{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZFCYEUOSUXFAQO75MAJUQ3XAUG","short_pith_number":"pith:ZFCYEUOS","canonical_record":{"source":{"id":"1210.4515","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-10-16T18:17:37Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"8a2ef30e12355a40364835826c1960070e1efc6190a14993fe8eebd9dbbe8f46","abstract_canon_sha256":"5165fd3491c5e51e47162cf0bd4a3b160a586ea37507fe2ecc6b203b07077b22"},"schema_version":"1.0"},"canonical_sha256":"c9458251d2a5ca083bfd6013486ee0a1b89ec9905b79d595987e7a131e4758ab","source":{"kind":"arxiv","id":"1210.4515","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4515","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4515v4","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4515","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZFCYEUOSUXFA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZFCYEUOSUXFAQO75","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZFCYEUOS","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZFCYEUOSUXFAQO75MAJUQ3XAUG","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4515","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-10-16T18:17:37Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"8a2ef30e12355a40364835826c1960070e1efc6190a14993fe8eebd9dbbe8f46","abstract_canon_sha256":"5165fd3491c5e51e47162cf0bd4a3b160a586ea37507fe2ecc6b203b07077b22"},"schema_version":"1.0"},"canonical_sha256":"c9458251d2a5ca083bfd6013486ee0a1b89ec9905b79d595987e7a131e4758ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:15.809519Z","signature_b64":"mAhwYLEeABvNI926D+cf0jZ1Cjb3LZN4mG1aXp0xeF9V8QoUv1C09HDq4/0A+pd0kHwueQCvi4LKAUCoCggmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9458251d2a5ca083bfd6013486ee0a1b89ec9905b79d595987e7a131e4758ab","last_reissued_at":"2026-05-18T03:36:15.808733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:15.808733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4515","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABtHExzEId5nHo3Z4paIuJTHAQyuGglw+bpRS37nCZNx7KOKQkWRdxQ2MAhztw8vZduvUO2M/2F10as/17xCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:56:25.898384Z"},"content_sha256":"4624e3f96d772ad1f64dcccaaf134ebfa5302919473cb5dfdcf8b78c5086cdf4","schema_version":"1.0","event_id":"sha256:4624e3f96d772ad1f64dcccaaf134ebfa5302919473cb5dfdcf8b78c5086cdf4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZFCYEUOSUXFAQO75MAJUQ3XAUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander V. Turbiner","submitted_at":"2012-10-16T18:17:37Z","abstract_excerpt":"A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits). These models are completely-integrable and admit extra particular integrals. All of them are characterized by (i) a number of polynomial eigenfunctions and quadratic in quantum numbers eigenvalues for exactly-solvable cases, (ii) a factorization property for eigenfunctions, (iii) a rational form of the potential and the polynomial entries of the metric in the Laplace-Beltrami operator in terms of affine-Weyl (exponential)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4515","kind":"arxiv","version":4},"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":"2026-05-18T03:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFhR3jimZhKJSE7p9VXAtb9sh1VTVQd4Y0NhzuHDQMvuk2D/kGarhsOQ+LG2nELpULgR0QiNSFr9RfeZlZHvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:56:25.899060Z"},"content_sha256":"de75a4c35bd548a22c5c0183d4e143ba7b28c16b6cc7497df5c07f63250ee13d","schema_version":"1.0","event_id":"sha256:de75a4c35bd548a22c5c0183d4e143ba7b28c16b6cc7497df5c07f63250ee13d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG/bundle.json","state_url":"https://pith.science/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG/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":"2026-05-22T04:56:25Z","links":{"resolver":"https://pith.science/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG","bundle":"https://pith.science/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG/bundle.json","state":"https://pith.science/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFCYEUOSUXFAQO75MAJUQ3XAUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZFCYEUOSUXFAQO75MAJUQ3XAUG","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":"5165fd3491c5e51e47162cf0bd4a3b160a586ea37507fe2ecc6b203b07077b22","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-10-16T18:17:37Z","title_canon_sha256":"8a2ef30e12355a40364835826c1960070e1efc6190a14993fe8eebd9dbbe8f46"},"schema_version":"1.0","source":{"id":"1210.4515","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4515","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4515v4","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4515","created_at":"2026-05-18T03:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZFCYEUOSUXFA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZFCYEUOSUXFAQO75","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZFCYEUOS","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:de75a4c35bd548a22c5c0183d4e143ba7b28c16b6cc7497df5c07f63250ee13d","target":"graph","created_at":"2026-05-18T03:36:15Z","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":"A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits). These models are completely-integrable and admit extra particular integrals. All of them are characterized by (i) a number of polynomial eigenfunctions and quadratic in quantum numbers eigenvalues for exactly-solvable cases, (ii) a factorization property for eigenfunctions, (iii) a rational form of the potential and the polynomial entries of the metric in the Laplace-Beltrami operator in terms of affine-Weyl (exponential)","authors_text":"Alexander V. Turbiner","cross_cats":["hep-th","math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-10-16T18:17:37Z","title":"From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4515","kind":"arxiv","version":4},"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":"sha256:4624e3f96d772ad1f64dcccaaf134ebfa5302919473cb5dfdcf8b78c5086cdf4","target":"record","created_at":"2026-05-18T03:36:15Z","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":"5165fd3491c5e51e47162cf0bd4a3b160a586ea37507fe2ecc6b203b07077b22","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2012-10-16T18:17:37Z","title_canon_sha256":"8a2ef30e12355a40364835826c1960070e1efc6190a14993fe8eebd9dbbe8f46"},"schema_version":"1.0","source":{"id":"1210.4515","kind":"arxiv","version":4}},"canonical_sha256":"c9458251d2a5ca083bfd6013486ee0a1b89ec9905b79d595987e7a131e4758ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9458251d2a5ca083bfd6013486ee0a1b89ec9905b79d595987e7a131e4758ab","first_computed_at":"2026-05-18T03:36:15.808733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:15.808733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mAhwYLEeABvNI926D+cf0jZ1Cjb3LZN4mG1aXp0xeF9V8QoUv1C09HDq4/0A+pd0kHwueQCvi4LKAUCoCggmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:15.809519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4515","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4624e3f96d772ad1f64dcccaaf134ebfa5302919473cb5dfdcf8b78c5086cdf4","sha256:de75a4c35bd548a22c5c0183d4e143ba7b28c16b6cc7497df5c07f63250ee13d"],"state_sha256":"cc624191214d636df9ba97de2ec31d78ac07294960863e81e0077b2178b28b43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P4dpGjhtmT+P//OSrFie8Ev6QDIkyD2tQIirwDRBP3sz8Shkl3JUIK8icK1M3kz1r1QZjkRVZRN6XcmgGjbpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T04:56:25.902894Z","bundle_sha256":"d005c74c9cbd438be57d50361350d0d3b666f40aad4b8a108cee2258aee647cc"}}