{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BQDAJT5VXSOO54U4W66FTHFMDV","short_pith_number":"pith:BQDAJT5V","canonical_record":{"source":{"id":"2606.31279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-30T07:53:22Z","cross_cats_sorted":[],"title_canon_sha256":"9b7c6f29e4ead06f82d6023139ca45ed429df831a601f5e2b14a091d126661ce","abstract_canon_sha256":"d8acc78cbdd94ca2859574da7a7cd026e12d30d4800ce2596f5275407d2dda8d"},"schema_version":"1.0"},"canonical_sha256":"0c0604cfb5bc9ceef29cb7bc599cac1d53aa24c150f99f3450e9a6d4fd463cf0","source":{"kind":"arxiv","id":"2606.31279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31279","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31279v1","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31279","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"BQDAJT5VXSOO","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"BQDAJT5VXSOO54U4","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"BQDAJT5V","created_at":"2026-07-01T01:17:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BQDAJT5VXSOO54U4W66FTHFMDV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.31279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-30T07:53:22Z","cross_cats_sorted":[],"title_canon_sha256":"9b7c6f29e4ead06f82d6023139ca45ed429df831a601f5e2b14a091d126661ce","abstract_canon_sha256":"d8acc78cbdd94ca2859574da7a7cd026e12d30d4800ce2596f5275407d2dda8d"},"schema_version":"1.0"},"canonical_sha256":"0c0604cfb5bc9ceef29cb7bc599cac1d53aa24c150f99f3450e9a6d4fd463cf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:57.886150Z","signature_b64":"ao8p2yQvJFJwzYDnWL7En5xoTgwkuMMSuE/LKCd/L700N9nFHoItYMWXOYMRWKTb5FQQVqp+jLa5gwCxlvvgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c0604cfb5bc9ceef29cb7bc599cac1d53aa24c150f99f3450e9a6d4fd463cf0","last_reissued_at":"2026-07-01T01:17:57.885722Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:57.885722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.31279","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":"2026-07-01T01:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"51Pk/7Y8gFo70cimJFGrsARMNde5yAM9RViUZDQggTkoWX/4aRC8mTdKQxVtnpNMyT6a495wAQA1XBnu1D1oAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:23:19.090837Z"},"content_sha256":"2a4d3f218046108f3f8345f3f477172e397603e27b02acd3097ee22615531971","schema_version":"1.0","event_id":"sha256:2a4d3f218046108f3f8345f3f477172e397603e27b02acd3097ee22615531971"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BQDAJT5VXSOO54U4W66FTHFMDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Hermitian Rayleigh-Schr\\\"{o}dinger-like Perturbation Theory at Exceptional Point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chia-Yi Ju, Wei-Ming Chen","submitted_at":"2026-06-30T07:53:22Z","abstract_excerpt":"We develop a Rayleigh--Schr\\\"{o}dinger-like perturbation theory for non-Hermitian quantum systems at an exceptional point of order $N$. Working in the Jordan basis of the unperturbed Hamiltonian and employing a Puiseux expansion of the perturbed eigenvalues and eigenstates, we derive explicit recursion relations for the expansion coefficients. The corrections to the unperturbed eigenvalue in the Puiseux expansion govern the splitting near the exceptional point; the first two are obtained iteratively in two equivalent forms. One is given in terms of the perturbation Hamiltonian in the Jordan ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31279","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31279/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-01T01:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+7YFIGVK0d+CtAzman/aPk0BBMpdcoe/xz0v+sFqypV86IwC1/RXT1oN/1OP5uWSAU+YX/3HWwvqy2Jei8aBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:23:19.091261Z"},"content_sha256":"1fa2c3873a2635ca1283a8710558f775e096e97e952f3dcd3e6ba4f90fda8073","schema_version":"1.0","event_id":"sha256:1fa2c3873a2635ca1283a8710558f775e096e97e952f3dcd3e6ba4f90fda8073"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQDAJT5VXSOO54U4W66FTHFMDV/bundle.json","state_url":"https://