{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YGEJ3RIC3SVROVUKFJSLBODX52","short_pith_number":"pith:YGEJ3RIC","canonical_record":{"source":{"id":"1712.09371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-26T19:02:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ee40a05a89604d56993f07ff215d5f952712c81d6be21fa6f7e6b1031e5bcd37","abstract_canon_sha256":"afdc137f60a188bb56407122021c3979976eb9e084401d5375800f583be94e3b"},"schema_version":"1.0"},"canonical_sha256":"c1889dc502dcab17568a2a64b0b877ee861aa9efd92199fb4877375c0a055b5b","source":{"kind":"arxiv","id":"1712.09371","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09371","created_at":"2026-05-18T00:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09371v2","created_at":"2026-05-18T00:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09371","created_at":"2026-05-18T00:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"YGEJ3RIC3SVR","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YGEJ3RIC3SVROVUK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YGEJ3RIC","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YGEJ3RIC3SVROVUKFJSLBODX52","target":"record","payload":{"canonical_record":{"source":{"id":"1712.09371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-26T19:02:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ee40a05a89604d56993f07ff215d5f952712c81d6be21fa6f7e6b1031e5bcd37","abstract_canon_sha256":"afdc137f60a188bb56407122021c3979976eb9e084401d5375800f583be94e3b"},"schema_version":"1.0"},"canonical_sha256":"c1889dc502dcab17568a2a64b0b877ee861aa9efd92199fb4877375c0a055b5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:53.711995Z","signature_b64":"8v661GExZOGbKsyVctmvkJ7+2dYWlgY6XWSg53Z9lNvXWhUUFoH0GYu67pR37h/uDPL8Bx0hTmkL9PlLeg1zAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1889dc502dcab17568a2a64b0b877ee861aa9efd92199fb4877375c0a055b5b","last_reissued_at":"2026-05-18T00:12:53.711459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:53.711459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.09371","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":"2026-05-18T00:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KkYKyK2BIevXXCdo0FEvGKz53iqm1rEdIb1JLGbIXIs85d7kCfWYt/Ed+dqlrSAaIloKPtivQU6rxrDH0gRTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:03:02.311891Z"},"content_sha256":"c2e9ed9f4b286fe37ebac5cb5d6e73a31353b20a016d222e845e9b5f37f461a6","schema_version":"1.0","event_id":"sha256:c2e9ed9f4b286fe37ebac5cb5d6e73a31353b20a016d222e845e9b5f37f461a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YGEJ3RIC3SVROVUKFJSLBODX52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A unified treatment of polynomial sectors and constraint polynomials of the Rabi models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alexander Moroz","submitted_at":"2017-12-26T19:02:20Z","abstract_excerpt":"General concept of a gradation slicing is used to analyze polynomial solutions of ordinary differential equations (ODE) with polynomial coefficients, ${\\cal L}\\psi=0$, where ${\\cal L}=\\sum_l p_l(z) d_z^l$, $p_l(z)$ are polynomials, $z$ is a one-dimensional coordinate, and $d_z=d/dz$. It is not required that ODE is either (i) Fuchsian or (ii) leads to a usual Sturm-Liouville eigenvalue problem. General necessary and sufficient conditions for the existence of a polynomial solution are formulated involving constraint relations. The necessary condition for a polynomial solution of $n$th degree to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09371","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":"2026-05-18T00:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8uf4391ZWo2+/PhLs28T9LPFddu89nUW+MgovU7giD4b3oMq5xO7SYOA+2DwPnmXGOdnEMvXYhyCSZMDPePAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:03:02.312581Z"},"content_sha256":"80f1012a7fcf2619cea117eec39cd14f4788f6f35d59b35173a97bf962844b92","schema_version":"1.0","event_id":"sha256:80f1012a7fcf2619cea117eec39cd14f4788f6f35d59b35173a97bf962844b92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YGEJ3RIC3SVROVUKFJSLBODX52/bundle.json","state_url":"https://pith.science/pith/YGEJ3RIC3SVROVUKFJSLBODX52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YGEJ3RIC3SVROVUKFJSLBODX52/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":"2026-06-06T16:03:02Z","links":{"resolver":"https://pith.science/pith/YGEJ3RIC3SVROVUKFJSLBODX52","bundle":"https://pith.science/pith/YGEJ3RIC3SVROVUKFJSLBODX52/bundle.json","state":"https://pith.science/pith/YGEJ3RIC3SVROVUKFJSLBODX52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YGEJ3RIC3SVROVUKFJSLBODX52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YGEJ3RIC3SVROVUKFJSLBODX52","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":"afdc137f60a188bb56407122021c3979976eb9e084401d5375800f583be94e3b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-26T19:02:20Z","title_canon_sha256":"ee40a05a89604d56993f07ff215d5f952712c81d6be21fa6f7e6b1031e5bcd37"},"schema_version":"1.0","source":{"id":"1712.09371","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09371","created_at":"2026-05-18T00:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09371v2","created_at":"2026-05-18T00:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09371","created_at":"2026-05-18T00:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"YGEJ3RIC3SVR","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YGEJ3RIC3SVROVUK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YGEJ3RIC","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:80f1012a7fcf2619cea117eec39cd14f4788f6f35d59b35173a97bf962844b92","target":"graph","created_at":"2026-05-18T00:12:53Z","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":"General concept of a gradation slicing is used to analyze polynomial solutions of ordinary differential equations (ODE) with polynomial coefficients, ${\\cal L}\\psi=0$, where ${\\cal L}=\\sum_l p_l(z) d_z^l$, $p_l(z)$ are polynomials, $z$ is a one-dimensional coordinate, and $d_z=d/dz$. It is not required that ODE is either (i) Fuchsian or (ii) leads to a usual Sturm-Liouville eigenvalue problem. General necessary and sufficient conditions for the existence of a polynomial solution are formulated involving constraint relations. The necessary condition for a polynomial solution of $n$th degree to ","authors_text":"Alexander Moroz","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-26T19:02:20Z","title":"A unified treatment of polynomial sectors and constraint polynomials of the Rabi models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09371","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:c2e9ed9f4b286fe37ebac5cb5d6e73a31353b20a016d222e845e9b5f37f461a6","target":"record","created_at":"2026-05-18T00:12:53Z","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":"afdc137f60a188bb56407122021c3979976eb9e084401d5375800f583be94e3b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-12-26T19:02:20Z","title_canon_sha256":"ee40a05a89604d56993f07ff215d5f952712c81d6be21fa6f7e6b1031e5bcd37"},"schema_version":"1.0","source":{"id":"1712.09371","kind":"arxiv","version":2}},"canonical_sha256":"c1889dc502dcab17568a2a64b0b877ee861aa9efd92199fb4877375c0a055b5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1889dc502dcab17568a2a64b0b877ee861aa9efd92199fb4877375c0a055b5b","first_computed_at":"2026-05-18T00:12:53.711459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:53.711459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8v661GExZOGbKsyVctmvkJ7+2dYWlgY6XWSg53Z9lNvXWhUUFoH0GYu67pR37h/uDPL8Bx0hTmkL9PlLeg1zAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:53.711995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09371","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2e9ed9f4b286fe37ebac5cb5d6e73a31353b20a016d222e845e9b5f37f461a6","sha256:80f1012a7fcf2619cea117eec39cd14f4788f6f35d59b35173a97bf962844b92"],"state_sha256":"61c0e505dff29ca50f41634b66a8c2cce8331e228e9dbf566e88ceacaa5db945"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTi4HYmeO/MdvwWmBapkr8Oea87IoJ1ivluKozhV4aLvTBJVc9stEQYVzM85Yu65uO+7SEGB52+zBZrxhtwABA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:03:02.316623Z","bundle_sha256":"f0ea0eb3dab4c0c947b3e18525436cce4414362a0e973612147c70a3f5bec3f3"}}