{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YTQZEGEM6HNOOD677EAY4DJJ4C","short_pith_number":"pith:YTQZEGEM","canonical_record":{"source":{"id":"1102.1512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-08T05:46:34Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"c405b7b4663c797e80976a8cdd67555e3eac86cfe333eaee871aee384e395490","abstract_canon_sha256":"b9ef3e730015a5e085bd37e34003b6ed66607fd4a02f965ebe8eec17ff7da730"},"schema_version":"1.0"},"canonical_sha256":"c4e192188cf1dae70fdff9018e0d29e08b3fd46ded9c16e9da332ab453191996","source":{"kind":"arxiv","id":"1102.1512","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1512","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1512v2","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1512","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"YTQZEGEM6HNO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YTQZEGEM6HNOOD67","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YTQZEGEM","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YTQZEGEM6HNOOD677EAY4DJJ4C","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-08T05:46:34Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"c405b7b4663c797e80976a8cdd67555e3eac86cfe333eaee871aee384e395490","abstract_canon_sha256":"b9ef3e730015a5e085bd37e34003b6ed66607fd4a02f965ebe8eec17ff7da730"},"schema_version":"1.0"},"canonical_sha256":"c4e192188cf1dae70fdff9018e0d29e08b3fd46ded9c16e9da332ab453191996","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:17.109172Z","signature_b64":"euGUxMwRxSKHbPGYMQslqEEcQTOGK4MVmpZbCEvufFVrm7pOthGVSn6Kb1STio0S+WNHXRGwd75CFqVfS+PNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4e192188cf1dae70fdff9018e0d29e08b3fd46ded9c16e9da332ab453191996","last_reissued_at":"2026-05-18T04:04:17.108437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:17.108437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1512","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrEh6NtbHY2kpzEcIYnpikiVbOxwHV5SEFsfG2R0y4tdXqEblTry0Yv51oSUbl000XYUnvu1rmWwkCw+zaNcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:58:55.872259Z"},"content_sha256":"5ef033ae9b989c112b95fb350017c0cc4de5bf1df797cd24ba25f26fe6f2c2e7","schema_version":"1.0","event_id":"sha256:5ef033ae9b989c112b95fb350017c0cc4de5bf1df797cd24ba25f26fe6f2c2e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YTQZEGEM6HNOOD677EAY4DJJ4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General Relativistic Contributions in Transformation Optics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"physics.optics","authors_text":"Robert T. Thompson","submitted_at":"2011-02-08T05:46:34Z","abstract_excerpt":"One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1512","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":"2026-05-18T04:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MOu6fepBJWFK83O7AEq9QSw7iunOfuq40xoZK7jSSgvNfdUWy6qaQu9BjHuXF50f42SV7gosAN2RSiCiCQQ+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:58:55.873048Z"},"content_sha256":"9c4f7f9c533f05696289825da856f9aeb9c519004a711c394e26bdc5f682a127","schema_version":"1.0","event_id":"sha256:9c4f7f9c533f05696289825da856f9aeb9c519004a711c394e26bdc5f682a127"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTQZEGEM6HNOOD677EAY4DJJ4C/bundle.json","state_url":"https://pith.science/pith/YTQZEGEM6HNOOD677EAY4DJJ4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTQZEGEM6HNOOD677EAY4DJJ4C/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":"2026-06-01T04:58:55Z","links":{"resolver":"https://pith.science/pith/YTQZEGEM6HNOOD677EAY4DJJ4C","bundle":"https://pith.science/pith/YTQZEGEM6HNOOD677EAY4DJJ4C/bundle.json","state":"https://pith.science/pith/YTQZEGEM6HNOOD677EAY4DJJ4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTQZEGEM6HNOOD677EAY4DJJ4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YTQZEGEM6HNOOD677EAY4DJJ4C","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":"b9ef3e730015a5e085bd37e34003b6ed66607fd4a02f965ebe8eec17ff7da730","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-08T05:46:34Z","title_canon_sha256":"c405b7b4663c797e80976a8cdd67555e3eac86cfe333eaee871aee384e395490"},"schema_version":"1.0","source":{"id":"1102.1512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1512","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1512v2","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1512","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"YTQZEGEM6HNO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YTQZEGEM6HNOOD67","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YTQZEGEM","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:9c4f7f9c533f05696289825da856f9aeb9c519004a711c394e26bdc5f682a127","target":"graph","created_at":"2026-05-18T04:04:17Z","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":"One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the ","authors_text":"Robert T. Thompson","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-08T05:46:34Z","title":"General Relativistic Contributions in Transformation Optics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1512","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":"sha256:5ef033ae9b989c112b95fb350017c0cc4de5bf1df797cd24ba25f26fe6f2c2e7","target":"record","created_at":"2026-05-18T04:04:17Z","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":"b9ef3e730015a5e085bd37e34003b6ed66607fd4a02f965ebe8eec17ff7da730","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-02-08T05:46:34Z","title_canon_sha256":"c405b7b4663c797e80976a8cdd67555e3eac86cfe333eaee871aee384e395490"},"schema_version":"1.0","source":{"id":"1102.1512","kind":"arxiv","version":2}},"canonical_sha256":"c4e192188cf1dae70fdff9018e0d29e08b3fd46ded9c16e9da332ab453191996","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4e192188cf1dae70fdff9018e0d29e08b3fd46ded9c16e9da332ab453191996","first_computed_at":"2026-05-18T04:04:17.108437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.108437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"euGUxMwRxSKHbPGYMQslqEEcQTOGK4MVmpZbCEvufFVrm7pOthGVSn6Kb1STio0S+WNHXRGwd75CFqVfS+PNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.109172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ef033ae9b989c112b95fb350017c0cc4de5bf1df797cd24ba25f26fe6f2c2e7","sha256:9c4f7f9c533f05696289825da856f9aeb9c519004a711c394e26bdc5f682a127"],"state_sha256":"b0dd24f15a08f2e5efe1501ea8a882c49ea23d6732abe3d0c7db4cb46a876971"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFtd07IXWxLXYDc7CYcoMHhj/6ZpjusNj14Ba3JlV36LNEJV6n5Cx74c2P340U2/18aFk6uyJoTVh6Y/u/81Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:58:55.876946Z","bundle_sha256":"d73f4bf729e42e8811a7f3953fd734b5488f1de5fef42fe0b7e79a2457062c7b"}}