pith.science/pith/BQDAJT5VXSOO54U4W66FTHFMDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQDAJT5VXSOO54U4W66FTHFMDV/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":"2026-07-01T20:23:19Z","links":{"resolver":"https://pith.science/pith/BQDAJT5VXSOO54U4W66FTHFMDV","bundle":"https://pith.science/pith/BQDAJT5VXSOO54U4W66FTHFMDV/bundle.json","state":"https://pith.science/pith/BQDAJT5VXSOO54U4W66FTHFMDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQDAJT5VXSOO54U4W66FTHFMDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BQDAJT5VXSOO54U4W66FTHFMDV","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":"d8acc78cbdd94ca2859574da7a7cd026e12d30d4800ce2596f5275407d2dda8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-30T07:53:22Z","title_canon_sha256":"9b7c6f29e4ead06f82d6023139ca45ed429df831a601f5e2b14a091d126661ce"},"schema_version":"1.0","source":{"id":"2606.31279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31279","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31279v1","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31279","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"BQDAJT5VXSOO","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"BQDAJT5VXSOO54U4","created_at":"2026-07-01T01:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"BQDAJT5V","created_at":"2026-07-01T01:17:57Z"}],"graph_snapshots":[{"event_id":"sha256:1fa2c3873a2635ca1283a8710558f775e096e97e952f3dcd3e6ba4f90fda8073","target":"graph","created_at":"2026-07-01T01:17:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.31279/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a Rayleigh--Schr\\\"{o}dinger-like perturbation theory for non-Hermitian quantum systems at an exceptional point of order $N$. Working in the Jordan basis of the unperturbed Hamiltonian and employing a Puiseux expansion of the perturbed eigenvalues and eigenstates, we derive explicit recursion relations for the expansion coefficients. The corrections to the unperturbed eigenvalue in the Puiseux expansion govern the splitting near the exceptional point; the first two are obtained iteratively in two equivalent forms. One is given in terms of the perturbation Hamiltonian in the Jordan ba","authors_text":"Chia-Yi Ju, Wei-Ming Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-30T07:53:22Z","title":"Non-Hermitian Rayleigh-Schr\\\"{o}dinger-like Perturbation Theory at Exceptional Point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31279","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":"sha256:2a4d3f218046108f3f8345f3f477172e397603e27b02acd3097ee22615531971","target":"record","created_at":"2026-07-01T01:17:57Z","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":"d8acc78cbdd94ca2859574da7a7cd026e12d30d4800ce2596f5275407d2dda8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-30T07:53:22Z","title_canon_sha256":"9b7c6f29e4ead06f82d6023139ca45ed429df831a601f5e2b14a091d126661ce"},"schema_version":"1.0","source":{"id":"2606.31279","kind":"arxiv","version":1}},"canonical_sha256":"0c0604cfb5bc9ceef29cb7bc599cac1d53aa24c150f99f3450e9a6d4fd463cf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c0604cfb5bc9ceef29cb7bc599cac1d53aa24c150f99f3450e9a6d4fd463cf0","first_computed_at":"2026-07-01T01:17:57.885722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:57.885722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ao8p2yQvJFJwzYDnWL7En5xoTgwkuMMSuE/LKCd/L700N9nFHoItYMWXOYMRWKTb5FQQVqp+jLa5gwCxlvvgBw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:57.886150Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a4d3f218046108f3f8345f3f477172e397603e27b02acd3097ee22615531971","sha256:1fa2c3873a2635ca1283a8710558f775e096e97e952f3dcd3e6ba4f90fda8073"],"state_sha256":"32699aded9f30f898bea79078ea8a1945d3a91542d9a6e0414a74126e0215f9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbRHUHiToZzpn694wFC51V5wSWBlSUgPv1r8ICD0HDQVLAwfxCjyuimYpfmtnDggjl7RvgDuh1npyPAh+oh4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T20:23:19.093697Z","bundle_sha256":"d118e42d54d6ae7623911c670d4f98803b4544f4b6175503e67aa4287921352b"}}