{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ERLI52U4CS6ANHT2VRDBMR6INU","short_pith_number":"pith:ERLI52U4","canonical_record":{"source":{"id":"1306.1978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-09T04:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"234004d5c1e50f151cd181a945b94235ff17632beb04bf879f005f7f75a08f86","abstract_canon_sha256":"e3571421344bd4c67acf2818b11b6583ad797fd3989f2e1107f29e940384b256"},"schema_version":"1.0"},"canonical_sha256":"24568eea9c14bc069e7aac461647c86d05bba994d2cf7b46bcb3ce8935905f4e","source":{"kind":"arxiv","id":"1306.1978","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1978","created_at":"2026-05-18T01:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1978v1","created_at":"2026-05-18T01:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1978","created_at":"2026-05-18T01:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"ERLI52U4CS6A","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ERLI52U4CS6ANHT2","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ERLI52U4","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ERLI52U4CS6ANHT2VRDBMR6INU","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-09T04:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"234004d5c1e50f151cd181a945b94235ff17632beb04bf879f005f7f75a08f86","abstract_canon_sha256":"e3571421344bd4c67acf2818b11b6583ad797fd3989f2e1107f29e940384b256"},"schema_version":"1.0"},"canonical_sha256":"24568eea9c14bc069e7aac461647c86d05bba994d2cf7b46bcb3ce8935905f4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:24.609500Z","signature_b64":"77AUPVHQFupZaVpmjUDemKXgE693V8yEKyVdomCT01WUSkTAX38NufvUS4bgQjztNElFJ6cgM4AfoZYab/fBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24568eea9c14bc069e7aac461647c86d05bba994d2cf7b46bcb3ce8935905f4e","last_reissued_at":"2026-05-18T01:49:24.608794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:24.608794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1978","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":"2026-05-18T01:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UC0qWMbx+FCWyzQs35WXtcgSHY3SSiIR2XzuGP+o7V6170IFJgVRprERM5LoF9mHkF9bWbXW55P506YVylMtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:42:10.221586Z"},"content_sha256":"7288bc01148adf48d689994b85e277720bab8909e22a58bc3337415524a500f9","schema_version":"1.0","event_id":"sha256:7288bc01148adf48d689994b85e277720bab8909e22a58bc3337415524a500f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ERLI52U4CS6ANHT2VRDBMR6INU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Coupled-Physics Inverse Problems with internal measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Montalto, Plamen Stefanov","submitted_at":"2013-06-09T04:18:24Z","abstract_excerpt":"In this paper, we develop a general approach to prove stability for the non linear second step of hybrid inverse problems. We work with general functionals of the form $\\sigma|\\nabla u|^p$, $0 < p \\leq 1$, where $u$ is the solution of the elliptic partial differential equation $\\nabla\\cdot \\sigma \\nabla u =0$ on a bounded domain $\\Omega$ with boundary conditions $u|_{\\partial \\Omega} = f$. We prove stability of the linearization and H\\\"older conditional stability for the non-linear problem of recovering $\\sigma$ from the internal measurement."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1978","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":"2026-05-18T01:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7u/IDmV+ffKGEzVZOxdhomyviVI/AivZcK7+6sFsq0NTLz5bY612dPiznXSpdJB4uyx6s7d4lvYYi/cvtSRhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:42:10.222293Z"},"content_sha256":"c2744ea72825bfcebd7a7a8bfac8cd693a82226ba5dfc54b232afed2445dca73","schema_version":"1.0","event_id":"sha256:c2744ea72825bfcebd7a7a8bfac8cd693a82226ba5dfc54b232afed2445dca73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERLI52U4CS6ANHT2VRDBMR6INU/bundle.json","state_url":"https://pith.science/pith/ERLI52U4CS6ANHT2VRDBMR6INU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERLI52U4CS6ANHT2VRDBMR6INU/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":"2026-06-06T08:42:10Z","links":{"resolver":"https://pith.science/pith/ERLI52U4CS6ANHT2VRDBMR6INU","bundle":"https://pith.science/pith/ERLI52U4CS6ANHT2VRDBMR6INU/bundle.json","state":"https://pith.science/pith/ERLI52U4CS6ANHT2VRDBMR6INU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERLI52U4CS6ANHT2VRDBMR6INU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ERLI52U4CS6ANHT2VRDBMR6INU","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":"e3571421344bd4c67acf2818b11b6583ad797fd3989f2e1107f29e940384b256","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-09T04:18:24Z","title_canon_sha256":"234004d5c1e50f151cd181a945b94235ff17632beb04bf879f005f7f75a08f86"},"schema_version":"1.0","source":{"id":"1306.1978","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1978","created_at":"2026-05-18T01:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1978v1","created_at":"2026-05-18T01:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1978","created_at":"2026-05-18T01:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"ERLI52U4CS6A","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ERLI52U4CS6ANHT2","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ERLI52U4","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:c2744ea72825bfcebd7a7a8bfac8cd693a82226ba5dfc54b232afed2445dca73","target":"graph","created_at":"2026-05-18T01:49:24Z","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 develop a general approach to prove stability for the non linear second step of hybrid inverse problems. We work with general functionals of the form $\\sigma|\\nabla u|^p$, $0 < p \\leq 1$, where $u$ is the solution of the elliptic partial differential equation $\\nabla\\cdot \\sigma \\nabla u =0$ on a bounded domain $\\Omega$ with boundary conditions $u|_{\\partial \\Omega} = f$. We prove stability of the linearization and H\\\"older conditional stability for the non-linear problem of recovering $\\sigma$ from the internal measurement.","authors_text":"Carlos Montalto, Plamen Stefanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-09T04:18:24Z","title":"Stability of Coupled-Physics Inverse Problems with internal measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1978","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":"sha256:7288bc01148adf48d689994b85e277720bab8909e22a58bc3337415524a500f9","target":"record","created_at":"2026-05-18T01:49:24Z","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":"e3571421344bd4c67acf2818b11b6583ad797fd3989f2e1107f29e940384b256","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-09T04:18:24Z","title_canon_sha256":"234004d5c1e50f151cd181a945b94235ff17632beb04bf879f005f7f75a08f86"},"schema_version":"1.0","source":{"id":"1306.1978","kind":"arxiv","version":1}},"canonical_sha256":"24568eea9c14bc069e7aac461647c86d05bba994d2cf7b46bcb3ce8935905f4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24568eea9c14bc069e7aac461647c86d05bba994d2cf7b46bcb3ce8935905f4e","first_computed_at":"2026-05-18T01:49:24.608794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:24.608794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"77AUPVHQFupZaVpmjUDemKXgE693V8yEKyVdomCT01WUSkTAX38NufvUS4bgQjztNElFJ6cgM4AfoZYab/fBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:24.609500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1978","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7288bc01148adf48d689994b85e277720bab8909e22a58bc3337415524a500f9","sha256:c2744ea72825bfcebd7a7a8bfac8cd693a82226ba5dfc54b232afed2445dca73"],"state_sha256":"6e8cfc39b7493e2843031cdce422e08f6466900eefd6c1bffb09702f2964a9ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFD4lT1By6Ol6sff/CHjjnB5X8T+SzS5+JkJwfs14GPzr8NouLkOrFvomt+iCAoRAOCznyZiI93BoksXYKqoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:42:10.226304Z","bundle_sha256":"2616cef888ab8307e63dffdabac45f115d910a3b79caad6a118e9b52a63514d1"}}