{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LJ753HYJQ33W6OVN7MJM6CQ3OQ","short_pith_number":"pith:LJ753HYJ","canonical_record":{"source":{"id":"1708.00792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-02T15:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"1f9c2690bb66554ba025846e26e9c465e0452aa6584c61558afc61fcd160822c","abstract_canon_sha256":"7d51089e05eccfea3464fbdbe4c52088ee8f3f81bde67e3a640bbbfed39e0d2a"},"schema_version":"1.0"},"canonical_sha256":"5a7fdd9f0986f76f3aadfb12cf0a1b74278aa450e76c5a87b27e46773f0a2853","source":{"kind":"arxiv","id":"1708.00792","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00792","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00792v2","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00792","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"LJ753HYJQ33W","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LJ753HYJQ33W6OVN","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LJ753HYJ","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LJ753HYJQ33W6OVN7MJM6CQ3OQ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-02T15:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"1f9c2690bb66554ba025846e26e9c465e0452aa6584c61558afc61fcd160822c","abstract_canon_sha256":"7d51089e05eccfea3464fbdbe4c52088ee8f3f81bde67e3a640bbbfed39e0d2a"},"schema_version":"1.0"},"canonical_sha256":"5a7fdd9f0986f76f3aadfb12cf0a1b74278aa450e76c5a87b27e46773f0a2853","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:24.444102Z","signature_b64":"2XownXhNX88M8DtLiuUFSl3U31JnJw12XUjr7xR+4mAAfNgKnOuLsFF1rD7gIfPbktvWUeWIz6gJHe1hmidRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a7fdd9f0986f76f3aadfb12cf0a1b74278aa450e76c5a87b27e46773f0a2853","last_reissued_at":"2026-05-17T23:45:24.443609Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:24.443609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00792","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1GDjZIUlMBWO6YprsPcczELpfLPGL1R/C8JHwjiLmie6IhoeWYipvkOjVcQftJlCVw3G0ZNd/36yGs3ejTIzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:25:26.062170Z"},"content_sha256":"28d597004f338c628384308867065da7eeb89e0a4a9984e3aa749e3e7372de7c","schema_version":"1.0","event_id":"sha256:28d597004f338c628384308867065da7eeb89e0a4a9984e3aa749e3e7372de7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LJ753HYJQ33W6OVN7MJM6CQ3OQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anzellotti's pairing theory and the Gauss--Green theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Graziano Crasta, Virginia De Cicco","submitted_at":"2017-08-02T15:19:46Z","abstract_excerpt":"In this paper we obtain a very general Gauss-Green formula for weakly differentiable functions and sets of finite perimeter. This result is obtained by revisiting Anzellotti's pairing theory and by characterizing the measure pairing $(\\boldsymbol{A}, Du)$ when $\\boldsymbol{A}$ is a bounded divergence measure vector field and $u$ is a bounded function of bounded variation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00792","kind":"arxiv","version":2},"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":"2026-05-17T23:45:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUHldf0ajgzFge51mS2pqpIIzBtiPNBIG/bn+0zm/+UZ6Zb6RmUAfvCIcPW3x5Shdnuvcnusac9Z2dqZiugsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:25:26.062737Z"},"content_sha256":"d677aac98f1f96e232dbe392b39d5b0b67931dabe047801d14d85306821fe6f8","schema_version":"1.0","event_id":"sha256:d677aac98f1f96e232dbe392b39d5b0b67931dabe047801d14d85306821fe6f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ/bundle.json","state_url":"https://pith.science/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ/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":"2026-06-07T23:25:26Z","links":{"resolver":"https://pith.science/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ","bundle":"https://pith.science/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ/bundle.json","state":"https://pith.science/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ753HYJQ33W6OVN7MJM6CQ3OQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LJ753HYJQ33W6OVN7MJM6CQ3OQ","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":"7d51089e05eccfea3464fbdbe4c52088ee8f3f81bde67e3a640bbbfed39e0d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-02T15:19:46Z","title_canon_sha256":"1f9c2690bb66554ba025846e26e9c465e0452aa6584c61558afc61fcd160822c"},"schema_version":"1.0","source":{"id":"1708.00792","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00792","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00792v2","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00792","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"LJ753HYJQ33W","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LJ753HYJQ33W6OVN","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LJ753HYJ","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:d677aac98f1f96e232dbe392b39d5b0b67931dabe047801d14d85306821fe6f8","target":"graph","created_at":"2026-05-17T23:45:24Z","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 this paper we obtain a very general Gauss-Green formula for weakly differentiable functions and sets of finite perimeter. This result is obtained by revisiting Anzellotti's pairing theory and by characterizing the measure pairing $(\\boldsymbol{A}, Du)$ when $\\boldsymbol{A}$ is a bounded divergence measure vector field and $u$ is a bounded function of bounded variation.","authors_text":"Graziano Crasta, Virginia De Cicco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-02T15:19:46Z","title":"Anzellotti's pairing theory and the Gauss--Green theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00792","kind":"arxiv","version":2},"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":"sha256:28d597004f338c628384308867065da7eeb89e0a4a9984e3aa749e3e7372de7c","target":"record","created_at":"2026-05-17T23:45:24Z","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":"7d51089e05eccfea3464fbdbe4c52088ee8f3f81bde67e3a640bbbfed39e0d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-02T15:19:46Z","title_canon_sha256":"1f9c2690bb66554ba025846e26e9c465e0452aa6584c61558afc61fcd160822c"},"schema_version":"1.0","source":{"id":"1708.00792","kind":"arxiv","version":2}},"canonical_sha256":"5a7fdd9f0986f76f3aadfb12cf0a1b74278aa450e76c5a87b27e46773f0a2853","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7fdd9f0986f76f3aadfb12cf0a1b74278aa450e76c5a87b27e46773f0a2853","first_computed_at":"2026-05-17T23:45:24.443609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:24.443609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2XownXhNX88M8DtLiuUFSl3U31JnJw12XUjr7xR+4mAAfNgKnOuLsFF1rD7gIfPbktvWUeWIz6gJHe1hmidRCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:24.444102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00792","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28d597004f338c628384308867065da7eeb89e0a4a9984e3aa749e3e7372de7c","sha256:d677aac98f1f96e232dbe392b39d5b0b67931dabe047801d14d85306821fe6f8"],"state_sha256":"bc25b03ba087c8dbd0daabd7e00d11b79400ac642f6924d1c75052db8f971448"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pxu9wZWunHWH5qSWXUuduKMqGmp1jhh59Rs4+8bAlP3MGYiD60vVvkQXuz5Kfz5ocV3XNzvJ3j1vFRTJhZm4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:25:26.065946Z","bundle_sha256":"71a03442c52c219b0f3a42da71e040bd893096e4a1c91b11987945ca511a85f7"}}