{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LZBNBDZTZFMPVV3BFE7ILS7D3A","short_pith_number":"pith:LZBNBDZT","canonical_record":{"source":{"id":"2605.19504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T07:59:28Z","cross_cats_sorted":[],"title_canon_sha256":"0db929b288c6bf58a6950d7bb28205a1e76f9dea761b4c1891206b1c0819051b","abstract_canon_sha256":"3df04770f365c4b23a490d0073dbc8ddfd1637be70eceb7e6701125996b9f910"},"schema_version":"1.0"},"canonical_sha256":"5e42d08f33c958fad761293e85cbe3d802d843582f68cee360f69de38760665f","source":{"kind":"arxiv","id":"2605.19504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19504","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19504v1","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19504","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"LZBNBDZTZFMP","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"LZBNBDZTZFMPVV3B","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"LZBNBDZT","created_at":"2026-05-20T01:05:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LZBNBDZTZFMPVV3BFE7ILS7D3A","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T07:59:28Z","cross_cats_sorted":[],"title_canon_sha256":"0db929b288c6bf58a6950d7bb28205a1e76f9dea761b4c1891206b1c0819051b","abstract_canon_sha256":"3df04770f365c4b23a490d0073dbc8ddfd1637be70eceb7e6701125996b9f910"},"schema_version":"1.0"},"canonical_sha256":"5e42d08f33c958fad761293e85cbe3d802d843582f68cee360f69de38760665f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:48.954024Z","signature_b64":"6rbQEA1X+QSNMeuHSdCfo1TPkWt9kryi8vmCMw3CP5YVEaCXXtSdJ36SFWyj4pdO7+ZWVMFlmzNfCBx3sqK/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e42d08f33c958fad761293e85cbe3d802d843582f68cee360f69de38760665f","last_reissued_at":"2026-05-20T01:05:48.953306Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:48.953306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19504","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":"2026-05-20T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3U+Mr6wLwth6kPcN8KxprtJOymf8i3Vt1YRH18rKuagya98HeQ/1mKboCqn1pI4MOlCIC65n7j7dtBqtk34YCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:19:35.993423Z"},"content_sha256":"e860a82cde5096481382355961cec71cd23ab579c56ed65a8ab37d4867404a60","schema_version":"1.0","event_id":"sha256:e860a82cde5096481382355961cec71cd23ab579c56ed65a8ab37d4867404a60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LZBNBDZTZFMPVV3BFE7ILS7D3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A regularity result for $BV^{\\mathcal{A}}(\\Omega)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jakob Deutsch, Samuele Ricc\\`o","submitted_at":"2026-05-19T07:59:28Z","abstract_excerpt":"It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space $BD$ on bounded domains with $\\mathcal{C}^1$ boundary. In this work, we extend this result to a broader class of first-order linear elliptic operators. More precisely, let $\\mathcal{A}$ be a first-order linear elliptic operator satisfying the rank-one property. We prove that if a distribution defined on a Lipschitz domain has bounded $\\mathcal{A}$-variation, then it belongs to the space $BV^{\\mathcal{A}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19504","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/2605.19504/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":"2026-05-20T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHEer003Sj2Y8nH4SgMbIwtNhMXnt2/NWCv7Eau84/t+onxjgRUuvrQ/aRcDTxqR2SoSggfQmMeU90b2Bp6hBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:19:35.993829Z"},"content_sha256":"cc9f76245ecea5194c553ce0c2cd19a84ffe3ff17f1b5e445fd0227f2b854bb8","schema_version":"1.0","event_id":"sha256:cc9f76245ecea5194c553ce0c2cd19a84ffe3ff17f1b5e445fd0227f2b854bb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A/bundle.json","state_url":"https://pith.science/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A/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":"2026-06-02T14:19:35Z","links":{"resolver":"https://pith.science/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A","bundle":"https://pith.science/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A/bundle.json","state":"https://pith.science/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZBNBDZTZFMPVV3BFE7ILS7D3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LZBNBDZTZFMPVV3BFE7ILS7D3A","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":"3df04770f365c4b23a490d0073dbc8ddfd1637be70eceb7e6701125996b9f910","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T07:59:28Z","title_canon_sha256":"0db929b288c6bf58a6950d7bb28205a1e76f9dea761b4c1891206b1c0819051b"},"schema_version":"1.0","source":{"id":"2605.19504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19504","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19504v1","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19504","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"LZBNBDZTZFMP","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"LZBNBDZTZFMPVV3B","created_at":"2026-05-20T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"LZBNBDZT","created_at":"2026-05-20T01:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:cc9f76245ecea5194c553ce0c2cd19a84ffe3ff17f1b5e445fd0227f2b854bb8","target":"graph","created_at":"2026-05-20T01:05:48Z","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/2605.19504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space $BD$ on bounded domains with $\\mathcal{C}^1$ boundary. In this work, we extend this result to a broader class of first-order linear elliptic operators. More precisely, let $\\mathcal{A}$ be a first-order linear elliptic operator satisfying the rank-one property. We prove that if a distribution defined on a Lipschitz domain has bounded $\\mathcal{A}$-variation, then it belongs to the space $BV^{\\mathcal{A}}$.","authors_text":"Jakob Deutsch, Samuele Ricc\\`o","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T07:59:28Z","title":"A regularity result for $BV^{\\mathcal{A}}(\\Omega)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19504","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:e860a82cde5096481382355961cec71cd23ab579c56ed65a8ab37d4867404a60","target":"record","created_at":"2026-05-20T01:05:48Z","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":"3df04770f365c4b23a490d0073dbc8ddfd1637be70eceb7e6701125996b9f910","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T07:59:28Z","title_canon_sha256":"0db929b288c6bf58a6950d7bb28205a1e76f9dea761b4c1891206b1c0819051b"},"schema_version":"1.0","source":{"id":"2605.19504","kind":"arxiv","version":1}},"canonical_sha256":"5e42d08f33c958fad761293e85cbe3d802d843582f68cee360f69de38760665f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e42d08f33c958fad761293e85cbe3d802d843582f68cee360f69de38760665f","first_computed_at":"2026-05-20T01:05:48.953306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:48.953306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6rbQEA1X+QSNMeuHSdCfo1TPkWt9kryi8vmCMw3CP5YVEaCXXtSdJ36SFWyj4pdO7+ZWVMFlmzNfCBx3sqK/Dg==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:48.954024Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e860a82cde5096481382355961cec71cd23ab579c56ed65a8ab37d4867404a60","sha256:cc9f76245ecea5194c553ce0c2cd19a84ffe3ff17f1b5e445fd0227f2b854bb8"],"state_sha256":"f3e0907afcc2ce3fa6abdf2190a3dbc9f04d09c39fd2dd36cb48ebfc9cbd8b95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IL3qRYuKEB3f3QA/0glPJUoaJrUbNUFs/RFehio/SNktmjGAWifaB9eviD94ufdO8w2dXbzCFwkonF+PhYtFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:19:35.996039Z","bundle_sha256":"999970741c2c4800f10d117668c9bde52bbeb1aa1065f650b1181ea100a6d69b"}}