{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:22X523I74KDLTHVVASSK45N7VG","short_pith_number":"pith:22X523I7","canonical_record":{"source":{"id":"1712.04636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T07:32:24Z","cross_cats_sorted":[],"title_canon_sha256":"5c802bbcad210db07c2c30e97ade9a485f9805b2990cc001ea1c47f02fc562cd","abstract_canon_sha256":"5f08a2322b1d183c0240c72c31b8d5bfb3307791c56410512d8f45cff8057087"},"schema_version":"1.0"},"canonical_sha256":"d6afdd6d1fe286b99eb504a4ae75bfa9be3e856422ccf3dc33b1f1e63ed0eefa","source":{"kind":"arxiv","id":"1712.04636","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04636","created_at":"2026-05-18T00:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04636v2","created_at":"2026-05-18T00:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04636","created_at":"2026-05-18T00:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"22X523I74KDL","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"22X523I74KDLTHVV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"22X523I7","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:22X523I74KDLTHVVASSK45N7VG","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T07:32:24Z","cross_cats_sorted":[],"title_canon_sha256":"5c802bbcad210db07c2c30e97ade9a485f9805b2990cc001ea1c47f02fc562cd","abstract_canon_sha256":"5f08a2322b1d183c0240c72c31b8d5bfb3307791c56410512d8f45cff8057087"},"schema_version":"1.0"},"canonical_sha256":"d6afdd6d1fe286b99eb504a4ae75bfa9be3e856422ccf3dc33b1f1e63ed0eefa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:45.197136Z","signature_b64":"VCukevqk4+I0X9xJrT3jupYj0MdrGW4Rr33oK3V49GvFAnwlJvUe4mSPto3Fln4RwdSIOmGEmzH0Ek1MkTX3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6afdd6d1fe286b99eb504a4ae75bfa9be3e856422ccf3dc33b1f1e63ed0eefa","last_reissued_at":"2026-05-18T00:13:45.196505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:45.196505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04636","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":"2026-05-18T00:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEiXH0gkV/z9UhTzOs92RXQy2sWoU8OqCASoEdx0ESe1ysE2xY4aD49EaQFvBsKZSlXzYfUIZouW/iZmG/eEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:14:44.605456Z"},"content_sha256":"c5c53a5c6ed3c052a92fba559ce8fad53d8990ad2ae4df7aa73f0cd82af92b3b","schema_version":"1.0","event_id":"sha256:c5c53a5c6ed3c052a92fba559ce8fad53d8990ad2ae4df7aa73f0cd82af92b3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:22X523I74KDLTHVVASSK45N7VG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"H\\\"older Stability for an Inverse Medium Problem with Internal Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Faouzi Triki (EDP), Mourad Choulli (EDP)","submitted_at":"2017-12-13T07:32:24Z","abstract_excerpt":"We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of H\\\"older type. For sake of simplicity, we limited our study to the class of Helmholtz equations $\\Delta$+V with bounded potential V."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04636","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":"2026-05-18T00:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xe+44jKNU3W/MNhcaLL1qdfMr8Bz+hku6vapALwWuNRfzZDCvICZXZ3PjX+Cbz4E1mvNwDFZIwUojSeif98Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:14:44.605811Z"},"content_sha256":"3d30cf8e15a176a84a2804de4a518b48296a1ec100d2de067d0a2c8483b77780","schema_version":"1.0","event_id":"sha256:3d30cf8e15a176a84a2804de4a518b48296a1ec100d2de067d0a2c8483b77780"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22X523I74KDLTHVVASSK45N7VG/bundle.json","state_url":"https://pith.science/pith/22X523I74KDLTHVVASSK45N7VG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22X523I74KDLTHVVASSK45N7VG/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":"2026-06-28T12:14:44Z","links":{"resolver":"https://pith.science/pith/22X523I74KDLTHVVASSK45N7VG","bundle":"https://pith.science/pith/22X523I74KDLTHVVASSK45N7VG/bundle.json","state":"https://pith.science/pith/22X523I74KDLTHVVASSK45N7VG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22X523I74KDLTHVVASSK45N7VG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:22X523I74KDLTHVVASSK45N7VG","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":"5f08a2322b1d183c0240c72c31b8d5bfb3307791c56410512d8f45cff8057087","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T07:32:24Z","title_canon_sha256":"5c802bbcad210db07c2c30e97ade9a485f9805b2990cc001ea1c47f02fc562cd"},"schema_version":"1.0","source":{"id":"1712.04636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04636","created_at":"2026-05-18T00:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04636v2","created_at":"2026-05-18T00:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04636","created_at":"2026-05-18T00:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"22X523I74KDL","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"22X523I74KDLTHVV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"22X523I7","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:3d30cf8e15a176a84a2804de4a518b48296a1ec100d2de067d0a2c8483b77780","target":"graph","created_at":"2026-05-18T00:13:45Z","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":"We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of H\\\"older type. For sake of simplicity, we limited our study to the class of Helmholtz equations $\\Delta$+V with bounded potential V.","authors_text":"Faouzi Triki (EDP), Mourad Choulli (EDP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T07:32:24Z","title":"H\\\"older Stability for an Inverse Medium Problem with Internal Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04636","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:c5c53a5c6ed3c052a92fba559ce8fad53d8990ad2ae4df7aa73f0cd82af92b3b","target":"record","created_at":"2026-05-18T00:13:45Z","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":"5f08a2322b1d183c0240c72c31b8d5bfb3307791c56410512d8f45cff8057087","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T07:32:24Z","title_canon_sha256":"5c802bbcad210db07c2c30e97ade9a485f9805b2990cc001ea1c47f02fc562cd"},"schema_version":"1.0","source":{"id":"1712.04636","kind":"arxiv","version":2}},"canonical_sha256":"d6afdd6d1fe286b99eb504a4ae75bfa9be3e856422ccf3dc33b1f1e63ed0eefa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6afdd6d1fe286b99eb504a4ae75bfa9be3e856422ccf3dc33b1f1e63ed0eefa","first_computed_at":"2026-05-18T00:13:45.196505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:45.196505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VCukevqk4+I0X9xJrT3jupYj0MdrGW4Rr33oK3V49GvFAnwlJvUe4mSPto3Fln4RwdSIOmGEmzH0Ek1MkTX3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:45.197136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5c53a5c6ed3c052a92fba559ce8fad53d8990ad2ae4df7aa73f0cd82af92b3b","sha256:3d30cf8e15a176a84a2804de4a518b48296a1ec100d2de067d0a2c8483b77780"],"state_sha256":"f4903e3fce96825c43f152b5bf4daa5072436dd41ce37307aa4bcb08872db855"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVO3+3F272lPWEvaBWdT80JdJrIHrFXtjxtiOjEFe5qJ17H3Qq4n+Gfz7sM89qoQmRa/y3sMgtdKVtNkmabdAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:14:44.607806Z","bundle_sha256":"aa54dc1d694d5c1cf64879558404a82869b5e38ead1069910e6cfaf525b5a973"}}