{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U2742SWKXYSZAGXWDXZDE5AWVR","short_pith_number":"pith:U2742SWK","canonical_record":{"source":{"id":"1303.4496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-19T06:55:26Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"cd49cc5a0d2f80e0738dd21ef451864d93370520c0733e71d54d92d768f2cf1e","abstract_canon_sha256":"cef6d4343927ae81f90e50cc7a3a6843635e9e48cc9e14879ca7146a8b2ed066"},"schema_version":"1.0"},"canonical_sha256":"a6bfcd4acabe25901af61df2327416ac6bef8355a55603d544f0413c8c0ab6e4","source":{"kind":"arxiv","id":"1303.4496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4496","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4496v1","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4496","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"pith_short_12","alias_value":"U2742SWKXYSZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2742SWKXYSZAGXW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2742SWK","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U2742SWKXYSZAGXWDXZDE5AWVR","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-19T06:55:26Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"cd49cc5a0d2f80e0738dd21ef451864d93370520c0733e71d54d92d768f2cf1e","abstract_canon_sha256":"cef6d4343927ae81f90e50cc7a3a6843635e9e48cc9e14879ca7146a8b2ed066"},"schema_version":"1.0"},"canonical_sha256":"a6bfcd4acabe25901af61df2327416ac6bef8355a55603d544f0413c8c0ab6e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:27.033468Z","signature_b64":"zyxzahnGcwGglpwtYPW5nKg3Lnlfeo9tNt9l5ilmsmF/5yK4yfTRHe0g07baH+IANrR6dAja4K4AvuwV8dqmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6bfcd4acabe25901af61df2327416ac6bef8355a55603d544f0413c8c0ab6e4","last_reissued_at":"2026-05-18T03:30:27.032887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:27.032887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4496","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":"2026-05-18T03:30:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CF9gi0xRZC0yABINqZNup8dLCSThDb5kTLbDVZ+uNdvwxUNL4gvpkoj5Mb8hnXLjsFHyBRfHFq3ylrR/ee/vDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:56:01.165305Z"},"content_sha256":"98e028dc332d6221351fbdfbd1b5d5948f125861fa7fa861b6efe5cf2a17f2ea","schema_version":"1.0","event_id":"sha256:98e028dc332d6221351fbdfbd1b5d5948f125861fa7fa861b6efe5cf2a17f2ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U2742SWKXYSZAGXWDXZDE5AWVR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Jones vector as a spinor and its representation on the Poincar\\'e sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G.F. Torres del Castillo, I. Rubalcava-Garcia","submitted_at":"2013-03-19T06:55:26Z","abstract_excerpt":"It is shown that the two complex Cartesian components of the electric field of a monochromatic electromagnetic plane wave, with a temporal and spatial dependence of the form ${\\rm e}^{{\\rm i} (kz - \\omega t)}$, form a SU(2) spinor that corresponds to a tangent vector to the Poincar\\'e sphere representing the state of polarization and phase of the wave. The geometrical representation on the Poincar\\'e sphere of the effect of some optical filters is reviewed. It is also shown that in the case of a partially polarized beam, the coherency matrix defines two diametrically opposite points of the Poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4496","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":"2026-05-18T03:30:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HslmunGKflY1z27JUNdosrWWXmasZmzvk0BatEgj6OyB7Be0yydakQc0DiEK7lYRvhLRbDLgfulVh8UpmrtQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:56:01.165672Z"},"content_sha256":"835e369727bfcb772eeff14be4db0b156c381d10477b98d43bfb20eb62cad4d0","schema_version":"1.0","event_id":"sha256:835e369727bfcb772eeff14be4db0b156c381d10477b98d43bfb20eb62cad4d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2742SWKXYSZAGXWDXZDE5AWVR/bundle.json","state_url":"https://pith.science/pith/U2742SWKXYSZAGXWDXZDE5AWVR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2742SWKXYSZAGXWDXZDE5AWVR/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":"2026-06-09T14:56:01Z","links":{"resolver":"https://pith.science/pith/U2742SWKXYSZAGXWDXZDE5AWVR","bundle":"https://pith.science/pith/U2742SWKXYSZAGXWDXZDE5AWVR/bundle.json","state":"https://pith.science/pith/U2742SWKXYSZAGXWDXZDE5AWVR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2742SWKXYSZAGXWDXZDE5AWVR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U2742SWKXYSZAGXWDXZDE5AWVR","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":"cef6d4343927ae81f90e50cc7a3a6843635e9e48cc9e14879ca7146a8b2ed066","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-19T06:55:26Z","title_canon_sha256":"cd49cc5a0d2f80e0738dd21ef451864d93370520c0733e71d54d92d768f2cf1e"},"schema_version":"1.0","source":{"id":"1303.4496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4496","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4496v1","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4496","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"pith_short_12","alias_value":"U2742SWKXYSZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2742SWKXYSZAGXW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2742SWK","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:835e369727bfcb772eeff14be4db0b156c381d10477b98d43bfb20eb62cad4d0","target":"graph","created_at":"2026-05-18T03:30:27Z","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":"It is shown that the two complex Cartesian components of the electric field of a monochromatic electromagnetic plane wave, with a temporal and spatial dependence of the form ${\\rm e}^{{\\rm i} (kz - \\omega t)}$, form a SU(2) spinor that corresponds to a tangent vector to the Poincar\\'e sphere representing the state of polarization and phase of the wave. The geometrical representation on the Poincar\\'e sphere of the effect of some optical filters is reviewed. It is also shown that in the case of a partially polarized beam, the coherency matrix defines two diametrically opposite points of the Poi","authors_text":"G.F. Torres del Castillo, I. Rubalcava-Garcia","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-19T06:55:26Z","title":"The Jones vector as a spinor and its representation on the Poincar\\'e sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4496","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":"sha256:98e028dc332d6221351fbdfbd1b5d5948f125861fa7fa861b6efe5cf2a17f2ea","target":"record","created_at":"2026-05-18T03:30:27Z","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":"cef6d4343927ae81f90e50cc7a3a6843635e9e48cc9e14879ca7146a8b2ed066","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-19T06:55:26Z","title_canon_sha256":"cd49cc5a0d2f80e0738dd21ef451864d93370520c0733e71d54d92d768f2cf1e"},"schema_version":"1.0","source":{"id":"1303.4496","kind":"arxiv","version":1}},"canonical_sha256":"a6bfcd4acabe25901af61df2327416ac6bef8355a55603d544f0413c8c0ab6e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6bfcd4acabe25901af61df2327416ac6bef8355a55603d544f0413c8c0ab6e4","first_computed_at":"2026-05-18T03:30:27.032887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:27.032887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zyxzahnGcwGglpwtYPW5nKg3Lnlfeo9tNt9l5ilmsmF/5yK4yfTRHe0g07baH+IANrR6dAja4K4AvuwV8dqmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:27.033468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98e028dc332d6221351fbdfbd1b5d5948f125861fa7fa861b6efe5cf2a17f2ea","sha256:835e369727bfcb772eeff14be4db0b156c381d10477b98d43bfb20eb62cad4d0"],"state_sha256":"8e7591dc057bcf9e926778b0101bc885ec87df2f1ca140630a87c0d66fad48e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+y3jTQjgKNdfBd0yhoqtNUsmk1QmwymX4yKQth174HJg6RiA3pqWAmZLAKxNYiFpQSptZ8X+Fi3/Z5JYZJVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:56:01.167871Z","bundle_sha256":"82a74d0405ebae627c7e08575146fe7822ddc605c66b04ab10397238b9468c03"}}