{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LHCCO5QDMKVVTSSJH67VSZEXEA","short_pith_number":"pith:LHCCO5QD","canonical_record":{"source":{"id":"1109.0126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T08:46:28Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"9baa6e4e767c8b1ac13cbe1807b978999b9878720028a78e5c4e4edbae1dc758","abstract_canon_sha256":"ec7655a6c78254933969e48e056c510365840601c89385854a7fed35604eba94"},"schema_version":"1.0"},"canonical_sha256":"59c427760362ab59ca493fbf59649720376969de8fab21a61b31c4921dc4620b","source":{"kind":"arxiv","id":"1109.0126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0126","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0126v1","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0126","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"LHCCO5QDMKVV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LHCCO5QDMKVVTSSJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LHCCO5QD","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LHCCO5QDMKVVTSSJH67VSZEXEA","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T08:46:28Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"9baa6e4e767c8b1ac13cbe1807b978999b9878720028a78e5c4e4edbae1dc758","abstract_canon_sha256":"ec7655a6c78254933969e48e056c510365840601c89385854a7fed35604eba94"},"schema_version":"1.0"},"canonical_sha256":"59c427760362ab59ca493fbf59649720376969de8fab21a61b31c4921dc4620b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:17.342595Z","signature_b64":"PtVc42OukacRdTD0+DnlJl7ra5AUNgE0+9ajndnpnOrGBgnmZ/aWfRajLI4VO7ijT/nluN03b0c5JU2PG5CPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59c427760362ab59ca493fbf59649720376969de8fab21a61b31c4921dc4620b","last_reissued_at":"2026-05-18T04:14:17.341842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:17.341842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0126","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":"2026-05-18T04:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlxaUkL2W17J7ukoEeXTG76+ANoozJKXyuu2Zhi9Rd9g11ajAYu2jQ3kL4eQxtue40kMFav3GJWbc/8wXXeIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:54:28.026781Z"},"content_sha256":"1e98f0afab84ffd926d3869861223ba5547d9073ad2e95f321846e7b7e6bcd94","schema_version":"1.0","event_id":"sha256:1e98f0afab84ffd926d3869861223ba5547d9073ad2e95f321846e7b7e6bcd94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LHCCO5QDMKVVTSSJH67VSZEXEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"E.M. Ovsiyuk, V.M. Red'kov","submitted_at":"2011-09-01T08:46:28Z","abstract_excerpt":"Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space models within the tetrad formalism, have been found in Lobachevsky space. The problem reduces to a second order differential equation which can be associated with an 1-dimensional Schrodinger problem for a particle in external potential field U(z) = U_{0} e^{2z}. In quantum mechanics, curved geometry acts as an effective potential barrier with reflection coeffic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0126","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":"2026-05-18T04:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3j+OD9zBpS79Lgq43fTdjvgKcKNWG5kFB29L1//4MhGvWfhLjEIE8T28CRJtnFIWuz6B+5zW/WUhwu5BH5fhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:54:28.027120Z"},"content_sha256":"1e18f240d9c12b2b80781fcac84a3871bbbaf45cb2422d52718fb0fb4f25eeaf","schema_version":"1.0","event_id":"sha256:1e18f240d9c12b2b80781fcac84a3871bbbaf45cb2422d52718fb0fb4f25eeaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHCCO5QDMKVVTSSJH67VSZEXEA/bundle.json","state_url":"https://pith.science/pith/LHCCO5QDMKVVTSSJH67VSZEXEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHCCO5QDMKVVTSSJH67VSZEXEA/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":"2026-06-02T03:54:28Z","links":{"resolver":"https://pith.science/pith/LHCCO5QDMKVVTSSJH67VSZEXEA","bundle":"https://pith.science/pith/LHCCO5QDMKVVTSSJH67VSZEXEA/bundle.json","state":"https://pith.science/pith/LHCCO5QDMKVVTSSJH67VSZEXEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHCCO5QDMKVVTSSJH67VSZEXEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LHCCO5QDMKVVTSSJH67VSZEXEA","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":"ec7655a6c78254933969e48e056c510365840601c89385854a7fed35604eba94","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T08:46:28Z","title_canon_sha256":"9baa6e4e767c8b1ac13cbe1807b978999b9878720028a78e5c4e4edbae1dc758"},"schema_version":"1.0","source":{"id":"1109.0126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0126","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0126v1","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0126","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"LHCCO5QDMKVV","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LHCCO5QDMKVVTSSJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LHCCO5QD","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:1e18f240d9c12b2b80781fcac84a3871bbbaf45cb2422d52718fb0fb4f25eeaf","target":"graph","created_at":"2026-05-18T04:14:17Z","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":"Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space models within the tetrad formalism, have been found in Lobachevsky space. The problem reduces to a second order differential equation which can be associated with an 1-dimensional Schrodinger problem for a particle in external potential field U(z) = U_{0} e^{2z}. In quantum mechanics, curved geometry acts as an effective potential barrier with reflection coeffic","authors_text":"E.M. Ovsiyuk, V.M. Red'kov","cross_cats":["math.MP","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T08:46:28Z","title":"On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0126","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":"sha256:1e98f0afab84ffd926d3869861223ba5547d9073ad2e95f321846e7b7e6bcd94","target":"record","created_at":"2026-05-18T04:14:17Z","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":"ec7655a6c78254933969e48e056c510365840601c89385854a7fed35604eba94","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T08:46:28Z","title_canon_sha256":"9baa6e4e767c8b1ac13cbe1807b978999b9878720028a78e5c4e4edbae1dc758"},"schema_version":"1.0","source":{"id":"1109.0126","kind":"arxiv","version":1}},"canonical_sha256":"59c427760362ab59ca493fbf59649720376969de8fab21a61b31c4921dc4620b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59c427760362ab59ca493fbf59649720376969de8fab21a61b31c4921dc4620b","first_computed_at":"2026-05-18T04:14:17.341842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:17.341842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PtVc42OukacRdTD0+DnlJl7ra5AUNgE0+9ajndnpnOrGBgnmZ/aWfRajLI4VO7ijT/nluN03b0c5JU2PG5CPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:17.342595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e98f0afab84ffd926d3869861223ba5547d9073ad2e95f321846e7b7e6bcd94","sha256:1e18f240d9c12b2b80781fcac84a3871bbbaf45cb2422d52718fb0fb4f25eeaf"],"state_sha256":"e3d1e8c6b4963a6b0074792412e5e5b7ec3d2d77ff38f007b4f6f76461af9368"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzi0BhRxx/5Tf1/DltX0EFBSFH9MCEX6smSNF5+STKGDQdBAM1jdatp1ilmxoGYw7eF6AKZhoLcLjPDdBgoCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:54:28.028990Z","bundle_sha256":"3733bc8ba6b57c2163f999d2ae82ed748cd5b61e82bc16e93e9bb67c4dde11c9"}}