{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3RMO2VVJI4NH3IZO7QBVGAXWCO","short_pith_number":"pith:3RMO2VVJ","canonical_record":{"source":{"id":"1410.3729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-14T15:26:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3f4b7534e98a7f37a4b810083a5d2346a871d1d1a15efaaf6e8f6b1e1ebf22b0","abstract_canon_sha256":"7001edae5d343879b43b99a33eb1a6f3d0aa05502524eb0ee07fb3ada9f798e0"},"schema_version":"1.0"},"canonical_sha256":"dc58ed56a9471a7da32efc035302f6139bbb71ed0a473d9918115e8ba1324ea5","source":{"kind":"arxiv","id":"1410.3729","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3729","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3729v1","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3729","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"pith_short_12","alias_value":"3RMO2VVJI4NH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3RMO2VVJI4NH3IZO","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3RMO2VVJ","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3RMO2VVJI4NH3IZO7QBVGAXWCO","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-14T15:26:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3f4b7534e98a7f37a4b810083a5d2346a871d1d1a15efaaf6e8f6b1e1ebf22b0","abstract_canon_sha256":"7001edae5d343879b43b99a33eb1a6f3d0aa05502524eb0ee07fb3ada9f798e0"},"schema_version":"1.0"},"canonical_sha256":"dc58ed56a9471a7da32efc035302f6139bbb71ed0a473d9918115e8ba1324ea5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:43.244035Z","signature_b64":"Qiuw3bVw0cKWmOO6yMR6sZvf9DhMDS4IWL3T4nxOjjQ75RjUhWLKbLSLvea/VOjC+KMKXoZs0sM/YP9LYsJLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc58ed56a9471a7da32efc035302f6139bbb71ed0a473d9918115e8ba1324ea5","last_reissued_at":"2026-05-18T01:30:43.243383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:43.243383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3729","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":"2026-05-18T01:30:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZ6Phyg/M9Lb2cVPpZhC5xgrajiqMQZ91nhI5O73VOam/pCgtwPGGC/L3kokKcHOF9g8CAklfedJt7ScoLocDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:52:02.569741Z"},"content_sha256":"50a4aca92df029bdd8231257f23f9a60fbac6b7c6efc6f5e1c762fe10528aaed","schema_version":"1.0","event_id":"sha256:50a4aca92df029bdd8231257f23f9a60fbac6b7c6efc6f5e1c762fe10528aaed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3RMO2VVJI4NH3IZO7QBVGAXWCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogenization approach for the transmission eigenvalue problem for periodic media and application to the inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Fioralba Cakoni, Houssem Haddar, Isaac Harris","submitted_at":"2014-10-14T15:26:20Z","abstract_excerpt":"We consider the interior transmission problem associated with the scattering by an inhomogeneous (possibly anisotropic) highly oscillating periodic media. We show that, under appropriate assumptions, the solution of the interior transmission problem converges to the solution of a homogenized problem as the period goes to zero. Furthermore, we prove that the associated real transmission eigenvalues converge to transmission eigenvalues of the homogenized problem. Finally we show how to use the first transmission eigenvalue of the period media, which is measurable from the scattering data, to obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3729","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":"2026-05-18T01:30:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYw2vAvAwxknW1qNYDCUMb6Q6Y0cZumNMBjxeCUe75NsEkkBsRC/JKR6JRXEBuigwu16ViYdPCe5wjQJ3+eWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:52:02.570409Z"},"content_sha256":"16bfc07ed77a55b3049196cc475f734d37c02a11894130218c6a7a42826e0b8f","schema_version":"1.0","event_id":"sha256:16bfc07ed77a55b3049196cc475f734d37c02a11894130218c6a7a42826e0b8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO/bundle.json","state_url":"https://pith.science/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO/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":"2026-06-07T08:52:02Z","links":{"resolver":"https://pith.science/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO","bundle":"https://pith.science/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO/bundle.json","state":"https://pith.science/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RMO2VVJI4NH3IZO7QBVGAXWCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3RMO2VVJI4NH3IZO7QBVGAXWCO","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":"7001edae5d343879b43b99a33eb1a6f3d0aa05502524eb0ee07fb3ada9f798e0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-14T15:26:20Z","title_canon_sha256":"3f4b7534e98a7f37a4b810083a5d2346a871d1d1a15efaaf6e8f6b1e1ebf22b0"},"schema_version":"1.0","source":{"id":"1410.3729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3729","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3729v1","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3729","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"pith_short_12","alias_value":"3RMO2VVJI4NH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3RMO2VVJI4NH3IZO","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3RMO2VVJ","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:16bfc07ed77a55b3049196cc475f734d37c02a11894130218c6a7a42826e0b8f","target":"graph","created_at":"2026-05-18T01:30:43Z","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 consider the interior transmission problem associated with the scattering by an inhomogeneous (possibly anisotropic) highly oscillating periodic media. We show that, under appropriate assumptions, the solution of the interior transmission problem converges to the solution of a homogenized problem as the period goes to zero. Furthermore, we prove that the associated real transmission eigenvalues converge to transmission eigenvalues of the homogenized problem. Finally we show how to use the first transmission eigenvalue of the period media, which is measurable from the scattering data, to obt","authors_text":"Fioralba Cakoni, Houssem Haddar, Isaac Harris","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-14T15:26:20Z","title":"Homogenization approach for the transmission eigenvalue problem for periodic media and application to the inverse problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3729","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":"sha256:50a4aca92df029bdd8231257f23f9a60fbac6b7c6efc6f5e1c762fe10528aaed","target":"record","created_at":"2026-05-18T01:30:43Z","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":"7001edae5d343879b43b99a33eb1a6f3d0aa05502524eb0ee07fb3ada9f798e0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-14T15:26:20Z","title_canon_sha256":"3f4b7534e98a7f37a4b810083a5d2346a871d1d1a15efaaf6e8f6b1e1ebf22b0"},"schema_version":"1.0","source":{"id":"1410.3729","kind":"arxiv","version":1}},"canonical_sha256":"dc58ed56a9471a7da32efc035302f6139bbb71ed0a473d9918115e8ba1324ea5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc58ed56a9471a7da32efc035302f6139bbb71ed0a473d9918115e8ba1324ea5","first_computed_at":"2026-05-18T01:30:43.243383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:43.243383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qiuw3bVw0cKWmOO6yMR6sZvf9DhMDS4IWL3T4nxOjjQ75RjUhWLKbLSLvea/VOjC+KMKXoZs0sM/YP9LYsJLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:43.244035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50a4aca92df029bdd8231257f23f9a60fbac6b7c6efc6f5e1c762fe10528aaed","sha256:16bfc07ed77a55b3049196cc475f734d37c02a11894130218c6a7a42826e0b8f"],"state_sha256":"de1107da91842d7d6526083fb6a3e0ee123eec6c0def902d9e317a9e0cfe42e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3V50sgrQ2mHjkdFgDlN4b16EsvdwFd+6QbH53e6ASTVpJihH1l9qaDQUxWmTpJR6CQAJLMfUqVXD5IOJghDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:52:02.573969Z","bundle_sha256":"10d1c76fd705ef30b75246b70766dfa214c99677f9cd22d431599ee671bac8b6"}}