{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3HFDFCRK7WFUXTL2N3UAVK6S4F","short_pith_number":"pith:3HFDFCRK","canonical_record":{"source":{"id":"2002.08133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-19T12:25:38Z","cross_cats_sorted":[],"title_canon_sha256":"de82e2c791337013802a87441de663760267995952be16a3d103602472c522eb","abstract_canon_sha256":"cadd2745bde1081b90e3bf83df1c96044a43e92df6423a036bc014d64c68566a"},"schema_version":"1.0"},"canonical_sha256":"d9ca328a2afd8b4bcd7a6ee80aabd2e17b753cad3fb5223119692e20ee2404ce","source":{"kind":"arxiv","id":"2002.08133","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.08133","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"2002.08133v3","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.08133","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"3HFDFCRK7WFU","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"pith_short_16","alias_value":"3HFDFCRK7WFUXTL2","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"pith_short_8","alias_value":"3HFDFCRK","created_at":"2026-07-05T01:57:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3HFDFCRK7WFUXTL2N3UAVK6S4F","target":"record","payload":{"canonical_record":{"source":{"id":"2002.08133","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-19T12:25:38Z","cross_cats_sorted":[],"title_canon_sha256":"de82e2c791337013802a87441de663760267995952be16a3d103602472c522eb","abstract_canon_sha256":"cadd2745bde1081b90e3bf83df1c96044a43e92df6423a036bc014d64c68566a"},"schema_version":"1.0"},"canonical_sha256":"d9ca328a2afd8b4bcd7a6ee80aabd2e17b753cad3fb5223119692e20ee2404ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:14.791810Z","signature_b64":"MWSj2P9QYylCYtmiT8hP6xeZKt8QKT7bJb601eDaV4tVaTztADRoWxmxJYU81NliloY/RFfVfbmIWMvzsw2CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9ca328a2afd8b4bcd7a6ee80aabd2e17b753cad3fb5223119692e20ee2404ce","last_reissued_at":"2026-07-05T01:57:14.791403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:14.791403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.08133","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:57:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7oKbIWk7puwUD00H5O8e9vHLP/BXLZz6ayBGjo8F0zij4Ljei/elsx11gcnvnmpx+f9arjiptJFH6MVwGtSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T13:45:43.524422Z"},"content_sha256":"5b93635e005e936de7117a673cef90762471cb28e3b3e00bea5accb0889382e0","schema_version":"1.0","event_id":"sha256:5b93635e005e936de7117a673cef90762471cb28e3b3e00bea5accb0889382e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3HFDFCRK7WFUXTL2N3UAVK6S4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower semicontinuity for functionals defined on piecewise rigid functions and on $GSBD$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Solombrino, Manuel Friedrich, Matteo Perugini","submitted_at":"2020-02-19T12:25:38Z","abstract_excerpt":"In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix. This characterization is achieved by means of an integral condition, called $BD$-ellipticity, which is in the spirit of $BV$-ellipticity defined by Ambrosio and Braides. By specific examples we show that this novel concept is in fact stronger compared to its $BV$ analog. We further provide a sufficient condition implying $BD$-e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.08133","kind":"arxiv","version":3},"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/2002.08133/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":"2026-07-05T01:57:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8QMXZrk/rbWahQ/0ZIEt/Y57loWsZB3DM1Zi++NP3mu1mTuBjHKSxo4eUJEsK1BCWF4m5SXr6euTZMbzviiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T13:45:43.525055Z"},"content_sha256":"f29ac7dcb94551f406c4aa45b42135adf1eb92171e910f58d97547dfbcca07df","schema_version":"1.0","event_id":"sha256:f29ac7dcb94551f406c4aa45b42135adf1eb92171e910f58d97547dfbcca07df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F/bundle.json","state_url":"https://pith.science/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F/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":"2026-07-08T13:45:43Z","links":{"resolver":"https://pith.science/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F","bundle":"https://pith.science/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F/bundle.json","state":"https://pith.science/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HFDFCRK7WFUXTL2N3UAVK6S4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3HFDFCRK7WFUXTL2N3UAVK6S4F","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":"cadd2745bde1081b90e3bf83df1c96044a43e92df6423a036bc014d64c68566a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-19T12:25:38Z","title_canon_sha256":"de82e2c791337013802a87441de663760267995952be16a3d103602472c522eb"},"schema_version":"1.0","source":{"id":"2002.08133","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.08133","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"2002.08133v3","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.08133","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"3HFDFCRK7WFU","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"pith_short_16","alias_value":"3HFDFCRK7WFUXTL2","created_at":"2026-07-05T01:57:14Z"},{"alias_kind":"pith_short_8","alias_value":"3HFDFCRK","created_at":"2026-07-05T01:57:14Z"}],"graph_snapshots":[{"event_id":"sha256:f29ac7dcb94551f406c4aa45b42135adf1eb92171e910f58d97547dfbcca07df","target":"graph","created_at":"2026-07-05T01:57:14Z","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/2002.08133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix. This characterization is achieved by means of an integral condition, called $BD$-ellipticity, which is in the spirit of $BV$-ellipticity defined by Ambrosio and Braides. By specific examples we show that this novel concept is in fact stronger compared to its $BV$ analog. We further provide a sufficient condition implying $BD$-e","authors_text":"Francesco Solombrino, Manuel Friedrich, Matteo Perugini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-19T12:25:38Z","title":"Lower semicontinuity for functionals defined on piecewise rigid functions and on $GSBD$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.08133","kind":"arxiv","version":3},"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":"sha256:5b93635e005e936de7117a673cef90762471cb28e3b3e00bea5accb0889382e0","target":"record","created_at":"2026-07-05T01:57:14Z","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":"cadd2745bde1081b90e3bf83df1c96044a43e92df6423a036bc014d64c68566a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-19T12:25:38Z","title_canon_sha256":"de82e2c791337013802a87441de663760267995952be16a3d103602472c522eb"},"schema_version":"1.0","source":{"id":"2002.08133","kind":"arxiv","version":3}},"canonical_sha256":"d9ca328a2afd8b4bcd7a6ee80aabd2e17b753cad3fb5223119692e20ee2404ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9ca328a2afd8b4bcd7a6ee80aabd2e17b753cad3fb5223119692e20ee2404ce","first_computed_at":"2026-07-05T01:57:14.791403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:57:14.791403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MWSj2P9QYylCYtmiT8hP6xeZKt8QKT7bJb601eDaV4tVaTztADRoWxmxJYU81NliloY/RFfVfbmIWMvzsw2CDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:57:14.791810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.08133","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b93635e005e936de7117a673cef90762471cb28e3b3e00bea5accb0889382e0","sha256:f29ac7dcb94551f406c4aa45b42135adf1eb92171e910f58d97547dfbcca07df"],"state_sha256":"0b181eb095ba2f9c7111d605e9d13f4c57c5ee509387304fa3e2d2e2557de13a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vRIiu+VbBhfew5+zLq42LGd/A4McfmpA10ltfm1kBrzuQXNNL2PvBQNJnwtP5bYBZtuK8SPYejq03B1m7zNYBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T13:45:43.528338Z","bundle_sha256":"dd2bed99aca0f1a5b5317828a8b9c383d3845b1a13ebedd0fdaa3ba6aebbac35"}}