fb6c3ebb65529708a96cb05481b13529bd28aafe3f1663a8118b3c0b6","target":"graph","created_at":"2026-05-18T02:40:54Z","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 prove that there are solutions to the Euler equation on the torus with $C^{1,\\alpha}$ vorticity and smooth except at one point such that the vorticity gradient grows in $L^\\infty$ at least exponentially as $t\\to\\infty$. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Sverak.","authors_text":"Andrej Zlatos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-23T07:01:07Z","title":"Exponential growth of the vorticity gradient for the Euler equation on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6128","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":"sha256:62c37472d66cc7ec7addf02760c36a88520f9277a99691011bb7568f8844809b","target":"record","created_at":"2026-05-18T02:40:54Z","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":"54a7306821cf2432293d8129637419b2e9fcc80dea79f96154534b2b9f51dd46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-23T07:01:07Z","title_canon_sha256":"3ede0e98e4e9814164cc71ebb0f833e3ef898ae194c0761d50bcd9691defa2b4"},"schema_version":"1.0","source":{"id":"1310.6128","kind":"arxiv","version":2}},"canonical_sha256":"909a66b0ceeea2be4d21c2353ef01b12e97a3a8ceb3110ed2e3dd8b546569c01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"909a66b0ceeea2be4d21c2353ef01b12e97a3a8ceb3110ed2e3dd8b546569c01","first_computed_at":"2026-05-18T02:40:54.184980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:54.184980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1gJt0bfqySNUkqoULjf6W853U+IzO6nAJYsxsF4XpzOVEG08h+lE0lVX3pjTUVQ9UvKY/2jXZ0S6H15+8keTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:54.185410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6128","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62c37472d66cc7ec7addf02760c36a88520f9277a99691011bb7568f8844809b","sha256:2f979e8fb6c3ebb65529708a96cb05481b13529bd28aafe3f1663a8118b3c0b6"],"state_sha256":"ad701403a15cf34016345e9d546416018f1c9561268f09b297bc7a0038882250"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LB5CoufZIDYheq/26Abq4mOB1M7sfhxNxJXGo6aw7QHannupmW0Jk5XLRa19N8RV96A0u7TuSvpoTn+60TvRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:34:24.334019Z","bundle_sha256":"18eb4171c0b486f71c021b3b42d06e753fe52497ec3475f222117bea21ade148"}}