{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KIXXEL6EAADYV2CWTJLA5TR67Y","short_pith_number":"pith:KIXXEL6E","canonical_record":{"source":{"id":"1307.4033","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T17:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"8b184e8b5f6fa7ea73b66ebeab6f4a653b5d515602a4d1a88e8395febf43362d","abstract_canon_sha256":"6525998f99a22291710e08b74edbd30773f0770fc1608af02defd822dd99baa3"},"schema_version":"1.0"},"canonical_sha256":"522f722fc400078ae8569a560ece3efe2afc83084ea767f5f2c0813b2c251796","source":{"kind":"arxiv","id":"1307.4033","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4033","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4033v3","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4033","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"KIXXEL6EAADY","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KIXXEL6EAADYV2CW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KIXXEL6E","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KIXXEL6EAADYV2CWTJLA5TR67Y","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4033","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T17:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"8b184e8b5f6fa7ea73b66ebeab6f4a653b5d515602a4d1a88e8395febf43362d","abstract_canon_sha256":"6525998f99a22291710e08b74edbd30773f0770fc1608af02defd822dd99baa3"},"schema_version":"1.0"},"canonical_sha256":"522f722fc400078ae8569a560ece3efe2afc83084ea767f5f2c0813b2c251796","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:28.188993Z","signature_b64":"nnF7cqFVqteaf+sFQbSZJg91LBFucZ4SBmiFd3NG7TjsUN7NEyay5ajL7qFPILJiwZ75aPywRyXcVgQ4bZEwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"522f722fc400078ae8569a560ece3efe2afc83084ea767f5f2c0813b2c251796","last_reissued_at":"2026-05-17T23:39:28.188357Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:28.188357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4033","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Ucd8K913XkIQTM6KY8CJ2ZN2o38dvA5LJV2jPEzaTQh6TzhCO2g4W76qKZmGkHB3/L3jh8wucWUYIYM7yWcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:32:06.997232Z"},"content_sha256":"3fb5b6fed4e2a6ea357789dd4bdbb6aaca5535e3c3478a3f40d527389fc5b9e4","schema_version":"1.0","event_id":"sha256:3fb5b6fed4e2a6ea357789dd4bdbb6aaca5535e3c3478a3f40d527389fc5b9e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KIXXEL6EAADYV2CWTJLA5TR67Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Hitchin systems on rational surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eric M. Rains","submitted_at":"2013-07-15T17:50:04Z","abstract_excerpt":"By analogy with work of Hitchin on integrable systems, we construct natural relaxations of several kinds of moduli spaces of difference equations, with special attention to a particular class of difference equations on an elliptic curve (arising in the theory of elliptic special functions). The common feature of the relaxations is that they can be identified with moduli spaces of sheaves on rational surfaces. Not only does this make various natural questions become purely geometric (rigid equations correspond to -2-curves), it also establishes a number of nontrivial correspondences between dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4033","kind":"arxiv","version":3},"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":"2026-05-17T23:39:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqqIfwYH8cKLDJ5KKPaN+GZP52CpS/9Z2Rqy7i+YLYuMTyhmd5rsfEOH1jdAS1+/+y/LRyNpI9s9P1CrqXEQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:32:06.997625Z"},"content_sha256":"f13452ae85b8cef331762f08b7dbf79454543d387512eb8a7a4fd754c995937a","schema_version":"1.0","event_id":"sha256:f13452ae85b8cef331762f08b7dbf79454543d387512eb8a7a4fd754c995937a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIXXEL6EAADYV2CWTJLA5TR67Y/bundle.json","state_url":"https://pith.science/pith/KIXXEL6EAADYV2CWTJLA5TR67Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIXXEL6EAADYV2CWTJLA5TR67Y/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":"2026-05-27T10:32:06Z","links":{"resolver":"https://pith.science/pith/KIXXEL6EAADYV2CWTJLA5TR67Y","bundle":"https://pith.science/pith/KIXXEL6EAADYV2CWTJLA5TR67Y/bundle.json","state":"https://pith.science/pith/KIXXEL6EAADYV2CWTJLA5TR67Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIXXEL6EAADYV2CWTJLA5TR67Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KIXXEL6EAADYV2CWTJLA5TR67Y","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":"6525998f99a22291710e08b74edbd30773f0770fc1608af02defd822dd99baa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T17:50:04Z","title_canon_sha256":"8b184e8b5f6fa7ea73b66ebeab6f4a653b5d515602a4d1a88e8395febf43362d"},"schema_version":"1.0","source":{"id":"1307.4033","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4033","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4033v3","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4033","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"KIXXEL6EAADY","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KIXXEL6EAADYV2CW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KIXXEL6E","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:f13452ae85b8cef331762f08b7dbf79454543d387512eb8a7a4fd754c995937a","target":"graph","created_at":"2026-05-17T23:39:28Z","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":"By analogy with work of Hitchin on integrable systems, we construct natural relaxations of several kinds of moduli spaces of difference equations, with special attention to a particular class of difference equations on an elliptic curve (arising in the theory of elliptic special functions). The common feature of the relaxations is that they can be identified with moduli spaces of sheaves on rational surfaces. Not only does this make various natural questions become purely geometric (rigid equations correspond to -2-curves), it also establishes a number of nontrivial correspondences between dif","authors_text":"Eric M. Rains","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T17:50:04Z","title":"Generalized Hitchin systems on rational surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4033","kind":"arxiv","version":3},"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":"sha256:3fb5b6fed4e2a6ea357789dd4bdbb6aaca5535e3c3478a3f40d527389fc5b9e4","target":"record","created_at":"2026-05-17T23:39:28Z","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":"6525998f99a22291710e08b74edbd30773f0770fc1608af02defd822dd99baa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T17:50:04Z","title_canon_sha256":"8b184e8b5f6fa7ea73b66ebeab6f4a653b5d515602a4d1a88e8395febf43362d"},"schema_version":"1.0","source":{"id":"1307.4033","kind":"arxiv","version":3}},"canonical_sha256":"522f722fc400078ae8569a560ece3efe2afc83084ea767f5f2c0813b2c251796","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"522f722fc400078ae8569a560ece3efe2afc83084ea767f5f2c0813b2c251796","first_computed_at":"2026-05-17T23:39:28.188357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:28.188357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nnF7cqFVqteaf+sFQbSZJg91LBFucZ4SBmiFd3NG7TjsUN7NEyay5ajL7qFPILJiwZ75aPywRyXcVgQ4bZEwDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:28.188993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4033","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fb5b6fed4e2a6ea357789dd4bdbb6aaca5535e3c3478a3f40d527389fc5b9e4","sha256:f13452ae85b8cef331762f08b7dbf79454543d387512eb8a7a4fd754c995937a"],"state_sha256":"ec141b0384b9b9f4393ff45e0f737ad0e5ca30f2dd8333de1278157cafc50aef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3IZwDZOxDaOYA4HobS7JbDDQInoJEn+TSsIxjvgO6jF8c1CEDiGaiw0DzTjOeUXvyZODdHM6SoyHxxLC/h+cCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:32:06.999831Z","bundle_sha256":"8a0b4be39a6bf2ff494cf32781f21f787e8148e97046f8d1885527014b729c81"}}