{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PV4XO4GIWDZXFPSDCTMKDSTXIA","short_pith_number":"pith:PV4XO4GI","canonical_record":{"source":{"id":"1104.0593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T15:00:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"37694710083e94ec63335153b4b5f83cd6a423e5b4c44f4263973ae3a8f54476","abstract_canon_sha256":"d217377f482f39f176589c04e05ea14593ee38bf6eb302764ed309484ae3cc2a"},"schema_version":"1.0"},"canonical_sha256":"7d797770c8b0f372be4314d8a1ca774003411cd46597177e32d43cdf9c737b2d","source":{"kind":"arxiv","id":"1104.0593","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0593","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0593v1","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0593","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"PV4XO4GIWDZX","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PV4XO4GIWDZXFPSD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PV4XO4GI","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PV4XO4GIWDZXFPSDCTMKDSTXIA","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T15:00:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"37694710083e94ec63335153b4b5f83cd6a423e5b4c44f4263973ae3a8f54476","abstract_canon_sha256":"d217377f482f39f176589c04e05ea14593ee38bf6eb302764ed309484ae3cc2a"},"schema_version":"1.0"},"canonical_sha256":"7d797770c8b0f372be4314d8a1ca774003411cd46597177e32d43cdf9c737b2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:37.192002Z","signature_b64":"QehUvB5FkiQ4yi9HPjVOtPy4F76ACqDTuqJjy6YS8ESkG2IEi3FM+scqSxrP239tEypnUofG4jR9+QWa+X/lCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d797770c8b0f372be4314d8a1ca774003411cd46597177e32d43cdf9c737b2d","last_reissued_at":"2026-05-18T01:24:37.191491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:37.191491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0593","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":"2026-05-18T01:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kDRBohfCpZyNuM3FCkhl6rLSu/KCRcw6eqslN1xr51I2fYnWU9PqTKmD6dEYjkqoEghhmeluYRgS2P850oDdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:11:01.780596Z"},"content_sha256":"a54a5872624441c462dc4d8bcd4e4e551c2287909b449d08a708da7368e367a0","schema_version":"1.0","event_id":"sha256:a54a5872624441c462dc4d8bcd4e4e551c2287909b449d08a708da7368e367a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PV4XO4GIWDZXFPSDCTMKDSTXIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On eigenvalues of the Schr\\\"odinger operator with an even complex-valued polynomial potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Per Alexandersson","submitted_at":"2011-04-04T15:00:39Z","abstract_excerpt":"In this paper, we generalize several results of the article \"Analytic continuation of eigenvalues of a quartic oscillator\" of A. Eremenko and A. Gabrielov.\n  We consider a family of eigenvalue problems for a Schr\\\"odinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k<(d+2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively.\n  In the case with k=(d+2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0593","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":"2026-05-18T01:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FowfHMb6MNkoE1kYE4JmcNoo+bsuRisv/+MBeGxEYaRCyFsQHtMwlFHPZ23lhgKP3SiADL38tZIty0GBa91VAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:11:01.780943Z"},"content_sha256":"1830038d332e6eacf5adbb9542bd59fc5dde9dcc5ecb2690101440c940fbc549","schema_version":"1.0","event_id":"sha256:1830038d332e6eacf5adbb9542bd59fc5dde9dcc5ecb2690101440c940fbc549"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA/bundle.json","state_url":"https://pith.science/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA/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":"2026-05-28T06:11:01Z","links":{"resolver":"https://pith.science/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA","bundle":"https://pith.science/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA/bundle.json","state":"https://pith.science/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PV4XO4GIWDZXFPSDCTMKDSTXIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PV4XO4GIWDZXFPSDCTMKDSTXIA","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":"d217377f482f39f176589c04e05ea14593ee38bf6eb302764ed309484ae3cc2a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T15:00:39Z","title_canon_sha256":"37694710083e94ec63335153b4b5f83cd6a423e5b4c44f4263973ae3a8f54476"},"schema_version":"1.0","source":{"id":"1104.0593","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0593","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0593v1","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0593","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"PV4XO4GIWDZX","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PV4XO4GIWDZXFPSD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PV4XO4GI","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:1830038d332e6eacf5adbb9542bd59fc5dde9dcc5ecb2690101440c940fbc549","target":"graph","created_at":"2026-05-18T01:24:37Z","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 this paper, we generalize several results of the article \"Analytic continuation of eigenvalues of a quartic oscillator\" of A. Eremenko and A. Gabrielov.\n  We consider a family of eigenvalue problems for a Schr\\\"odinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k<(d+2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively.\n  In the case with k=(d+2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many","authors_text":"Per Alexandersson","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T15:00:39Z","title":"On eigenvalues of the Schr\\\"odinger operator with an even complex-valued polynomial potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0593","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:a54a5872624441c462dc4d8bcd4e4e551c2287909b449d08a708da7368e367a0","target":"record","created_at":"2026-05-18T01:24:37Z","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":"d217377f482f39f176589c04e05ea14593ee38bf6eb302764ed309484ae3cc2a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T15:00:39Z","title_canon_sha256":"37694710083e94ec63335153b4b5f83cd6a423e5b4c44f4263973ae3a8f54476"},"schema_version":"1.0","source":{"id":"1104.0593","kind":"arxiv","version":1}},"canonical_sha256":"7d797770c8b0f372be4314d8a1ca774003411cd46597177e32d43cdf9c737b2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d797770c8b0f372be4314d8a1ca774003411cd46597177e32d43cdf9c737b2d","first_computed_at":"2026-05-18T01:24:37.191491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:37.191491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QehUvB5FkiQ4yi9HPjVOtPy4F76ACqDTuqJjy6YS8ESkG2IEi3FM+scqSxrP239tEypnUofG4jR9+QWa+X/lCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:37.192002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0593","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a54a5872624441c462dc4d8bcd4e4e551c2287909b449d08a708da7368e367a0","sha256:1830038d332e6eacf5adbb9542bd59fc5dde9dcc5ecb2690101440c940fbc549"],"state_sha256":"1040a06af937043b0d215f6bd7cf7c0cc1f13c5217f4611387c8c69f375d4486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ExyBjYIqFCzmqbb4keUUwkGATQZ5v/cqvM4MuA63SiOw5J6qdFIlx1qbUlaHjAMJsmanrff4z8zktakyIgs7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:11:01.783176Z","bundle_sha256":"6d4fab98eb57c37ba0684775ea07483507b5ac190b75700b50ff8258df6ca935"}}