{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2K5L6AZ5TFWNFEEI3WU2O75LZO","short_pith_number":"pith:2K5L6AZ5","canonical_record":{"source":{"id":"1205.2852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-13T10:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"7250771a7f67917b56ae70248775f70a21198d64e814299f830d36e2ebe7feab","abstract_canon_sha256":"bb4f3a8a3f1e8a281d32094b95b1500e2a25a3d58a44c6330c751dbc15bf3a34"},"schema_version":"1.0"},"canonical_sha256":"d2babf033d996cd29088dda9a77fabcb9c9fbc99a3f8b88dfccf3597e6b344cd","source":{"kind":"arxiv","id":"1205.2852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2852","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2852v1","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2852","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"2K5L6AZ5TFWN","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2K5L6AZ5TFWNFEEI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2K5L6AZ5","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2K5L6AZ5TFWNFEEI3WU2O75LZO","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-13T10:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"7250771a7f67917b56ae70248775f70a21198d64e814299f830d36e2ebe7feab","abstract_canon_sha256":"bb4f3a8a3f1e8a281d32094b95b1500e2a25a3d58a44c6330c751dbc15bf3a34"},"schema_version":"1.0"},"canonical_sha256":"d2babf033d996cd29088dda9a77fabcb9c9fbc99a3f8b88dfccf3597e6b344cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:45.918073Z","signature_b64":"N8b/XIvwpTZ0SkveAWGW+xf3pY7SqignIs8wNz4F3Triuy3HC80JmZEgbh6ryvULtakV8wOEsZI92g/jWJyXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2babf033d996cd29088dda9a77fabcb9c9fbc99a3f8b88dfccf3597e6b344cd","last_reissued_at":"2026-05-18T01:34:45.917479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:45.917479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2852","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":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLumFTeWCDY5YJ6IIOj9y9voHq2KfedWQpnhZ+06ANT02m1EVP8+acWF+ScaoYcPSEdFiDqBpUeRtczZonBBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:10:10.141430Z"},"content_sha256":"559387bd21af8819eff334007480e507de49019ee578c8e6384018ee3eca9be6","schema_version":"1.0","event_id":"sha256:559387bd21af8819eff334007480e507de49019ee578c8e6384018ee3eca9be6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2K5L6AZ5TFWNFEEI3WU2O75LZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"\\epsilon-regularity for systems involving non-local, antisymmetric operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra","submitted_at":"2012-05-13T10:54:29Z","abstract_excerpt":"We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side.\n  These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\\`ere.\n  In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\\`ere, Rivi\\`ere-Struwe, Da-Lio-Rivi\\`ere, and also the integrability results by Sharp-Topping and Sharp, not dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2852","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":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQ0iYjCxAVdQMyzuPqCYsnQ3fj5VE/a+bzQ3Q6AHPrPEVtycZTeKH/MU0T/Rizen0SiuOJ/B1itwl35IyUTtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:10:10.142144Z"},"content_sha256":"2ac04e31c95a7c9db0b7b1db258c3353473dab7a2040a33c3484065828245342","schema_version":"1.0","event_id":"sha256:2ac04e31c95a7c9db0b7b1db258c3353473dab7a2040a33c3484065828245342"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO/bundle.json","state_url":"https://pith.science/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO/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":"2026-06-11T08:10:10Z","links":{"resolver":"https://pith.science/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO","bundle":"https://pith.science/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO/bundle.json","state":"https://pith.science/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2K5L6AZ5TFWNFEEI3WU2O75LZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2K5L6AZ5TFWNFEEI3WU2O75LZO","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":"bb4f3a8a3f1e8a281d32094b95b1500e2a25a3d58a44c6330c751dbc15bf3a34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-13T10:54:29Z","title_canon_sha256":"7250771a7f67917b56ae70248775f70a21198d64e814299f830d36e2ebe7feab"},"schema_version":"1.0","source":{"id":"1205.2852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2852","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2852v1","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2852","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"2K5L6AZ5TFWN","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2K5L6AZ5TFWNFEEI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2K5L6AZ5","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:2ac04e31c95a7c9db0b7b1db258c3353473dab7a2040a33c3484065828245342","target":"graph","created_at":"2026-05-18T01:34:45Z","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 an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side.\n  These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\\`ere.\n  In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\\`ere, Rivi\\`ere-Struwe, Da-Lio-Rivi\\`ere, and also the integrability results by Sharp-Topping and Sharp, not dis","authors_text":"Armin Schikorra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-13T10:54:29Z","title":"\\epsilon-regularity for systems involving non-local, antisymmetric operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2852","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":"sha256:559387bd21af8819eff334007480e507de49019ee578c8e6384018ee3eca9be6","target":"record","created_at":"2026-05-18T01:34:45Z","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":"bb4f3a8a3f1e8a281d32094b95b1500e2a25a3d58a44c6330c751dbc15bf3a34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-13T10:54:29Z","title_canon_sha256":"7250771a7f67917b56ae70248775f70a21198d64e814299f830d36e2ebe7feab"},"schema_version":"1.0","source":{"id":"1205.2852","kind":"arxiv","version":1}},"canonical_sha256":"d2babf033d996cd29088dda9a77fabcb9c9fbc99a3f8b88dfccf3597e6b344cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2babf033d996cd29088dda9a77fabcb9c9fbc99a3f8b88dfccf3597e6b344cd","first_computed_at":"2026-05-18T01:34:45.917479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:45.917479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N8b/XIvwpTZ0SkveAWGW+xf3pY7SqignIs8wNz4F3Triuy3HC80JmZEgbh6ryvULtakV8wOEsZI92g/jWJyXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:45.918073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:559387bd21af8819eff334007480e507de49019ee578c8e6384018ee3eca9be6","sha256:2ac04e31c95a7c9db0b7b1db258c3353473dab7a2040a33c3484065828245342"],"state_sha256":"64ca8ff61a131f9c459d9cd0162d35cfdd3ed0409b3cc431a1bb9ce2c1cfde59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCJsuaTr2pQbt95eow4QIrKYBVAf/tHqUT2GrNaUIN9tFY4AJaMLMtrQKZUYNaLh8pF27bzOTJRdpyDC2B0SAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:10:10.146353Z","bundle_sha256":"80885310a390b8897d21d11a6b2e63a2224925fc5f74c37c69b10d5a74862a47"}}