{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y2SU43P2HUN5KBTNDRLXBYYWGZ","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":"7030aea1a1791672da936d70058b29bb258010dc0fc3d6d7caf87c4100b1465b","cross_cats_sorted":["math-ph","math.MP","physics.app-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2017-05-26T11:27:28Z","title_canon_sha256":"d871da3ccfe1bacdc9d08c1afcc7dbbceaf66118b6c5d8ad1789acc3a84aff9f"},"schema_version":"1.0","source":{"id":"1705.09535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09535","created_at":"2026-05-18T00:32:09Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09535v1","created_at":"2026-05-18T00:32:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09535","created_at":"2026-05-18T00:32:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y2SU43P2HUN5","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y2SU43P2HUN5KBTN","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y2SU43P2","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:5f9242aa4ad4d016d786311337bd9b696f31dd61b5440961f3a0871b78a0a83a","target":"graph","created_at":"2026-05-18T00:32:09Z","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 optical properties of a multilayer system of dielectric media with arbitrary $N$ layers is investigated. Each layer is one of two dielectric media, with thickness one-quarter the wavelength of light in that medium, corresponding to a central frequency. Using the transfer matrix method, the transmittance $T$ is calculated for all possible $2^N$ sequences for small $N$. Unexpectedly, it is found that instead of $2^N$ different values of $T$ at the central frequency ($T_0$), there are either $(N/2+1)$ or $(N+1)$ discrete values of $T_0$ for even or odd $N$, respectively. We explain the high d","authors_text":"Haihao Liu, M. Shoufie Ukhtary, Riichiro Saito","cross_cats":["math-ph","math.MP","physics.app-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2017-05-26T11:27:28Z","title":"Hidden symmetries in $N$-layer dielectric stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09535","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":"sha256:1a6fe5828846e75b226d9f11ec9d70a4358e4d8c4dc0049b3077893c6ca7bd64","target":"record","created_at":"2026-05-18T00:32:09Z","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":"7030aea1a1791672da936d70058b29bb258010dc0fc3d6d7caf87c4100b1465b","cross_cats_sorted":["math-ph","math.MP","physics.app-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2017-05-26T11:27:28Z","title_canon_sha256":"d871da3ccfe1bacdc9d08c1afcc7dbbceaf66118b6c5d8ad1789acc3a84aff9f"},"schema_version":"1.0","source":{"id":"1705.09535","kind":"arxiv","version":1}},"canonical_sha256":"c6a54e6dfa3d1bd5066d1c5770e316366cfc3a1e1ae4b1530164f24debd738f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6a54e6dfa3d1bd5066d1c5770e316366cfc3a1e1ae4b1530164f24debd738f0","first_computed_at":"2026-05-18T00:32:09.971727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:09.971727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fN4HmcGHEFRGF+8chzIcgxbhUqGd+gPvCUFmUc/5/UFk46RTKt5L8HS1+sum+bdrFnZ56cYduVEC039rMwgjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:09.972412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a6fe5828846e75b226d9f11ec9d70a4358e4d8c4dc0049b3077893c6ca7bd64","sha256:5f9242aa4ad4d016d786311337bd9b696f31dd61b5440961f3a0871b78a0a83a"],"state_sha256":"6474b4d4dcc283fbfff63e6a1ed69624117596f9f6923d3b886be313e98321d5"}