{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DNC4CDCAKBU5ZME65ZR72LVUVF","short_pith_number":"pith:DNC4CDCA","canonical_record":{"source":{"id":"1509.03441","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T09:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"08c5f4ef999767168f4144815154aa0c0fdef7d70fbeef66b74cdb71e9b6daf8","abstract_canon_sha256":"dc55f021681bf974dce1493a8ac46e85348095245dbf04fd6c4175cd44bd6c67"},"schema_version":"1.0"},"canonical_sha256":"1b45c10c405069dcb09eee63fd2eb4a97059d46facc96353e4e4b9c02bca34f5","source":{"kind":"arxiv","id":"1509.03441","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03441","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03441v2","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03441","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"pith_short_12","alias_value":"DNC4CDCAKBU5","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNC4CDCAKBU5ZME6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNC4CDCA","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DNC4CDCAKBU5ZME65ZR72LVUVF","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03441","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T09:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"08c5f4ef999767168f4144815154aa0c0fdef7d70fbeef66b74cdb71e9b6daf8","abstract_canon_sha256":"dc55f021681bf974dce1493a8ac46e85348095245dbf04fd6c4175cd44bd6c67"},"schema_version":"1.0"},"canonical_sha256":"1b45c10c405069dcb09eee63fd2eb4a97059d46facc96353e4e4b9c02bca34f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:18.298821Z","signature_b64":"ZLy4oIToa76bevjR60j2ShlTMgT2FvpifDBHC2Ybwzw/3b+u3BarclVXwYZgsl+lG7Ur1248pTLRFBN9xQTWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b45c10c405069dcb09eee63fd2eb4a97059d46facc96353e4e4b9c02bca34f5","last_reissued_at":"2026-05-18T01:24:18.298193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:18.298193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03441","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":"2026-05-18T01:24:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"thjF6MXbbYWb/vqUOuCbMsDZg2aeWFQx6CnVbM03yeRZ7ENIk9hWvGFp9Eg185DP80SEi4+qXbYjY3Pfu0zeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:13:34.405076Z"},"content_sha256":"c14d6327f087b2bb66e17514157eef98e6ca9e8b7615a2a7b5703191a353885a","schema_version":"1.0","event_id":"sha256:c14d6327f087b2bb66e17514157eef98e6ca9e8b7615a2a7b5703191a353885a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DNC4CDCAKBU5ZME65ZR72LVUVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant quantities of a Mueller matrix under rotation and retarder transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Jose J. Gil","submitted_at":"2015-09-11T09:53:11Z","abstract_excerpt":"Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic waves. The polarimetric quantities that are invariant under rotations of the said reference frames about the respective directions of propagation (rotation transformations) provide particularly interesting physical information. Moreover, certain properties are also invariant with respect to the action of birefringent devices located at both sides of the medium under consideration (retarder transformations). The polarime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03441","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":"2026-05-18T01:24:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWh1A4SL6ZGs8O8mxg4CyS4a5TtcJn44r3nfWLVoAmjH5XTxbvPSX8V7Jr8JER+csYNBZiY6a8J0N77KR1zhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:13:34.405629Z"},"content_sha256":"85c9382f17e32b23da85925049fdff08f67a642e5f280ef033150e8176e95b16","schema_version":"1.0","event_id":"sha256:85c9382f17e32b23da85925049fdff08f67a642e5f280ef033150e8176e95b16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNC4CDCAKBU5ZME65ZR72LVUVF/bundle.json","state_url":"https://pith.science/pith/DNC4CDCAKBU5ZME65ZR72LVUVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNC4CDCAKBU5ZME65ZR72LVUVF/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":"2026-08-19T22:13:34Z","links":{"resolver":"https://pith.science/pith/DNC4CDCAKBU5ZME65ZR72LVUVF","bundle":"https://pith.science/pith/DNC4CDCAKBU5ZME65ZR72LVUVF/bundle.json","state":"https://pith.science/pith/DNC4CDCAKBU5ZME65ZR72LVUVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNC4CDCAKBU5ZME65ZR72LVUVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DNC4CDCAKBU5ZME65ZR72LVUVF","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":"dc55f021681bf974dce1493a8ac46e85348095245dbf04fd6c4175cd44bd6c67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T09:53:11Z","title_canon_sha256":"08c5f4ef999767168f4144815154aa0c0fdef7d70fbeef66b74cdb71e9b6daf8"},"schema_version":"1.0","source":{"id":"1509.03441","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03441","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03441v2","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03441","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"pith_short_12","alias_value":"DNC4CDCAKBU5","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNC4CDCAKBU5ZME6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNC4CDCA","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:85c9382f17e32b23da85925049fdff08f67a642e5f280ef033150e8176e95b16","target":"graph","created_at":"2026-05-18T01:24:18Z","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":"Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic waves. The polarimetric quantities that are invariant under rotations of the said reference frames about the respective directions of propagation (rotation transformations) provide particularly interesting physical information. Moreover, certain properties are also invariant with respect to the action of birefringent devices located at both sides of the medium under consideration (retarder transformations). The polarime","authors_text":"Jose J. Gil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T09:53:11Z","title":"Invariant quantities of a Mueller matrix under rotation and retarder transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03441","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:c14d6327f087b2bb66e17514157eef98e6ca9e8b7615a2a7b5703191a353885a","target":"record","created_at":"2026-05-18T01:24:18Z","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":"dc55f021681bf974dce1493a8ac46e85348095245dbf04fd6c4175cd44bd6c67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T09:53:11Z","title_canon_sha256":"08c5f4ef999767168f4144815154aa0c0fdef7d70fbeef66b74cdb71e9b6daf8"},"schema_version":"1.0","source":{"id":"1509.03441","kind":"arxiv","version":2}},"canonical_sha256":"1b45c10c405069dcb09eee63fd2eb4a97059d46facc96353e4e4b9c02bca34f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b45c10c405069dcb09eee63fd2eb4a97059d46facc96353e4e4b9c02bca34f5","first_computed_at":"2026-05-18T01:24:18.298193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:18.298193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZLy4oIToa76bevjR60j2ShlTMgT2FvpifDBHC2Ybwzw/3b+u3BarclVXwYZgsl+lG7Ur1248pTLRFBN9xQTWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:18.298821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03441","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c14d6327f087b2bb66e17514157eef98e6ca9e8b7615a2a7b5703191a353885a","sha256:85c9382f17e32b23da85925049fdff08f67a642e5f280ef033150e8176e95b16"],"state_sha256":"3408d7f8a0982cb91640e465b4813072c405d97d73059f849e2cf1fd83ce5532"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zz2xJnMsXEZhGHZUqylpfXdInPTJTsPx1+fOG9za8Tp8pnXA0nsEO1wyX5Bhk3z0oleNy2hKvopfmIlz4gZfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:13:34.409692Z","bundle_sha256":"692c41e4379e68b46a1a8d557ba013aaca2665e4003c109c9ff83bb913be4ac7"}}