{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:U5KJCDDBK32GHW7ZKRURUI5YGU","short_pith_number":"pith:U5KJCDDB","canonical_record":{"source":{"id":"1901.04897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-01-15T16:07:37Z","cross_cats_sorted":["nlin.SI","quant-ph"],"title_canon_sha256":"ed812a245e2f342dc0b8ea5cd1d3d0e915ed7f8e6edb687158c4f0654f0ccda9","abstract_canon_sha256":"968a46bdd6725526eb29c32a387881e8a23625188c97367b629255a074a1eb16"},"schema_version":"1.0"},"canonical_sha256":"a754910c6156f463dbf954691a23b835284242f05e1693844f5f264918a72286","source":{"kind":"arxiv","id":"1901.04897","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04897","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04897v2","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04897","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"pith_short_12","alias_value":"U5KJCDDBK32G","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U5KJCDDBK32GHW7Z","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U5KJCDDB","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:U5KJCDDBK32GHW7ZKRURUI5YGU","target":"record","payload":{"canonical_record":{"source":{"id":"1901.04897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-01-15T16:07:37Z","cross_cats_sorted":["nlin.SI","quant-ph"],"title_canon_sha256":"ed812a245e2f342dc0b8ea5cd1d3d0e915ed7f8e6edb687158c4f0654f0ccda9","abstract_canon_sha256":"968a46bdd6725526eb29c32a387881e8a23625188c97367b629255a074a1eb16"},"schema_version":"1.0"},"canonical_sha256":"a754910c6156f463dbf954691a23b835284242f05e1693844f5f264918a72286","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:58.471726Z","signature_b64":"l41OTwfDXhBidpWxtvmz6aaVVnhRkV4jOZFc64N8GHUPqlGsSHOV33VH3YAbU34bh/zC+AaSF3xj7aKgjOWkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a754910c6156f463dbf954691a23b835284242f05e1693844f5f264918a72286","last_reissued_at":"2026-05-17T23:47:58.471215Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:58.471215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.04897","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":"2026-05-17T23:47:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7i3waJDtxQDAr8FAQ6Db1Qr29NsZhMVcuDGCOVmHBUyT80E91rtlmFWudAsvO9XlTDAytpec9RwLKj+MmxNCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:03:04.394233Z"},"content_sha256":"49eb9b1d9c964ba18353941e92844ec5932b1ee9edfc2f4699c03cd5fe770a44","schema_version":"1.0","event_id":"sha256:49eb9b1d9c964ba18353941e92844ec5932b1ee9edfc2f4699c03cd5fe770a44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:U5KJCDDBK32GHW7ZKRURUI5YGU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry-based analytical solutions to the \\chi^{(2)} nonlinear directional coupler","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI","quant-ph"],"primary_cat":"physics.optics","authors_text":"David Barral, Juan Ariel Levenson, Kamel Bencheikh, Nadia Belabas, Peter J. Olver","submitted_at":"2019-01-15T16:07:37Z","abstract_excerpt":"In general the ubiquitous \\chi^{(2)} nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes yields dynamical analytical solutions for any phase matching in a symmetric coupler. We analyze second harmonic generation and optical parametric amplification regimes and study the influence of fundamental fields parity and power on the operation of the device. These fundamental solutions are useful to develop applications in classical and quantum fields suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04897","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":"2026-05-17T23:47:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q/4B9C2psll2yrtnGqIcrkwh/YNDTMQi4K++la307ukrTtQC1u3zYP0v7YAyWngkJB6MMlpDm04rcy2bOh4tAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:03:04.394599Z"},"content_sha256":"5a0d212e524cc0223f66353576158e773505f0b2436d19e624ad66798be8cac9","schema_version":"1.0","event_id":"sha256:5a0d212e524cc0223f66353576158e773505f0b2436d19e624ad66798be8cac9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5KJCDDBK32GHW7ZKRURUI5YGU/bundle.json