{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:F5Q2XVIYOOFAQ6AEOMRC2TRLRT","short_pith_number":"pith:F5Q2XVIY","canonical_record":{"source":{"id":"2301.00804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-02T18:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"379b3f51a65b781dc6a73626671c7e86bea855a7600999c23c82c9431059be61","abstract_canon_sha256":"a4cf886e5d570b094a0660b74e848d24ecda4b51a50453ba2824f22d329887ba"},"schema_version":"1.0"},"canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","source":{"kind":"arxiv","id":"2301.00804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.00804","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"arxiv_version","alias_value":"2301.00804v1","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.00804","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"pith_short_12","alias_value":"F5Q2XVIYOOFA","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"F5Q2XVIYOOFAQ6AE","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"F5Q2XVIY","created_at":"2026-07-05T05:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:F5Q2XVIYOOFAQ6AEOMRC2TRLRT","target":"record","payload":{"canonical_record":{"source":{"id":"2301.00804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-02T18:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"379b3f51a65b781dc6a73626671c7e86bea855a7600999c23c82c9431059be61","abstract_canon_sha256":"a4cf886e5d570b094a0660b74e848d24ecda4b51a50453ba2824f22d329887ba"},"schema_version":"1.0"},"canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:29:50.348965Z","signature_b64":"8x7alpyDP7pFv5aao8hSVO0PPG28nnH6pi3XT/lOn7mzBqzq5wwuyL8vDwUJ9wpv2dxl3fwh3JV+b/G6pG1RCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","last_reissued_at":"2026-07-05T05:29:50.348478Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:29:50.348478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.00804","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":"2026-07-05T05:29:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jxIqYi2mx0l0ql6YJ46EA4wYnE7O8ETY59ZjGqONXowsOmiwMNgYVw/uf12EWPuQuiyqL3NnTQsRTykOoKLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:25:56.111082Z"},"content_sha256":"0c13be9cfda1e2d2d69a816fc549d0f40390aac5cc9b222ad796199956faa38a","schema_version":"1.0","event_id":"sha256:0c13be9cfda1e2d2d69a816fc549d0f40390aac5cc9b222ad796199956faa38a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:F5Q2XVIYOOFAQ6AEOMRC2TRLRT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex integration above the Onsager exponent for the forced Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aynur Bulut, Manh Khang Huynh, Stan Palasek","submitted_at":"2023-01-02T18:50:46Z","abstract_excerpt":"We establish new non-uniqueness results for the Euler equations with external force on $\\mathbb{T}^{d}$ $(d\\geq3)$. By introducing a novel alternating convex integration scheme, we construct non-unique, almost-everywhere smooth, H\\\"older-continuous solutions with regularity $\\frac{1}{2}-$, which is notably above the Onsager threshold of $\\frac{1}{3}$.\n  The solutions we construct differ significantly in nature from those which arise from the recent unstable vortex construction of Vishik; in particular, our solutions are genuinely $d$-dimensional ($d\\geq3$), and give non-uniqueness results for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.00804","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.00804/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:29:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6hAJ9ZQqzzJfx8AgHbIWrobYKgOX0k8B91ITL9uUQbR7jDyKbvxGhsl+odHueyLe6K6lLUsisYNggttAKOMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:25:56.111477Z"},"content_sha256":"a39be0427512a527d55358313552f370b209645ce30654bb2a0c1e72c003f19a","schema_version":"1.0","event_id":"sha256:a39be0427512a527d55358313552f370b209645ce30654bb2a0c1e72c003f19a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/bundle.json","state_url":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/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":"2026-08-06T10:25:56Z","links":{"resolver":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT","bundle":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/bundle.json","state":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:F5Q2XVIYOOFAQ6AEOMRC2TRLRT","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":"a4cf886e5d570b094a0660b74e848d24ecda4b51a50453ba2824f22d329887ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-02T18:50:46Z","title_canon_sha256":"379b3f51a65b781dc6a73626671c7e86bea855a7600999c23c82c9431059be61"},"schema_version":"1.0","source":{"id":"2301.00804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.00804","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"arxiv_version","alias_value":"2301.00804v1","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.00804","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"pith_short_12","alias_value":"F5Q2XVIYOOFA","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"F5Q2XVIYOOFAQ6AE","created_at":"2026-07-05T05:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"F5Q2XVIY","created_at":"2026-07-05T05:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:a39be0427512a527d55358313552f370b209645ce30654bb2a0c1e72c003f19a","target":"graph","created_at":"2026-07-05T05:29:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.00804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish new non-uniqueness results for the Euler equations with external force on $\\mathbb{T}^{d}$ $(d\\geq3)$. By introducing a novel alternating convex integration scheme, we construct non-unique, almost-everywhere smooth, H\\\"older-continuous solutions with regularity $\\frac{1}{2}-$, which is notably above the Onsager threshold of $\\frac{1}{3}$.\n  The solutions we construct differ significantly in nature from those which arise from the recent unstable vortex construction of Vishik; in particular, our solutions are genuinely $d$-dimensional ($d\\geq3$), and give non-uniqueness results for ","authors_text":"Aynur Bulut, Manh Khang Huynh, Stan Palasek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-02T18:50:46Z","title":"Convex integration above the Onsager exponent for the forced Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.00804","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":"sha256:0c13be9cfda1e2d2d69a816fc549d0f40390aac5cc9b222ad796199956faa38a","target":"record","created_at":"2026-07-05T05:29:50Z","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":"a4cf886e5d570b094a0660b74e848d24ecda4b51a50453ba2824f22d329887ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-02T18:50:46Z","title_canon_sha256":"379b3f51a65b781dc6a73626671c7e86bea855a7600999c23c82c9431059be61"},"schema_version":"1.0","source":{"id":"2301.00804","kind":"arxiv","version":1}},"canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","first_computed_at":"2026-07-05T05:29:50.348478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:29:50.348478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8x7alpyDP7pFv5aao8hSVO0PPG28nnH6pi3XT/lOn7mzBqzq5wwuyL8vDwUJ9wpv2dxl3fwh3JV+b/G6pG1RCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:29:50.348965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.00804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c13be9cfda1e2d2d69a816fc549d0f40390aac5cc9b222ad796199956faa38a","sha256:a39be0427512a527d55358313552f370b209645ce30654bb2a0c1e72c003f19a"],"state_sha256":"bd020092983f485ad458143e4a08ea6cd81628c0b84e43eadb66dc0dfc8c7fb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGcRKhmGknfaxx6Z9MecfJy7czwmP1t16QT07tXIwJt/BgeT4nXl59/T1EIuKTRfxkD/3f72m+doEk8kjvL9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T10:25:56.115786Z","bundle_sha256":"8b6a6d02714d6d75f80b5751b5f9baf804c600ba97acc639b36721af46824721"}}