{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:N43NPORKYWAVO76YW5DS3YJKK4","short_pith_number":"pith:N43NPORK","canonical_record":{"source":{"id":"1112.2916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-13T15:26:39Z","cross_cats_sorted":["math.CA","math.LO"],"title_canon_sha256":"59b55988e65ced6d1f567b2edab4359750a63e75d43d22d65fa2ae0c111f754a","abstract_canon_sha256":"9cdd453cb431930587891af47e6e1001a427f495ee880d144d741c9aa427a320"},"schema_version":"1.0"},"canonical_sha256":"6f36d7ba2ac581577fd8b7472de12a570f2092f2d826d6ec00e7c435b131da2f","source":{"kind":"arxiv","id":"1112.2916","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2916","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2916v1","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2916","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"pith_short_12","alias_value":"N43NPORKYWAV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N43NPORKYWAVO76Y","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N43NPORK","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:N43NPORKYWAVO76YW5DS3YJKK4","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-13T15:26:39Z","cross_cats_sorted":["math.CA","math.LO"],"title_canon_sha256":"59b55988e65ced6d1f567b2edab4359750a63e75d43d22d65fa2ae0c111f754a","abstract_canon_sha256":"9cdd453cb431930587891af47e6e1001a427f495ee880d144d741c9aa427a320"},"schema_version":"1.0"},"canonical_sha256":"6f36d7ba2ac581577fd8b7472de12a570f2092f2d826d6ec00e7c435b131da2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:06.730403Z","signature_b64":"zEk866Wfugy3RCtfI6tS26pC66HjPgE98R5SjHw19GBQPCZuh2Ie8xJqhhZHRGNzQZFaZX6fbbDXATf70fvCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f36d7ba2ac581577fd8b7472de12a570f2092f2d826d6ec00e7c435b131da2f","last_reissued_at":"2026-05-18T00:38:06.729875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:06.729875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2916","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":"2026-05-18T00:38:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OmA7vBNkIkJHN8F2AUk7vnpV+iBw9Y4kykY2vByT5gQXmutZYZZLhLEi9KHKcSWtK+pA8+Nmk7Td/QGL6OWRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:32:09.937688Z"},"content_sha256":"21d44e5da276cce76585f59f423b81f4505c60ed5d152336876b6bb1aef7be60","schema_version":"1.0","event_id":"sha256:21d44e5da276cce76585f59f423b81f4505c60ed5d152336876b6bb1aef7be60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:N43NPORKYWAVO76YW5DS3YJKK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On algebraic relations between solutions of a generic Painleve equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.LO"],"primary_cat":"math.AG","authors_text":"Anand Pillay, Ronnie Nagloo","submitted_at":"2011-12-13T15:26:39Z","abstract_excerpt":"We prove that if y\" = f(y,y',t,\\alpha, \\beta,..) is a generic Painleve equation (i.e. an equation in one of the families PI-PVI but with the complex parameters \\alpha, \\beta,.. algebraically independent) then any algebraic dependence over C(t) between a set of solutions and their derivatives (y_1,..,y_n,y_1',..,y_n') is witnessed by a pair of solutions and their derivatives (y_i,y_i',y_j,y_j'). The proof combines work by the Japanese school on \"irreducibility\" of the Painleve equations, with the trichomoty theorem for strongly minimal sets in differentially closed fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2916","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":"2026-05-18T00:38:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sR6HV1zduR6qGFcs75w2Z1H5SKJp4mVTsv87TXyzTWRwpX4KtNf/fAvSOiOgO0TLOWlPMSwnF7RetmJMn6o7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:32:09.938046Z"},"content_sha256":"61e79aac68be3d72bd47b639747a573cca2e4b163e81d9a18809c32b80685748","schema_version":"1.0","event_id":"sha256:61e79aac68be3d72bd47b639747a573cca2e4b163e81d9a18809c32b80685748"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N43NPORKYWAVO76YW5DS3YJKK4/bundle.json","state_url":"https://pith.science/pith/