","state_url":"https://pith.science/pith/U5KJCDDBK32GHW7ZKRURUI5YGU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5KJCDDBK32GHW7ZKRURUI5YGU/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":"2026-05-21T21:03:04Z","links":{"resolver":"https://pith.science/pith/U5KJCDDBK32GHW7ZKRURUI5YGU","bundle":"https://pith.science/pith/U5KJCDDBK32GHW7ZKRURUI5YGU/bundle.json","state":"https://pith.science/pith/U5KJCDDBK32GHW7ZKRURUI5YGU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5KJCDDBK32GHW7ZKRURUI5YGU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:U5KJCDDBK32GHW7ZKRURUI5YGU","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":"968a46bdd6725526eb29c32a387881e8a23625188c97367b629255a074a1eb16","cross_cats_sorted":["nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-01-15T16:07:37Z","title_canon_sha256":"ed812a245e2f342dc0b8ea5cd1d3d0e915ed7f8e6edb687158c4f0654f0ccda9"},"schema_version":"1.0","source":{"id":"1901.04897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04897","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04897v2","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04897","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"pith_short_12","alias_value":"U5KJCDDBK32G","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U5KJCDDBK32GHW7Z","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U5KJCDDB","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:5a0d212e524cc0223f66353576158e773505f0b2436d19e624ad66798be8cac9","target":"graph","created_at":"2026-05-17T23:47:58Z","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":"In general the ubiquitous \\chi^{(2)} nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes yields dynamical analytical solutions for any phase matching in a symmetric coupler. We analyze second harmonic generation and optical parametric amplification regimes and study the influence of fundamental fields parity and power on the operation of the device. These fundamental solutions are useful to develop applications in classical and quantum fields suc","authors_text":"David Barral, Juan Ariel Levenson, Kamel Bencheikh, Nadia Belabas, Peter J. Olver","cross_cats":["nlin.SI","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-01-15T16:07:37Z","title":"Symmetry-based analytical solutions to the \\chi^{(2)} nonlinear directional coupler"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04897","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":"sha256:49eb9b1d9c964ba18353941e92844ec5932b1ee9edfc2f4699c03cd5fe770a44","target":"record","created_at":"2026-05-17T23:47:58Z","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":"968a46bdd6725526eb29c32a387881e8a23625188c97367b629255a074a1eb16","cross_cats_sorted":["nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-01-15T16:07:37Z","title_canon_sha256":"ed812a245e2f342dc0b8ea5cd1d3d0e915ed7f8e6edb687158c4f0654f0ccda9"},"schema_version":"1.0","source":{"id":"1901.04897","kind":"arxiv","version":2}},"canonical_sha256":"a754910c6156f463dbf954691a23b835284242f05e1693844f5f264918a72286","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a754910c6156f463dbf954691a23b835284242f05e1693844f5f264918a72286","first_computed_at":"2026-05-17T23:47:58.471215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:58.471215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l41OTwfDXhBidpWxtvmz6aaVVnhRkV4jOZFc64N8GHUPqlGsSHOV33VH3YAbU34bh/zC+AaSF3xj7aKgjOWkCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:58.471726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49eb9b1d9c964ba18353941e92844ec5932b1ee9edfc2f4699c03cd5fe770a44","sha256:5a0d212e524cc0223f66353576158e773505f0b2436d19e624ad66798be8cac9"],"state_sha256":"d7e0063f01d551a02eb367de48363057ed3f3d58af23c7ad4f497af06cae70eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lqWbG64PaGU/0yDwSd+ivhX9bAUZ/1BCFIEw9tEJrn5/npi4fxeoVsvrOOX7exbCler/hnHdpmPj/uyBdS8WDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T21:03:04.396934Z","bundle_sha256":"355aae55ea82dbf3b0d239c30276da9b7c8f0de3da3e83a3919dcc28b5d7ada7"}}