{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4WSZRPFOT5D52W7CYRAQNREIHE","short_pith_number":"pith:4WSZRPFO","canonical_record":{"source":{"id":"1207.1604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-06T12:30:42Z","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"title_canon_sha256":"22fcae864379cf952271e34e7b586960dfc90069e9afe2d4e2c0786b73114638","abstract_canon_sha256":"8cf19333d4652ed336233380a851fd0ed29fe389016038e043f15e8f47a10174"},"schema_version":"1.0"},"canonical_sha256":"e5a598bcae9f47dd5be2c44106c4883930937958e056e3b003cb625a5eae21d0","source":{"kind":"arxiv","id":"1207.1604","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1604","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1604v2","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1604","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"4WSZRPFOT5D5","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4WSZRPFOT5D52W7C","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4WSZRPFO","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4WSZRPFOT5D52W7CYRAQNREIHE","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-06T12:30:42Z","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"title_canon_sha256":"22fcae864379cf952271e34e7b586960dfc90069e9afe2d4e2c0786b73114638","abstract_canon_sha256":"8cf19333d4652ed336233380a851fd0ed29fe389016038e043f15e8f47a10174"},"schema_version":"1.0"},"canonical_sha256":"e5a598bcae9f47dd5be2c44106c4883930937958e056e3b003cb625a5eae21d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.428727Z","signature_b64":"Yr2ZJIqO6t3g7Znq8/FrtvunBRNge7MB6Efl3dsoxNn/jphd/r9cgaSheOUCMGFOOutQtP8gQYro+hmtI0PeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a598bcae9f47dd5be2c44106c4883930937958e056e3b003cb625a5eae21d0","last_reissued_at":"2026-05-18T03:20:45.427978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.427978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1604","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auzw/Dl7kP3hf8pboFqj0oJqxch/qtlC0CFChxHW8BOMOZ0y6b4t8jXZK/d6tztMDGiI0uftOeIoB70IZLShCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:35:37.730838Z"},"content_sha256":"d3b25ebc7243781ca8f5152f1cacff9674e1c49e3b59beea6c036a610a883cd0","schema_version":"1.0","event_id":"sha256:d3b25ebc7243781ca8f5152f1cacff9674e1c49e3b59beea6c036a610a883cd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4WSZRPFOT5D52W7CYRAQNREIHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radiative transfer and diffusion limits for wave field correlations in locally shifted random media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","physics.optics"],"primary_cat":"math-ph","authors_text":"Emmanuel Bossy, Habib Ammari, Josselin Garnier, Laurent Seppecher, Wenjia Jing","submitted_at":"2012-07-06T12:30:42Z","abstract_excerpt":"The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1604","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGn/bQF2ghRhrCW/2izDY1kRv1Ae7nJxaB/wGzmInsMH9zmbXSoSc8W4B6Q1wpr+vTxJ2YR6thLyaP7BLgCOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:35:37.731188Z"},"content_sha256":"763d7d4c349a21201ceeb89cb61addba8066e59804d20e197322f62094b5155b","schema_version":"1.0","event_id":"sha256:763d7d4c349a21201ceeb89cb61addba8066e59804d20e197322f62094b5155b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WSZRPFOT5D52W7CYRAQNREIHE/bundle.json","state_url":"https://pith.science/pith/4WSZRPFOT5D52W7CYRAQNREIHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WSZRPFOT5D52W7CYRAQNREIHE/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":"2026-06-03T00:35:37Z","links":{"resolver":"https://pith.science/pith/4WSZRPFOT5D52W7CYRAQNREIHE","bundle":"https://pith.science/pith/4WSZRPFOT5D52W7CYRAQNREIHE/bundle.json","state":"https://pith.science/pith/4WSZRPFOT5D52W7CYRAQNREIHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WSZRPFOT5D52W7CYRAQNREIHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4WSZRPFOT5D52W7CYRAQNREIHE","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":"8cf19333d4652ed336233380a851fd0ed29fe389016038e043f15e8f47a10174","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-06T12:30:42Z","title_canon_sha256":"22fcae864379cf952271e34e7b586960dfc90069e9afe2d4e2c0786b73114638"},"schema_version":"1.0","source":{"id":"1207.1604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1604","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1604v2","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1604","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"4WSZRPFOT5D5","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4WSZRPFOT5D52W7C","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4WSZRPFO","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:763d7d4c349a21201ceeb89cb61addba8066e59804d20e197322f62094b5155b","target":"graph","created_at":"2026-05-18T03:20:45Z","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":"The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate th","authors_text":"Emmanuel Bossy, Habib Ammari, Josselin Garnier, Laurent Seppecher, Wenjia Jing","cross_cats":["math.AP","math.MP","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-06T12:30:42Z","title":"Radiative transfer and diffusion limits for wave field correlations in locally shifted random media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1604","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:d3b25ebc7243781ca8f5152f1cacff9674e1c49e3b59beea6c036a610a883cd0","target":"record","created_at":"2026-05-18T03:20:45Z","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":"8cf19333d4652ed336233380a851fd0ed29fe389016038e043f15e8f47a10174","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-06T12:30:42Z","title_canon_sha256":"22fcae864379cf952271e34e7b586960dfc90069e9afe2d4e2c0786b73114638"},"schema_version":"1.0","source":{"id":"1207.1604","kind":"arxiv","version":2}},"canonical_sha256":"e5a598bcae9f47dd5be2c44106c4883930937958e056e3b003cb625a5eae21d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5a598bcae9f47dd5be2c44106c4883930937958e056e3b003cb625a5eae21d0","first_computed_at":"2026-05-18T03:20:45.427978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:45.427978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yr2ZJIqO6t3g7Znq8/FrtvunBRNge7MB6Efl3dsoxNn/jphd/r9cgaSheOUCMGFOOutQtP8gQYro+hmtI0PeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:45.428727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3b25ebc7243781ca8f5152f1cacff9674e1c49e3b59beea6c036a610a883cd0","sha256:763d7d4c349a21201ceeb89cb61addba8066e59804d20e197322f62094b5155b"],"state_sha256":"d3100b09c0cd08a6e511b0dae7849079088f6e8b41fe9a79051b25d621c4ddd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OEE1n4NYhQAnoHNRfYqKrSYRQmYMeGMX4kgB/Z77Q4bYCThEk+HL/f25nw9PTp3FZAxvHnd0oYrOlQdjBt3KBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:35:37.733117Z","bundle_sha256":"fc0506334b165cc8dfc3dfdce66430b143878ea1781114553d16d73dadcf3acb"}}