{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VLY5WAHQACPGMGOR3WEDKQYZUW","short_pith_number":"pith:VLY5WAHQ","canonical_record":{"source":{"id":"1202.3100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T17:42:46Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"51c2f4f236a35e80c39a1a96e609ecf47b516c54e3ed984f9fad6a77f881857e","abstract_canon_sha256":"be7f7adca9940a48ffb22f498f8b5995300ac2c1deece97ccf0138e84922e53c"},"schema_version":"1.0"},"canonical_sha256":"aaf1db00f0009e6619d1dd88354319a5ae3670c1a037b4122423afdc4acaf281","source":{"kind":"arxiv","id":"1202.3100","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3100","created_at":"2026-05-18T01:44:20Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3100v2","created_at":"2026-05-18T01:44:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3100","created_at":"2026-05-18T01:44:20Z"},{"alias_kind":"pith_short_12","alias_value":"VLY5WAHQACPG","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VLY5WAHQACPGMGOR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VLY5WAHQ","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VLY5WAHQACPGMGOR3WEDKQYZUW","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T17:42:46Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"51c2f4f236a35e80c39a1a96e609ecf47b516c54e3ed984f9fad6a77f881857e","abstract_canon_sha256":"be7f7adca9940a48ffb22f498f8b5995300ac2c1deece97ccf0138e84922e53c"},"schema_version":"1.0"},"canonical_sha256":"aaf1db00f0009e6619d1dd88354319a5ae3670c1a037b4122423afdc4acaf281","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:20.900091Z","signature_b64":"EZMLl/8HTGYmnBPbxYtV/H5huOFnSd+czptEesNSIlGeyhQuv9a7uqhOMI0DNxPTrzX262gyM8Xa7qQS/IsUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaf1db00f0009e6619d1dd88354319a5ae3670c1a037b4122423afdc4acaf281","last_reissued_at":"2026-05-18T01:44:20.899384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:20.899384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3100","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:44:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pgkNGMhYfeSaJEJlQqfP0JWwyq3U2YyzdOhg91a4LT8PY8eUBDfHarGKp6DwRRae8H57uPwS7bDed9wdLcaBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:31:01.037661Z"},"content_sha256":"54f22717975b2d3be801fdc13f75ec6a7e1c3ca1017e3d9d04c1a5698dee1833","schema_version":"1.0","event_id":"sha256:54f22717975b2d3be801fdc13f75ec6a7e1c3ca1017e3d9d04c1a5698dee1833"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VLY5WAHQACPGMGOR3WEDKQYZUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeta-regularisation for exact-WKB resolution of a general 1D Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Andr\\'e Voros","submitted_at":"2012-02-14T17:42:46Z","abstract_excerpt":"We review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schr\\\"odinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual) vs \"classical\" (newer) zeta-regularisations in parallel. The central results are a set of Bohr--Sommerfeld-like but exact quantisation conditions, directly drawn from Wronskian identities, and appearing to extend Bethe-Ansatz formulae of integrable systems. Such exact quantisation conditions do not just select the eigenvalues; some evaluate the spectral dete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3100","kind":"arxiv","version":2},"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":"2026-05-18T01:44:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8dCK4rLRPy7qiL970hWvh6zmTsuHPKjcfS8h6XxjDjixnhsjm192dbWE+Z9OAPO8/avM2iQ8F/9utgKAYDRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:31:01.038227Z"},"content_sha256":"1620a8cae1378a3839cd4b6dcba4bb03d9c73dd0dd1107e1feb1e9b270829660","schema_version":"1.0","event_id":"sha256:1620a8cae1378a3839cd4b6dcba4bb03d9c73dd0dd1107e1feb1e9b270829660"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VLY5WAHQACPGMGOR3WEDKQYZUW/bundle.json","state_url":"https://pith.science/pith/VLY5WAHQACPGMGOR3WEDKQYZUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VLY5WAHQACPGMGOR3WEDKQYZUW/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":"2026-06-11T13:31:01Z","links":{"resolver":"https://pith.science/pith/VLY5WAHQACPGMGOR3WEDKQYZUW","bundle":"https://pith.science/pith/VLY5WAHQACPGMGOR3WEDKQYZUW/bundle.json","state":"https://pith.science/pith/VLY5WAHQACPGMGOR3WEDKQYZUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VLY5WAHQACPGMGOR3WEDKQYZUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VLY5WAHQACPGMGOR3WEDKQYZUW","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":"be7f7adca9940a48ffb22f498f8b5995300ac2c1deece97ccf0138e84922e53c","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T17:42:46Z","title_canon_sha256":"51c2f4f236a35e80c39a1a96e609ecf47b516c54e3ed984f9fad6a77f881857e"},"schema_version":"1.0","source":{"id":"1202.3100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3100","created_at":"2026-05-18T01:44:20Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3100v2","created_at":"2026-05-18T01:44:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3100","created_at":"2026-05-18T01:44:20Z"},{"alias_kind":"pith_short_12","alias_value":"VLY5WAHQACPG","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VLY5WAHQACPGMGOR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VLY5WAHQ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1620a8cae1378a3839cd4b6dcba4bb03d9c73dd0dd1107e1feb1e9b270829660","target":"graph","created_at":"2026-05-18T01:44:20Z","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 review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schr\\\"odinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual) vs \"classical\" (newer) zeta-regularisations in parallel. The central results are a set of Bohr--Sommerfeld-like but exact quantisation conditions, directly drawn from Wronskian identities, and appearing to extend Bethe-Ansatz formulae of integrable systems. Such exact quantisation conditions do not just select the eigenvalues; some evaluate the spectral dete","authors_text":"Andr\\'e Voros","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T17:42:46Z","title":"Zeta-regularisation for exact-WKB resolution of a general 1D Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3100","kind":"arxiv","version":2},"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":"sha256:54f22717975b2d3be801fdc13f75ec6a7e1c3ca1017e3d9d04c1a5698dee1833","target":"record","created_at":"2026-05-18T01:44:20Z","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":"be7f7adca9940a48ffb22f498f8b5995300ac2c1deece97ccf0138e84922e53c","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T17:42:46Z","title_canon_sha256":"51c2f4f236a35e80c39a1a96e609ecf47b516c54e3ed984f9fad6a77f881857e"},"schema_version":"1.0","source":{"id":"1202.3100","kind":"arxiv","version":2}},"canonical_sha256":"aaf1db00f0009e6619d1dd88354319a5ae3670c1a037b4122423afdc4acaf281","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaf1db00f0009e6619d1dd88354319a5ae3670c1a037b4122423afdc4acaf281","first_computed_at":"2026-05-18T01:44:20.899384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:20.899384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZMLl/8HTGYmnBPbxYtV/H5huOFnSd+czptEesNSIlGeyhQuv9a7uqhOMI0DNxPTrzX262gyM8Xa7qQS/IsUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:20.900091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54f22717975b2d3be801fdc13f75ec6a7e1c3ca1017e3d9d04c1a5698dee1833","sha256:1620a8cae1378a3839cd4b6dcba4bb03d9c73dd0dd1107e1feb1e9b270829660"],"state_sha256":"63dd1b205501269b69470b669349ab8035699c788f2f80214ba607d98bb63654"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJ6AHNymgEZkWSCvwsjaxLKkuUVCwZHJqhLg2WjMHJfzeAsF0cpjgdT5gi66CdzArkUr2iuvUpf9L1KIjgexDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T13:31:01.040897Z","bundle_sha256":"795b7d15cc5da2a88ae3f82218af6ebc536074bedf5a2c8c95655e2dbbf75a93"}}