{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EPQY3M7AZRLPRNMVB75DCS2FPO","short_pith_number":"pith:EPQY3M7A","schema_version":"1.0","canonical_sha256":"23e18db3e0cc56f8b5950ffa314b457b8d076b7d752903113cd0f734310089a1","source":{"kind":"arxiv","id":"1106.4277","version":2},"attestation_state":"computed","paper":{"title":"Inverse diffusion problems with redundant internal information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francois Monard, Guillaume Bal","submitted_at":"2011-06-21T17:39:00Z","abstract_excerpt":"This paper concerns the reconstruction of a scalar diffusion coefficient $\\sigma(x)$ from redundant functionals of the form $H_i(x)=\\sigma^{2\\alpha}(x)|\\nabla u_i|^2(x)$ where $\\alpha\\in\\Rm$ and $u_i$ is a solution of the elliptic problem $\\nabla\\cdot \\sigma \\nabla u_i=0$ for $1\\leq i\\leq I$. The case $\\alpha=\\frac12$ is used to model measurements obtained from modulating a domain of interest by ultrasound and finds applications in ultrasound modulated electrical impedance tomography (UMEIT) as well as ultrasound modulated optical tomography (UMOT). The case $\\alpha=1$ finds applications in Ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.4277","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-21T17:39:00Z","cross_cats_sorted":[],"title_canon_sha256":"0776a07cc584087d92c69529dd4c90b3a68fe6bbff7b0eba76ff9177d9748b20","abstract_canon_sha256":"beb9c5c57b693e10cdb0622fd7a6edf9a410a3dd929bc7ac848afce487ba0dd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:25.077919Z","signature_b64":"HFooIioGgAlOYlQrX41TtAMskxsjQRaFN9/XKy0yBM7QGkSw6U4qmy72qmlpbPZSf/gUIWJuyJ8UKvg6TCtsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23e18db3e0cc56f8b5950ffa314b457b8d076b7d752903113cd0f734310089a1","last_reissued_at":"2026-05-18T03:57:25.077245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:25.077245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse diffusion problems with redundant internal information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francois Monard, Guillaume Bal","submitted_at":"2011-06-21T17:39:00Z","abstract_excerpt":"This paper concerns the reconstruction of a scalar diffusion coefficient $\\sigma(x)$ from redundant functionals of the form $H_i(x)=\\sigma^{2\\alpha}(x)|\\nabla u_i|^2(x)$ where $\\alpha\\in\\Rm$ and $u_i$ is a solution of the elliptic problem $\\nabla\\cdot \\sigma \\nabla u_i=0$ for $1\\leq i\\leq I$. The case $\\alpha=\\frac12$ is used to model measurements obtained from modulating a domain of interest by ultrasound and finds applications in ultrasound modulated electrical impedance tomography (UMEIT) as well as ultrasound modulated optical tomography (UMOT). The case $\\alpha=1$ finds applications in Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4277","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.4277","created_at":"2026-05-18T03:57:25.077372+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.4277v2","created_at":"2026-05-18T03:57:25.077372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4277","created_at":"2026-05-18T03:57:25.077372+00:00"},{"alias_kind":"pith_short_12","alias_value":"EPQY3M7AZRLP","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EPQY3M7AZRLPRNMV","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EPQY3M7A","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO","json":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO.json","graph_json":"https://pith.science/api/pith-number/EPQY3M7AZRLPRNMVB75DCS2FPO/graph.json","events_json":"https://pith.science/api/pith-number/EPQY3M7AZRLPRNMVB75DCS2FPO/events.json","paper":"https://pith.science/paper/EPQY3M7A"},"agent_actions":{"view_html":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO","download_json":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO.json","view_paper":"https://pith.science/paper/EPQY3M7A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.4277&json=true","fetch_graph":"https://pith.science/api/pith-number/EPQY3M7AZRLPRNMVB75DCS2FPO/graph.json","fetch_events":"https://pith.science/api/pith-number/EPQY3M7AZRLPRNMVB75DCS2FPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO/action/storage_attestation","attest_author":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO/action/author_attestation","sign_citation":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO/action/citation_signature","submit_replication":"https://pith.science/pith/EPQY3M7AZRLPRNMVB75DCS2FPO/action/replication_record"}},"created_at":"2026-05-18T03:57:25.077372+00:00","updated_at":"2026-05-18T03:57:25.077372+00:00"}