{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BDWIJA67EQ4RKXPBW5T7FDNAIM","short_pith_number":"pith:BDWIJA67","canonical_record":{"source":{"id":"2312.05022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-08T13:04:00Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"425d7880557dd9d8575e04cd77623abcfceeff40ee114474884de2b5d3e29111","abstract_canon_sha256":"0485f6cecad01ef9cd924e902cf05830214a92dfac53599ac24ab85be330f974"},"schema_version":"1.0"},"canonical_sha256":"08ec8483df2439155de1b767f28da0431e283f93328a335d7751138d16bf7966","source":{"kind":"arxiv","id":"2312.05022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.05022","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"2312.05022v1","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.05022","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"BDWIJA67EQ4R","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"pith_short_16","alias_value":"BDWIJA67EQ4RKXPB","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"pith_short_8","alias_value":"BDWIJA67","created_at":"2026-07-05T07:21:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BDWIJA67EQ4RKXPBW5T7FDNAIM","target":"record","payload":{"canonical_record":{"source":{"id":"2312.05022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-08T13:04:00Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"425d7880557dd9d8575e04cd77623abcfceeff40ee114474884de2b5d3e29111","abstract_canon_sha256":"0485f6cecad01ef9cd924e902cf05830214a92dfac53599ac24ab85be330f974"},"schema_version":"1.0"},"canonical_sha256":"08ec8483df2439155de1b767f28da0431e283f93328a335d7751138d16bf7966","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:21:55.889071Z","signature_b64":"LRmdhZxILR037+NICjD1Xeg9OYA9oQ4VroFqoDZQm9tprGtbu6GnaaZaL/PKgL/ZHzuBpLhDxIvf3In8IIFOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08ec8483df2439155de1b767f28da0431e283f93328a335d7751138d16bf7966","last_reissued_at":"2026-07-05T07:21:55.888658Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:21:55.888658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.05022","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":"2026-07-05T07:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dossxNcA5pj40LY7Do4arEcN3D8NsNr3wN1LIpEygWvoyiJjxBxw3B8SDPaZC1GeD7/VinMaDie4ipPdXXmMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:10:48.081172Z"},"content_sha256":"54a838b76859187ee4ea5eede1bd229e16f59c83e06a30ee82384db1ee8edad8","schema_version":"1.0","event_id":"sha256:54a838b76859187ee4ea5eede1bd229e16f59c83e06a30ee82384db1ee8edad8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BDWIJA67EQ4RKXPBW5T7FDNAIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unique continuation for differential inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Andr\\'e Guerra, Guido De Philippis, Riccardo Tione","submitted_at":"2023-12-08T13:04:00Z","abstract_excerpt":"We consider the following question arising in the theory of differential inclusions: given an elliptic set $\\Gamma$ and a Sobolev map $u$ whose gradient lies in the quasiconformal envelope of $\\Gamma$ and touches $\\Gamma$ on a set of positive measure, must $u$ be affine? We answer this question positively for a suitable notion of ellipticity, which for instance encompasses the case where $\\Gamma \\subset \\mathbb R^{2\\times 2}$ is an elliptic, smooth, closed curve. More precisely, we prove that the distance of $D u$ to $\\Gamma$ satisfies the strong unique continuation property. As a by-product, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.05022","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/2312.05022/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":"2026-07-05T07:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"as6o6WzFJtLaZURhzynpZfIUMlu796oGEXzv6mOMaGMLm+5HDqkPULW/zl9telx0otDhJTVUgTrOoy0/m11SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:10:48.081683Z"},"content_sha256":"5832fc0694bd4f898eed61807cb0a6c999b47146b86cac62fa35562fd11cc15a","schema_version":"1.0","event_id":"sha256:5832fc0694bd4f898eed61807cb0a6c999b47146b86cac62fa35562fd11cc15a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM/bundle.json","state_url":"https://pith.science/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM/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":"2026-08-07T05:10:48Z","links":{"resolver":"https://pith.science/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM","bundle":"https://pith.science/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM/bundle.json","state":"https://pith.science/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDWIJA67EQ4RKXPBW5T7FDNAIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BDWIJA67EQ4RKXPBW5T7FDNAIM","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":"0485f6cecad01ef9cd924e902cf05830214a92dfac53599ac24ab85be330f974","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-08T13:04:00Z","title_canon_sha256":"425d7880557dd9d8575e04cd77623abcfceeff40ee114474884de2b5d3e29111"},"schema_version":"1.0","source":{"id":"2312.05022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.05022","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"2312.05022v1","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.05022","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"BDWIJA67EQ4R","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"pith_short_16","alias_value":"BDWIJA67EQ4RKXPB","created_at":"2026-07-05T07:21:55Z"},{"alias_kind":"pith_short_8","alias_value":"BDWIJA67","created_at":"2026-07-05T07:21:55Z"}],"graph_snapshots":[{"event_id":"sha256:5832fc0694bd4f898eed61807cb0a6c999b47146b86cac62fa35562fd11cc15a","target":"graph","created_at":"2026-07-05T07:21:55Z","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/2312.05022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the following question arising in the theory of differential inclusions: given an elliptic set $\\Gamma$ and a Sobolev map $u$ whose gradient lies in the quasiconformal envelope of $\\Gamma$ and touches $\\Gamma$ on a set of positive measure, must $u$ be affine? We answer this question positively for a suitable notion of ellipticity, which for instance encompasses the case where $\\Gamma \\subset \\mathbb R^{2\\times 2}$ is an elliptic, smooth, closed curve. More precisely, we prove that the distance of $D u$ to $\\Gamma$ satisfies the strong unique continuation property. As a by-product, ","authors_text":"Andr\\'e Guerra, Guido De Philippis, Riccardo Tione","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-08T13:04:00Z","title":"Unique continuation for differential inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.05022","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":"sha256:54a838b76859187ee4ea5eede1bd229e16f59c83e06a30ee82384db1ee8edad8","target":"record","created_at":"2026-07-05T07:21:55Z","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":"0485f6cecad01ef9cd924e902cf05830214a92dfac53599ac24ab85be330f974","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-08T13:04:00Z","title_canon_sha256":"425d7880557dd9d8575e04cd77623abcfceeff40ee114474884de2b5d3e29111"},"schema_version":"1.0","source":{"id":"2312.05022","kind":"arxiv","version":1}},"canonical_sha256":"08ec8483df2439155de1b767f28da0431e283f93328a335d7751138d16bf7966","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08ec8483df2439155de1b767f28da0431e283f93328a335d7751138d16bf7966","first_computed_at":"2026-07-05T07:21:55.888658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:21:55.888658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LRmdhZxILR037+NICjD1Xeg9OYA9oQ4VroFqoDZQm9tprGtbu6GnaaZaL/PKgL/ZHzuBpLhDxIvf3In8IIFOAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:21:55.889071Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.05022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54a838b76859187ee4ea5eede1bd229e16f59c83e06a30ee82384db1ee8edad8","sha256:5832fc0694bd4f898eed61807cb0a6c999b47146b86cac62fa35562fd11cc15a"],"state_sha256":"5db98703b330b9a57f1388b7e9a192bee2d796c545d2f4d8239dbeaf7a7fefc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVbhrh7d6J/vbiT2C2hnft9BTSd7Naxo/EMQM4Sasd4PEgJ15fSox863krqxXRvXC6hWzhifsdCZi6SZjTfOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T05:10:48.086616Z","bundle_sha256":"695e90afdf06fcb269bd23723241fd85a11e17ad37c85d386b905b64a41c3f00"}}