N43NPORKYWAVO76YW5DS3YJKK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N43NPORKYWAVO76YW5DS3YJKK4/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":"2026-05-30T05:32:09Z","links":{"resolver":"https://pith.science/pith/N43NPORKYWAVO76YW5DS3YJKK4","bundle":"https://pith.science/pith/N43NPORKYWAVO76YW5DS3YJKK4/bundle.json","state":"https://pith.science/pith/N43NPORKYWAVO76YW5DS3YJKK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N43NPORKYWAVO76YW5DS3YJKK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N43NPORKYWAVO76YW5DS3YJKK4","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":"9cdd453cb431930587891af47e6e1001a427f495ee880d144d741c9aa427a320","cross_cats_sorted":["math.CA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-13T15:26:39Z","title_canon_sha256":"59b55988e65ced6d1f567b2edab4359750a63e75d43d22d65fa2ae0c111f754a"},"schema_version":"1.0","source":{"id":"1112.2916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2916","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2916v1","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2916","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"pith_short_12","alias_value":"N43NPORKYWAV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N43NPORKYWAVO76Y","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N43NPORK","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:61e79aac68be3d72bd47b639747a573cca2e4b163e81d9a18809c32b80685748","target":"graph","created_at":"2026-05-18T00:38:06Z","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 prove that if y\" = f(y,y',t,\\alpha, \\beta,..) is a generic Painleve equation (i.e. an equation in one of the families PI-PVI but with the complex parameters \\alpha, \\beta,.. algebraically independent) then any algebraic dependence over C(t) between a set of solutions and their derivatives (y_1,..,y_n,y_1',..,y_n') is witnessed by a pair of solutions and their derivatives (y_i,y_i',y_j,y_j'). The proof combines work by the Japanese school on \"irreducibility\" of the Painleve equations, with the trichomoty theorem for strongly minimal sets in differentially closed fields.","authors_text":"Anand Pillay, Ronnie Nagloo","cross_cats":["math.CA","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-13T15:26:39Z","title":"On algebraic relations between solutions of a generic Painleve equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2916","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":"sha256:21d44e5da276cce76585f59f423b81f4505c60ed5d152336876b6bb1aef7be60","target":"record","created_at":"2026-05-18T00:38:06Z","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":"9cdd453cb431930587891af47e6e1001a427f495ee880d144d741c9aa427a320","cross_cats_sorted":["math.CA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-13T15:26:39Z","title_canon_sha256":"59b55988e65ced6d1f567b2edab4359750a63e75d43d22d65fa2ae0c111f754a"},"schema_version":"1.0","source":{"id":"1112.2916","kind":"arxiv","version":1}},"canonical_sha256":"6f36d7ba2ac581577fd8b7472de12a570f2092f2d826d6ec00e7c435b131da2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f36d7ba2ac581577fd8b7472de12a570f2092f2d826d6ec00e7c435b131da2f","first_computed_at":"2026-05-18T00:38:06.729875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:06.729875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zEk866Wfugy3RCtfI6tS26pC66HjPgE98R5SjHw19GBQPCZuh2Ie8xJqhhZHRGNzQZFaZX6fbbDXATf70fvCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:06.730403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d44e5da276cce76585f59f423b81f4505c60ed5d152336876b6bb1aef7be60","sha256:61e79aac68be3d72bd47b639747a573cca2e4b163e81d9a18809c32b80685748"],"state_sha256":"d5ff694720618c0fbea8b5eada3c2e05609dee27fe33030f3dc6ae7977e5d3b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8TIAqt+31IytLwYc7zMsM5KGAQ9fBc0VUTb1e5kGqZgt1nPbk7HtPXLxTyNuasaAZUAvdqXGmid0+rq4u68Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:32:09.940035Z","bundle_sha256":"182334fc56d726a334b6e994d55726d090bd2fcb37fe6a760abd3afa7ca2fabf"}}