{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BVTWBRNFJY4HQ3FYXY7DB2VCRO","short_pith_number":"pith:BVTWBRNF","canonical_record":{"source":{"id":"1312.3376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-12-12T00:33:21Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"cdce7dd9b44bdf98307cf4bbc3d5a8cdd3a093f8455bba721b63ed74e968761c","abstract_canon_sha256":"8d1123393e34ee4a234dbc4fc86d7dd40b26129f1c0bd79744a050e578e8aa36"},"schema_version":"1.0"},"canonical_sha256":"0d6760c5a54e38786cb8be3e30eaa28b9ebecc40c2141fc722b3f3ea6f3a5dbe","source":{"kind":"arxiv","id":"1312.3376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3376","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3376v1","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3376","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"BVTWBRNFJY4H","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BVTWBRNFJY4HQ3FY","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BVTWBRNF","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BVTWBRNFJY4HQ3FYXY7DB2VCRO","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-12-12T00:33:21Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"cdce7dd9b44bdf98307cf4bbc3d5a8cdd3a093f8455bba721b63ed74e968761c","abstract_canon_sha256":"8d1123393e34ee4a234dbc4fc86d7dd40b26129f1c0bd79744a050e578e8aa36"},"schema_version":"1.0"},"canonical_sha256":"0d6760c5a54e38786cb8be3e30eaa28b9ebecc40c2141fc722b3f3ea6f3a5dbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:58.758972Z","signature_b64":"UazuqIWiA/vUY300732yhjw7ZB6b/pldnPq8lD0JYXtp19hTkxwhzwcDI1jjP/WHjbumviBOOv44ltMi2tydCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d6760c5a54e38786cb8be3e30eaa28b9ebecc40c2141fc722b3f3ea6f3a5dbe","last_reissued_at":"2026-05-18T03:04:58.758472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:58.758472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3376","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":"2026-05-18T03:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3uwwr3CsxfZzPEpvlQBMejor/ffA6Qli5P1xHlGP3maH8C2CdAe0/5pP4gPVNUqSYDco4+UZDYS9P9VvWTiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:21:08.062668Z"},"content_sha256":"b75e834e6c5fbf0ee37252ed9896d38ba6c2bb543b9f7527cb96dc044b3ddd02","schema_version":"1.0","event_id":"sha256:b75e834e6c5fbf0ee37252ed9896d38ba6c2bb543b9f7527cb96dc044b3ddd02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BVTWBRNFJY4HQ3FYXY7DB2VCRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear modes and symmetries in linearly-coupled pairs of PT-invariant dimers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.optics"],"primary_cat":"nlin.PS","authors_text":"B. A. Malomed, K. Li, P. G. Kevrekidis","submitted_at":"2013-12-12T00:33:21Z","abstract_excerpt":"The subject of the work are pairs of linearly coupled PT-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled dimers, with each gain site coupled to two lossy ones. The latter pair with equal coupling coefficients represents a \"PT-hypersymmetric\" quadrimer. We find symmetric and antisymmetric solutions in these systems, chiefly in an analytical form, and explore the existence, stability and dynamical behavior of such solutions by means of numerical methods. We thus ide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3376","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":"2026-05-18T03:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5NXpDwzD/zPCCiIcESRhrtZ0pBFsOxFq0Kf71P68Tbg7RhpCPS3GVKyYZC1O2cfxRaCS8dxywdwvSBta3193CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:21:08.063006Z"},"content_sha256":"a023386a9e34b0f24eace066f9bc85289995f8c3e3cb1c04d4097bbd7caf32d8","schema_version":"1.0","event_id":"sha256:a023386a9e34b0f24eace066f9bc85289995f8c3e3cb1c04d4097bbd7caf32d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO/bundle.json","state_url":"https://pith.science/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO/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":"2026-06-04T12:21:08Z","links":{"resolver":"https://pith.science/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO","bundle":"https://pith.science/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO/bundle.json","state":"https://pith.science/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVTWBRNFJY4HQ3FYXY7DB2VCRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BVTWBRNFJY4HQ3FYXY7DB2VCRO","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":"8d1123393e34ee4a234dbc4fc86d7dd40b26129f1c0bd79744a050e578e8aa36","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-12-12T00:33:21Z","title_canon_sha256":"cdce7dd9b44bdf98307cf4bbc3d5a8cdd3a093f8455bba721b63ed74e968761c"},"schema_version":"1.0","source":{"id":"1312.3376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3376","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3376v1","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3376","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"BVTWBRNFJY4H","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BVTWBRNFJY4HQ3FY","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BVTWBRNF","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:a023386a9e34b0f24eace066f9bc85289995f8c3e3cb1c04d4097bbd7caf32d8","target":"graph","created_at":"2026-05-18T03:04:58Z","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":"The subject of the work are pairs of linearly coupled PT-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled dimers, with each gain site coupled to two lossy ones. The latter pair with equal coupling coefficients represents a \"PT-hypersymmetric\" quadrimer. We find symmetric and antisymmetric solutions in these systems, chiefly in an analytical form, and explore the existence, stability and dynamical behavior of such solutions by means of numerical methods. We thus ide","authors_text":"B. A. Malomed, K. Li, P. G. Kevrekidis","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-12-12T00:33:21Z","title":"Nonlinear modes and symmetries in linearly-coupled pairs of PT-invariant dimers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3376","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:b75e834e6c5fbf0ee37252ed9896d38ba6c2bb543b9f7527cb96dc044b3ddd02","target":"record","created_at":"2026-05-18T03:04:58Z","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":"8d1123393e34ee4a234dbc4fc86d7dd40b26129f1c0bd79744a050e578e8aa36","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-12-12T00:33:21Z","title_canon_sha256":"cdce7dd9b44bdf98307cf4bbc3d5a8cdd3a093f8455bba721b63ed74e968761c"},"schema_version":"1.0","source":{"id":"1312.3376","kind":"arxiv","version":1}},"canonical_sha256":"0d6760c5a54e38786cb8be3e30eaa28b9ebecc40c2141fc722b3f3ea6f3a5dbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d6760c5a54e38786cb8be3e30eaa28b9ebecc40c2141fc722b3f3ea6f3a5dbe","first_computed_at":"2026-05-18T03:04:58.758472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:58.758472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UazuqIWiA/vUY300732yhjw7ZB6b/pldnPq8lD0JYXtp19hTkxwhzwcDI1jjP/WHjbumviBOOv44ltMi2tydCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:58.758972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b75e834e6c5fbf0ee37252ed9896d38ba6c2bb543b9f7527cb96dc044b3ddd02","sha256:a023386a9e34b0f24eace066f9bc85289995f8c3e3cb1c04d4097bbd7caf32d8"],"state_sha256":"237b8523a8cba495d4b01c2ad8bf2f41dd55649a34bb33261ff7fa205a546d3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ox5x7jfgbxpIg/2NqPtVeciHvgNesz66LcLD3b+Wt4ppc22/7GY2fIkN+cKoQYUNCAasQXgVEE2iRWUY9eSnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:21:08.065060Z","bundle_sha256":"92ba950065009e93d9d31473d1e56acdd5be839bdd6891a76b47c7b7703bbd8b"}}