{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3E2LTPQ2JY5D3DLCBWN4C4NXPY","short_pith_number":"pith:3E2LTPQ2","canonical_record":{"source":{"id":"1108.2079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-10T01:36:25Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"267cbe71fddf8cc3d185feee586d6e99dbc34134f132bdacd8bf44595fd0ad9c","abstract_canon_sha256":"108e07f92e2d57c8d5dcf2db1438c28c6a35c0c48e7bcabfb12e74cd11c4e4ed"},"schema_version":"1.0"},"canonical_sha256":"d934b9be1a4e3a3d8d620d9bc171b77e288ce427b4adfc7f770c7bc880da7260","source":{"kind":"arxiv","id":"1108.2079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2079","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2079v1","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2079","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"3E2LTPQ2JY5D","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3E2LTPQ2JY5D3DLC","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3E2LTPQ2","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3E2LTPQ2JY5D3DLCBWN4C4NXPY","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-10T01:36:25Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"267cbe71fddf8cc3d185feee586d6e99dbc34134f132bdacd8bf44595fd0ad9c","abstract_canon_sha256":"108e07f92e2d57c8d5dcf2db1438c28c6a35c0c48e7bcabfb12e74cd11c4e4ed"},"schema_version":"1.0"},"canonical_sha256":"d934b9be1a4e3a3d8d620d9bc171b77e288ce427b4adfc7f770c7bc880da7260","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:59.518654Z","signature_b64":"exg1biGFI4D2KIquPE6reqwu7GD00qhYScmId/bi4873TrXYGfC85k/SYYP4LmTwBJJRLp7e/pML8gv1j3GnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d934b9be1a4e3a3d8d620d9bc171b77e288ce427b4adfc7f770c7bc880da7260","last_reissued_at":"2026-05-18T02:00:59.517960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:59.517960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2079","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":"2026-05-18T02:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bzy62vZ4HeeLq4MxVn0DBqmtI4kwGYo4OsEaaR3i2yLBXiYfUxbXH7NTXLUhwpPbdlBpE3iiGMbZRpCvvi3jAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:07:38.518461Z"},"content_sha256":"49d052485f66cf5ebe0def804e2266f4232cbd0cf1e74a89438eb8bebc92b910","schema_version":"1.0","event_id":"sha256:49d052485f66cf5ebe0def804e2266f4232cbd0cf1e74a89438eb8bebc92b910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3E2LTPQ2JY5D3DLCBWN4C4NXPY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the flow map for 2D Euler equations with unbounded vorticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"James P. Kelliher","submitted_at":"2011-08-10T01:36:25Z","abstract_excerpt":"In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2079","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":"2026-05-18T02:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uIrOCQGV1YHya6Ettp/5mFjxait2Dkw8wy8+xFuxgLTWd9nFE015qUhzDtux0DhyctQxazjsTd9T3DWfu6mxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:07:38.519157Z"},"content_sha256":"2b0988db53b3c4ecdf5830e40378ff9e090851a5d1aed5c9720e518df6f96a46","schema_version":"1.0","event_id":"sha256:2b0988db53b3c4ecdf5830e40378ff9e090851a5d1aed5c9720e518df6f96a46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY/bundle.json","state_url":"https://pith.science/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY/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":"2026-06-05T22:07:38Z","links":{"resolver":"https://pith.science/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY","bundle":"https://pith.science/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY/bundle.json","state":"https://pith.science/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3E2LTPQ2JY5D3DLCBWN4C4NXPY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3E2LTPQ2JY5D3DLCBWN4C4NXPY","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":"108e07f92e2d57c8d5dcf2db1438c28c6a35c0c48e7bcabfb12e74cd11c4e4ed","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-10T01:36:25Z","title_canon_sha256":"267cbe71fddf8cc3d185feee586d6e99dbc34134f132bdacd8bf44595fd0ad9c"},"schema_version":"1.0","source":{"id":"1108.2079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2079","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2079v1","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2079","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"3E2LTPQ2JY5D","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3E2LTPQ2JY5D3DLC","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3E2LTPQ2","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:2b0988db53b3c4ecdf5830e40378ff9e090851a5d1aed5c9720e518df6f96a46","target":"graph","created_at":"2026-05-18T02:00:59Z","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":"In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.","authors_text":"James P. Kelliher","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-10T01:36:25Z","title":"On the flow map for 2D Euler equations with unbounded vorticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2079","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":"sha256:49d052485f66cf5ebe0def804e2266f4232cbd0cf1e74a89438eb8bebc92b910","target":"record","created_at":"2026-05-18T02:00:59Z","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":"108e07f92e2d57c8d5dcf2db1438c28c6a35c0c48e7bcabfb12e74cd11c4e4ed","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-10T01:36:25Z","title_canon_sha256":"267cbe71fddf8cc3d185feee586d6e99dbc34134f132bdacd8bf44595fd0ad9c"},"schema_version":"1.0","source":{"id":"1108.2079","kind":"arxiv","version":1}},"canonical_sha256":"d934b9be1a4e3a3d8d620d9bc171b77e288ce427b4adfc7f770c7bc880da7260","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d934b9be1a4e3a3d8d620d9bc171b77e288ce427b4adfc7f770c7bc880da7260","first_computed_at":"2026-05-18T02:00:59.517960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:59.517960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"exg1biGFI4D2KIquPE6reqwu7GD00qhYScmId/bi4873TrXYGfC85k/SYYP4LmTwBJJRLp7e/pML8gv1j3GnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:59.518654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49d052485f66cf5ebe0def804e2266f4232cbd0cf1e74a89438eb8bebc92b910","sha256:2b0988db53b3c4ecdf5830e40378ff9e090851a5d1aed5c9720e518df6f96a46"],"state_sha256":"acdac2b772f7ef3b94349721d621ab83d242bec554834f4220c964128120eecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9ykE0TILFaYkyY2GizeihAoUCXv4tWwOkx22myYc7GBiXLWsq/svtEo8x38WmOAWRDzzJTHSflqRfudNl/TAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:07:38.522420Z","bundle_sha256":"3cb7e68361d687f495579f487812fd001cd5835c717069f7c5d1dcb548b34fb3"}}