{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BDGWJIQ42DU45VGHESO7PJPXT4","short_pith_number":"pith:BDGWJIQ4","canonical_record":{"source":{"id":"1506.01898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-05T13:16:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c5a5f1a947ab5d6306263ca9e016eb8cd19e32b4e96105ff6c561f960c497b11","abstract_canon_sha256":"09a39b074eb6c2a7c1bf9d00aaeee5f902209ae773c920cc4f4b636a34baf219"},"schema_version":"1.0"},"canonical_sha256":"08cd64a21cd0e9ced4c7249df7a5f79f1c3bb9912398d6fda8593dc6349f08c4","source":{"kind":"arxiv","id":"1506.01898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01898","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01898v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01898","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"BDGWJIQ42DU4","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BDGWJIQ42DU45VGH","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BDGWJIQ4","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BDGWJIQ42DU45VGHESO7PJPXT4","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-05T13:16:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c5a5f1a947ab5d6306263ca9e016eb8cd19e32b4e96105ff6c561f960c497b11","abstract_canon_sha256":"09a39b074eb6c2a7c1bf9d00aaeee5f902209ae773c920cc4f4b636a34baf219"},"schema_version":"1.0"},"canonical_sha256":"08cd64a21cd0e9ced4c7249df7a5f79f1c3bb9912398d6fda8593dc6349f08c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:08.457411Z","signature_b64":"KDErS0Xw716Bf7//b3sxO5Ghlgfb4wQajQUsLMcXh1ZbJRf8pPl1hs2ON9oF+jjSHwcJGNrD14se2oOCCbWqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08cd64a21cd0e9ced4c7249df7a5f79f1c3bb9912398d6fda8593dc6349f08c4","last_reissued_at":"2026-05-18T01:12:08.456903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:08.456903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01898","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ojB4KNAV0wKLqBNma+AMWaZcP0W4StJF5b76iKPRfB8m3Gdym8ahrtl5s2mqqDxVA3EHmU81S8CCUXUh/Lf4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:27:58.038965Z"},"content_sha256":"ee30ca1a3b47f6bb0358bf91bbf93926060b9d3ae646afd6a6f2179599f32fac","schema_version":"1.0","event_id":"sha256:ee30ca1a3b47f6bb0358bf91bbf93926060b9d3ae646afd6a6f2179599f32fac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BDGWJIQ42DU45VGHESO7PJPXT4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-real Eigenvalues for PT-Symmetric Double Wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Amina Benbernou, Johannes Sjoestrand, Naima Boussekkine, Nawal Mecherout, Thierry Ramond","submitted_at":"2015-06-05T13:16:03Z","abstract_excerpt":"We study small, PT-symmetric perturbations of self-adjoint double-well Schr\\\"odinger operators in dimension $n\\geq 1$. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01898","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBZ3VSB2nL65k5Ts08LqRcBhU93ckIiVg3lYds2DbgCWfULvORHU95LOEW3mg+GvGP16AnKEoxE/znPlB1BEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:27:58.039327Z"},"content_sha256":"bd622e8bcde1b533b521ef661cd6e4b6ad720633401faf0ea7e37434f8d78a82","schema_version":"1.0","event_id":"sha256:bd622e8bcde1b533b521ef661cd6e4b6ad720633401faf0ea7e37434f8d78a82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDGWJIQ42DU45VGHESO7PJPXT4/bundle.json","state_url":"https://pith.science/pith/BDGWJIQ42DU45VGHESO7PJPXT4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDGWJIQ42DU45VGHESO7PJPXT4/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":"2026-06-02T13:27:58Z","links":{"resolver":"https://pith.science/pith/BDGWJIQ42DU45VGHESO7PJPXT4","bundle":"https://pith.science/pith/BDGWJIQ42DU45VGHESO7PJPXT4/bundle.json","state":"https://pith.science/pith/BDGWJIQ42DU45VGHESO7PJPXT4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDGWJIQ42DU45VGHESO7PJPXT4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BDGWJIQ42DU45VGHESO7PJPXT4","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":"09a39b074eb6c2a7c1bf9d00aaeee5f902209ae773c920cc4f4b636a34baf219","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-05T13:16:03Z","title_canon_sha256":"c5a5f1a947ab5d6306263ca9e016eb8cd19e32b4e96105ff6c561f960c497b11"},"schema_version":"1.0","source":{"id":"1506.01898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01898","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01898v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01898","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"BDGWJIQ42DU4","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BDGWJIQ42DU45VGH","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BDGWJIQ4","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:bd622e8bcde1b533b521ef661cd6e4b6ad720633401faf0ea7e37434f8d78a82","target":"graph","created_at":"2026-05-18T01:12:08Z","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":"We study small, PT-symmetric perturbations of self-adjoint double-well Schr\\\"odinger operators in dimension $n\\geq 1$. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger.","authors_text":"Amina Benbernou, Johannes Sjoestrand, Naima Boussekkine, Nawal Mecherout, Thierry Ramond","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-05T13:16:03Z","title":"Non-real Eigenvalues for PT-Symmetric Double Wells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01898","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:ee30ca1a3b47f6bb0358bf91bbf93926060b9d3ae646afd6a6f2179599f32fac","target":"record","created_at":"2026-05-18T01:12:08Z","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":"09a39b074eb6c2a7c1bf9d00aaeee5f902209ae773c920cc4f4b636a34baf219","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-05T13:16:03Z","title_canon_sha256":"c5a5f1a947ab5d6306263ca9e016eb8cd19e32b4e96105ff6c561f960c497b11"},"schema_version":"1.0","source":{"id":"1506.01898","kind":"arxiv","version":1}},"canonical_sha256":"08cd64a21cd0e9ced4c7249df7a5f79f1c3bb9912398d6fda8593dc6349f08c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08cd64a21cd0e9ced4c7249df7a5f79f1c3bb9912398d6fda8593dc6349f08c4","first_computed_at":"2026-05-18T01:12:08.456903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:08.456903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KDErS0Xw716Bf7//b3sxO5Ghlgfb4wQajQUsLMcXh1ZbJRf8pPl1hs2ON9oF+jjSHwcJGNrD14se2oOCCbWqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:08.457411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee30ca1a3b47f6bb0358bf91bbf93926060b9d3ae646afd6a6f2179599f32fac","sha256:bd622e8bcde1b533b521ef661cd6e4b6ad720633401faf0ea7e37434f8d78a82"],"state_sha256":"cf343d4904dd8b9d00a3559832c3dc86dc933e435f2d8d729c7755f659377da9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FuQr73SODwdO6lxjawl8LEBH2efMqhGPrsk269sZkSuCyqABQIVuY++F9+cX2LjQRz2xtu34lYYKgncYf+MXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:27:58.041277Z","bundle_sha256":"49fd1d21b7e778fffef3ffedf69ee27726198e3106fb6f2309c38ed94cb361e5"}}