{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2UPJAMEQLVGHYNOXJ52R6I7WLV","short_pith_number":"pith:2UPJAMEQ","canonical_record":{"source":{"id":"1506.06545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-22T10:48:49Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"188c494cf596bcefdb0faeafd3a3095740c4a421afcff0dfad48931b94df7037","abstract_canon_sha256":"f488a6c796efa50a3a4f326d4dd23f3f900a2b960fc28fd8763ace5cc3c6c752"},"schema_version":"1.0"},"canonical_sha256":"d51e9030905d4c7c35d74f751f23f65d6a876ca095991aa7430280fa58fdd921","source":{"kind":"arxiv","id":"1506.06545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06545","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06545v1","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06545","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"2UPJAMEQLVGH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2UPJAMEQLVGHYNOX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2UPJAMEQ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2UPJAMEQLVGHYNOXJ52R6I7WLV","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-22T10:48:49Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"188c494cf596bcefdb0faeafd3a3095740c4a421afcff0dfad48931b94df7037","abstract_canon_sha256":"f488a6c796efa50a3a4f326d4dd23f3f900a2b960fc28fd8763ace5cc3c6c752"},"schema_version":"1.0"},"canonical_sha256":"d51e9030905d4c7c35d74f751f23f65d6a876ca095991aa7430280fa58fdd921","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:44.881382Z","signature_b64":"/3GXFpHdXpIAcasClUIioEI3mJZ+sJWFrdU57dAiFHg+g9s6/XnVB64PRzxMbmbab7QkJyll/2wU5BVFRG0ACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d51e9030905d4c7c35d74f751f23f65d6a876ca095991aa7430280fa58fdd921","last_reissued_at":"2026-05-18T01:41:44.880862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:44.880862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06545","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":"2026-05-18T01:41:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ur4FM5WRXCxcC/qe76ITGJtqLAVLxlJd3TMnDbmFNRShhvGd1bXHDjJM3R1HUUAjs1A+RlfQEeSVa4UE4EZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:09:03.535254Z"},"content_sha256":"c69fd3a6fc3e83b5b936ec52c4a680d3f1960a9eb417d3988fc32feb1ee888d8","schema_version":"1.0","event_id":"sha256:c69fd3a6fc3e83b5b936ec52c4a680d3f1960a9eb417d3988fc32feb1ee888d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2UPJAMEQLVGHYNOXJ52R6I7WLV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian system for the elliptic form of Painlev\\'{e} VI equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AG","authors_text":"Chang-shou Lin, Ting-Jung Kuo, Zhijie Chen","submitted_at":"2015-06-22T10:48:49Z","abstract_excerpt":"In literature, it is known that any solution of Painlev\\'{e} VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on $\\mathbb{CP}^{1}$. In this paper, we extend this isomonodromy theory on $\\mathbb{CP}^{1}$ to the moduli space of elliptic curves by studying the isomonodromic deformation of the generalized Lam\\'{e} equation. Among other things, we prove that the isomonodromic equation is a new Hamiltonian system, which is equivalent to the elliptic form of Painlev\\'{e} VI equation for generic parameters. For Painlev\\'{e} VI equation with some special parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06545","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":"2026-05-18T01:41:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFmyPBwgHI/nmMP26Jv1UTWlemxpuyQVXHJCghgMKvqYKWEq1B2XclpgTvzVrfy4C5BLU4tHrO2oSJ6V5h+ZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:09:03.535638Z"},"content_sha256":"d26b106a123a0e23fcf10e452aa817a5cd8d19d9559b21cc0a7721f55e553f89","schema_version":"1.0","event_id":"sha256:d26b106a123a0e23fcf10e452aa817a5cd8d19d9559b21cc0a7721f55e553f89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV/bundle.json","state_url":"https://pith.science/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV/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":"2026-05-27T18:09:03Z","links":{"resolver":"https://pith.science/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV","bundle":"https://pith.science/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV/bundle.json","state":"https://pith.science/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UPJAMEQLVGHYNOXJ52R6I7WLV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2UPJAMEQLVGHYNOXJ52R6I7WLV","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":"f488a6c796efa50a3a4f326d4dd23f3f900a2b960fc28fd8763ace5cc3c6c752","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-22T10:48:49Z","title_canon_sha256":"188c494cf596bcefdb0faeafd3a3095740c4a421afcff0dfad48931b94df7037"},"schema_version":"1.0","source":{"id":"1506.06545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06545","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06545v1","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06545","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"2UPJAMEQLVGH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2UPJAMEQLVGHYNOX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2UPJAMEQ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:d26b106a123a0e23fcf10e452aa817a5cd8d19d9559b21cc0a7721f55e553f89","target":"graph","created_at":"2026-05-18T01:41:44Z","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 literature, it is known that any solution of Painlev\\'{e} VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on $\\mathbb{CP}^{1}$. In this paper, we extend this isomonodromy theory on $\\mathbb{CP}^{1}$ to the moduli space of elliptic curves by studying the isomonodromic deformation of the generalized Lam\\'{e} equation. Among other things, we prove that the isomonodromic equation is a new Hamiltonian system, which is equivalent to the elliptic form of Painlev\\'{e} VI equation for generic parameters. For Painlev\\'{e} VI equation with some special parameter","authors_text":"Chang-shou Lin, Ting-Jung Kuo, Zhijie Chen","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-22T10:48:49Z","title":"Hamiltonian system for the elliptic form of Painlev\\'{e} VI equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06545","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:c69fd3a6fc3e83b5b936ec52c4a680d3f1960a9eb417d3988fc32feb1ee888d8","target":"record","created_at":"2026-05-18T01:41:44Z","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":"f488a6c796efa50a3a4f326d4dd23f3f900a2b960fc28fd8763ace5cc3c6c752","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-22T10:48:49Z","title_canon_sha256":"188c494cf596bcefdb0faeafd3a3095740c4a421afcff0dfad48931b94df7037"},"schema_version":"1.0","source":{"id":"1506.06545","kind":"arxiv","version":1}},"canonical_sha256":"d51e9030905d4c7c35d74f751f23f65d6a876ca095991aa7430280fa58fdd921","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d51e9030905d4c7c35d74f751f23f65d6a876ca095991aa7430280fa58fdd921","first_computed_at":"2026-05-18T01:41:44.880862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:44.880862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3GXFpHdXpIAcasClUIioEI3mJZ+sJWFrdU57dAiFHg+g9s6/XnVB64PRzxMbmbab7QkJyll/2wU5BVFRG0ACw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:44.881382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c69fd3a6fc3e83b5b936ec52c4a680d3f1960a9eb417d3988fc32feb1ee888d8","sha256:d26b106a123a0e23fcf10e452aa817a5cd8d19d9559b21cc0a7721f55e553f89"],"state_sha256":"c77271a9e0c7b0a5a5e2925088cbdd139c82b70397a5fdb37cab2f7e9216b264"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGgUMU+J8TeTOGB0/xumVA55h6pblZ04bsFXkTPB7SUGs4n0nqEo84hqdxaP1Kj/Z3ZmjqIy2kJa+UM8YKjuBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:09:03.538302Z","bundle_sha256":"294c5fa8ab13396a113b554fbf6887c82f8359123913f7f8846a6a85d629aae5"}}