{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SJV4BFFA7C335DZ6NWOMJS6RQB","short_pith_number":"pith:SJV4BFFA","canonical_record":{"source":{"id":"1611.06313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-19T06:15:37Z","cross_cats_sorted":["math.CA","math.MP","quant-ph"],"title_canon_sha256":"17623a801702eb4531431ebabddbb59e938a3baa128c7847f26f2adfe17e1789","abstract_canon_sha256":"f658e9e6da1b5690521be9dc73daf16d731974917ca2ea413b584a0bb928387c"},"schema_version":"1.0"},"canonical_sha256":"926bc094a0f8b7be8f3e6d9cc4cbd18077ac062f16d4646d4c62edc01f1f4e51","source":{"kind":"arxiv","id":"1611.06313","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06313","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06313v1","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06313","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"SJV4BFFA7C33","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SJV4BFFA7C335DZ6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SJV4BFFA","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SJV4BFFA7C335DZ6NWOMJS6RQB","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-19T06:15:37Z","cross_cats_sorted":["math.CA","math.MP","quant-ph"],"title_canon_sha256":"17623a801702eb4531431ebabddbb59e938a3baa128c7847f26f2adfe17e1789","abstract_canon_sha256":"f658e9e6da1b5690521be9dc73daf16d731974917ca2ea413b584a0bb928387c"},"schema_version":"1.0"},"canonical_sha256":"926bc094a0f8b7be8f3e6d9cc4cbd18077ac062f16d4646d4c62edc01f1f4e51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:39.048653Z","signature_b64":"xyYrTp2x3RxFQlvUGTRlWXBn9H9J9SGl3Hu7uoqY6P+PpE/YWU1TKVdEz3uwjBsP2GLDiknEO3JM9CzA17CFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"926bc094a0f8b7be8f3e6d9cc4cbd18077ac062f16d4646d4c62edc01f1f4e51","last_reissued_at":"2026-05-18T00:57:39.048063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:39.048063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06313","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":"2026-05-18T00:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MN2snBx4+ivppoRp+5syqBBGm/XOVvLVDKKjka17aoyrc2ZBzk0E+k0Bg+ogCK8bPtVWhyscOs+7573w8Or4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:25:20.265951Z"},"content_sha256":"b80cd3d04b5683b97e6ccbcc5e087e9b8420502dc663bedb0d7df0ed33f04b30","schema_version":"1.0","event_id":"sha256:b80cd3d04b5683b97e6ccbcc5e087e9b8420502dc663bedb0d7df0ed33f04b30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SJV4BFFA7C335DZ6NWOMJS6RQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics and monodromy of the algebraic spectrum of quasi-exactly solvable sextic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Boris Shapiro, Milos Tater","submitted_at":"2016-11-19T06:15:37Z","abstract_excerpt":"Below we study theoretically and numerically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential, its level crossing points, and its monodromy in the complex plane of its parameter. We also discuss connection between the quasi-exactly solvable sextic and the classical quartic potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06313","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":"2026-05-18T00:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6I700vmG7r80V/iyhV/iRdraUnCTvSmZdHAs0jhOEzCjcilXnZHqCCozu8aHJ3ahLOw/AV88rOUUBKImKTMODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:25:20.266652Z"},"content_sha256":"427aa629ef114ee79c2f6f79e9cd32d83ef03cc0e62fed9d7712fa4a86a3205c","schema_version":"1.0","event_id":"sha256:427aa629ef114ee79c2f6f79e9cd32d83ef03cc0e62fed9d7712fa4a86a3205c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJV4BFFA7C335DZ6NWOMJS6RQB/bundle.json","state_url":"https://pith.science/pith/SJV4BFFA7C335DZ6NWOMJS6RQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJV4BFFA7C335DZ6NWOMJS6RQB/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":"2026-05-26T09:25:20Z","links":{"resolver":"https://pith.science/pith/SJV4BFFA7C335DZ6NWOMJS6RQB","bundle":"https://pith.science/pith/SJV4BFFA7C335DZ6NWOMJS6RQB/bundle.json","state":"https://pith.science/pith/SJV4BFFA7C335DZ6NWOMJS6RQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJV4BFFA7C335DZ6NWOMJS6RQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SJV4BFFA7C335DZ6NWOMJS6RQB","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":"f658e9e6da1b5690521be9dc73daf16d731974917ca2ea413b584a0bb928387c","cross_cats_sorted":["math.CA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-19T06:15:37Z","title_canon_sha256":"17623a801702eb4531431ebabddbb59e938a3baa128c7847f26f2adfe17e1789"},"schema_version":"1.0","source":{"id":"1611.06313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06313","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06313v1","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06313","created_at":"2026-05-18T00:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"SJV4BFFA7C33","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SJV4BFFA7C335DZ6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SJV4BFFA","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:427aa629ef114ee79c2f6f79e9cd32d83ef03cc0e62fed9d7712fa4a86a3205c","target":"graph","created_at":"2026-05-18T00:57:39Z","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":"Below we study theoretically and numerically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential, its level crossing points, and its monodromy in the complex plane of its parameter. We also discuss connection between the quasi-exactly solvable sextic and the classical quartic potential.","authors_text":"Boris Shapiro, Milos Tater","cross_cats":["math.CA","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-19T06:15:37Z","title":"Asymptotics and monodromy of the algebraic spectrum of quasi-exactly solvable sextic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06313","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:b80cd3d04b5683b97e6ccbcc5e087e9b8420502dc663bedb0d7df0ed33f04b30","target":"record","created_at":"2026-05-18T00:57:39Z","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":"f658e9e6da1b5690521be9dc73daf16d731974917ca2ea413b584a0bb928387c","cross_cats_sorted":["math.CA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-19T06:15:37Z","title_canon_sha256":"17623a801702eb4531431ebabddbb59e938a3baa128c7847f26f2adfe17e1789"},"schema_version":"1.0","source":{"id":"1611.06313","kind":"arxiv","version":1}},"canonical_sha256":"926bc094a0f8b7be8f3e6d9cc4cbd18077ac062f16d4646d4c62edc01f1f4e51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"926bc094a0f8b7be8f3e6d9cc4cbd18077ac062f16d4646d4c62edc01f1f4e51","first_computed_at":"2026-05-18T00:57:39.048063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:39.048063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xyYrTp2x3RxFQlvUGTRlWXBn9H9J9SGl3Hu7uoqY6P+PpE/YWU1TKVdEz3uwjBsP2GLDiknEO3JM9CzA17CFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:39.048653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b80cd3d04b5683b97e6ccbcc5e087e9b8420502dc663bedb0d7df0ed33f04b30","sha256:427aa629ef114ee79c2f6f79e9cd32d83ef03cc0e62fed9d7712fa4a86a3205c"],"state_sha256":"713c7efc4137d52ba1fa9be4af07da08104cf926d1ea87f06d250aefa2fa5763"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HITyXfbtWs49eWFmk50ZuHrWCfeGtfTidLOvybOIbKzvXErQ3RGHA8RAactQtwnMGKFfuF0DpsLAffl2MtzEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:25:20.270225Z","bundle_sha256":"4e81c36028d4e99e11ea24c8515039f2793c2ba2217d1e93901cab4269b304fb"}}