{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J3BLIA7IAY2A5QQZG2UQ4TXCNO","short_pith_number":"pith:J3BLIA7I","canonical_record":{"source":{"id":"1107.4685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-23T12:26:38Z","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"title_canon_sha256":"32a37d5a2d68c4c6d72a2f828de8a76b84eb734fe3b8d0974868e4c45d8a74cf","abstract_canon_sha256":"04ceef107c43b0ea12165e3bdacf9e92c82c2e0ce107674a1866e94923a0b46d"},"schema_version":"1.0"},"canonical_sha256":"4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b","source":{"kind":"arxiv","id":"1107.4685","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4685","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4685v1","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4685","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"pith_short_12","alias_value":"J3BLIA7IAY2A","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J3BLIA7IAY2A5QQZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J3BLIA7I","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J3BLIA7IAY2A5QQZG2UQ4TXCNO","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-23T12:26:38Z","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"title_canon_sha256":"32a37d5a2d68c4c6d72a2f828de8a76b84eb734fe3b8d0974868e4c45d8a74cf","abstract_canon_sha256":"04ceef107c43b0ea12165e3bdacf9e92c82c2e0ce107674a1866e94923a0b46d"},"schema_version":"1.0"},"canonical_sha256":"4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:00.649638Z","signature_b64":"sVF2/WqaP5PUjpHlQ35Ka5FoWskznFR5Q8Q/W4+M622zgxsOsQJFvlZ6kGoNrtRvRtJVP8NR7/yi0mCSJ4LfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b","last_reissued_at":"2026-05-18T01:15:00.649174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:00.649174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4685","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":"2026-05-18T01:15:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLIFkx3wXb59yNEOVm5PPaxKyPSwHERefkg9nijSds8xUnIJl9W2WnGs1x72qzFLt4q6qnUXhDA4lbT6eEdrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:54:52.137800Z"},"content_sha256":"d067d400e03194d0b8d317d763c778b59a8f35603e7adfbd27287473d850ee92","schema_version":"1.0","event_id":"sha256:d067d400e03194d0b8d317d763c778b59a8f35603e7adfbd27287473d850ee92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J3BLIA7IAY2A5QQZG2UQ4TXCNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schrodinger's Hat: Electromagnetic, acoustic and quantum amplifiers via transformation optics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","physics.optics"],"primary_cat":"math-ph","authors_text":"Allan Greenleaf, Gunther Uhlmann, Matti Lassas, Yaroslav Kurylev","submitted_at":"2011-07-23T12:26:38Z","abstract_excerpt":"The advent of transformation optics and metamaterials has made possible devices producing extreme effects on wave propagation. Here we give theoretical designs for devices, Schr\\\"odinger hats, acting as invisible concentrators of waves. These exist for any wave phenomenon modeled by either the Helmholtz or Schr\\\"odinger equations, e.g., polarized waves in EM, pressure waves in acoustics and matter waves in QM, and occupy one part of a parameter space continuum of wave-manipulating structures which also contains standard transformation optics based cloaks, resonant cloaks and cloaked sensors. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4685","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":"2026-05-18T01:15:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1b60uo68Gw7QvWT8MK2ZIMLe+KLHduyqap0R9f2VlspEg33vz3YkoIAhSUCNVNzeYk3/VCRWGmxwdoLplad0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:54:52.138397Z"},"content_sha256":"70d63f2fd1cfba43ca7477f434d89be552e916ce1499ad41cddb5fb3e8ad4a0f","schema_version":"1.0","event_id":"sha256:70d63f2fd1cfba43ca7477f434d89be552e916ce1499ad41cddb5fb3e8ad4a0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO/bundle.json","state_url":"https://pith.science/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO/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":"2026-06-05T17:54:52Z","links":{"resolver":"https://pith.science/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO","bundle":"https://pith.science/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO/bundle.json","state":"https://pith.science/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3BLIA7IAY2A5QQZG2UQ4TXCNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J3BLIA7IAY2A5QQZG2UQ4TXCNO","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":"04ceef107c43b0ea12165e3bdacf9e92c82c2e0ce107674a1866e94923a0b46d","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-23T12:26:38Z","title_canon_sha256":"32a37d5a2d68c4c6d72a2f828de8a76b84eb734fe3b8d0974868e4c45d8a74cf"},"schema_version":"1.0","source":{"id":"1107.4685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4685","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4685v1","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4685","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"pith_short_12","alias_value":"J3BLIA7IAY2A","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J3BLIA7IAY2A5QQZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J3BLIA7I","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:70d63f2fd1cfba43ca7477f434d89be552e916ce1499ad41cddb5fb3e8ad4a0f","target":"graph","created_at":"2026-05-18T01:15:00Z","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 advent of transformation optics and metamaterials has made possible devices producing extreme effects on wave propagation. Here we give theoretical designs for devices, Schr\\\"odinger hats, acting as invisible concentrators of waves. These exist for any wave phenomenon modeled by either the Helmholtz or Schr\\\"odinger equations, e.g., polarized waves in EM, pressure waves in acoustics and matter waves in QM, and occupy one part of a parameter space continuum of wave-manipulating structures which also contains standard transformation optics based cloaks, resonant cloaks and cloaked sensors. F","authors_text":"Allan Greenleaf, Gunther Uhlmann, Matti Lassas, Yaroslav Kurylev","cross_cats":["math.AP","math.MP","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-23T12:26:38Z","title":"Schrodinger's Hat: Electromagnetic, acoustic and quantum amplifiers via transformation optics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4685","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:d067d400e03194d0b8d317d763c778b59a8f35603e7adfbd27287473d850ee92","target":"record","created_at":"2026-05-18T01:15:00Z","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":"04ceef107c43b0ea12165e3bdacf9e92c82c2e0ce107674a1866e94923a0b46d","cross_cats_sorted":["math.AP","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-23T12:26:38Z","title_canon_sha256":"32a37d5a2d68c4c6d72a2f828de8a76b84eb734fe3b8d0974868e4c45d8a74cf"},"schema_version":"1.0","source":{"id":"1107.4685","kind":"arxiv","version":1}},"canonical_sha256":"4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b","first_computed_at":"2026-05-18T01:15:00.649174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:00.649174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sVF2/WqaP5PUjpHlQ35Ka5FoWskznFR5Q8Q/W4+M622zgxsOsQJFvlZ6kGoNrtRvRtJVP8NR7/yi0mCSJ4LfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:00.649638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d067d400e03194d0b8d317d763c778b59a8f35603e7adfbd27287473d850ee92","sha256:70d63f2fd1cfba43ca7477f434d89be552e916ce1499ad41cddb5fb3e8ad4a0f"],"state_sha256":"0dc6e4d84267e8854e9de39838f33530a69ea03081ab50714f89957325196ab2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zN3eGHjnDdBO88WLYQTKw794DDJ+64QTnzuGP8P0gUWd7bj1ewiDcO6MEvVhmlbs/qCWEG6sBQsZa7QKt5jzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T17:54:52.141610Z","bundle_sha256":"d038aa0b066a323ddb0b6e8fead76c20a435f7b2f2787ebdc716b57f6a9c2b16"}}