{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FGRETZ3GZU46B4KXAN76PVU5FA","short_pith_number":"pith:FGRETZ3G","canonical_record":{"source":{"id":"1102.3858","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-18T15:47:18Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"21507cb52342b14049a65e05dadd86298201038700a4a7efc6ae97dfc8def919","abstract_canon_sha256":"053f9c262f0ea922f128ba1167896af690d2622035de0f48616655178d9ce7b4"},"schema_version":"1.0"},"canonical_sha256":"29a249e766cd39e0f157037fe7d69d2807cb9090f95bc4229cca1cbcfa18c1dc","source":{"kind":"arxiv","id":"1102.3858","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3858","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3858v2","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3858","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"FGRETZ3GZU46","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FGRETZ3GZU46B4KX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FGRETZ3G","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FGRETZ3GZU46B4KXAN76PVU5FA","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3858","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-18T15:47:18Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"21507cb52342b14049a65e05dadd86298201038700a4a7efc6ae97dfc8def919","abstract_canon_sha256":"053f9c262f0ea922f128ba1167896af690d2622035de0f48616655178d9ce7b4"},"schema_version":"1.0"},"canonical_sha256":"29a249e766cd39e0f157037fe7d69d2807cb9090f95bc4229cca1cbcfa18c1dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:44.029805Z","signature_b64":"l9GWwkLiNERq6wN+BJhLiL40uCB5IVcoT3y4RCY8krPuRljJk2IcaOzyvjlO8NjnEYmB1cvoyppQN0GWZ6tTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29a249e766cd39e0f157037fe7d69d2807cb9090f95bc4229cca1cbcfa18c1dc","last_reissued_at":"2026-05-18T01:09:44.029203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:44.029203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3858","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":"2026-05-18T01:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9TuvqAo60MIwTzUFrocL5qe58jn5vBwj5rUoNcv5+O5XmNm/R7ser9cPdR+rhPMwzpRg4+L05l/6HgIxn8QSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:17:50.191216Z"},"content_sha256":"7d4f442e475e033360b1a7b2a123a98832c500d86316f858d8ce9b3b20dcf5bd","schema_version":"1.0","event_id":"sha256:7d4f442e475e033360b1a7b2a123a98832c500d86316f858d8ce9b3b20dcf5bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FGRETZ3GZU46B4KXAN76PVU5FA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The dimension of the space of Garnier equations with fixed locus of apparent singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AG","authors_text":"Szilard Szabo","submitted_at":"2011-02-18T15:47:18Z","abstract_excerpt":"We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and apparent singularities at a finite set $Q$ (disjoint from $P$) determine a linear system of maximal rank. In addition, we show that certain auxiliary parameters can also be fixed. This enables us to conclude that the family of such differential equations is of the expected dimension and to define a birational map between an open subset of the moduli space of loga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3858","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":"2026-05-18T01:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JoOM00jbseTDhHOZAtOf0hoPuYodWVxVAyjzLvWoJhqoBvYL6VrrHBPYGjlRj9SzlzwQRbjylUt1YFT/hfKTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:17:50.191591Z"},"content_sha256":"6b14be693e0d25871e193710e4f3ab86a71944bc17da764d2ba5fe83f93fefd3","schema_version":"1.0","event_id":"sha256:6b14be693e0d25871e193710e4f3ab86a71944bc17da764d2ba5fe83f93fefd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGRETZ3GZU46B4KXAN76PVU5FA/bundle.json","state_url":"https://pith.science/pith/FGRETZ3GZU46B4KXAN76PVU5FA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGRETZ3GZU46B4KXAN76PVU5FA/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":"2026-06-24T03:17:50Z","links":{"resolver":"https://pith.science/pith/FGRETZ3GZU46B4KXAN76PVU5FA","bundle":"https://pith.science/pith/FGRETZ3GZU46B4KXAN76PVU5FA/bundle.json","state":"https://pith.science/pith/FGRETZ3GZU46B4KXAN76PVU5FA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGRETZ3GZU46B4KXAN76PVU5FA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FGRETZ3GZU46B4KXAN76PVU5FA","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":"053f9c262f0ea922f128ba1167896af690d2622035de0f48616655178d9ce7b4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-18T15:47:18Z","title_canon_sha256":"21507cb52342b14049a65e05dadd86298201038700a4a7efc6ae97dfc8def919"},"schema_version":"1.0","source":{"id":"1102.3858","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3858","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3858v2","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3858","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"FGRETZ3GZU46","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FGRETZ3GZU46B4KX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FGRETZ3G","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:6b14be693e0d25871e193710e4f3ab86a71944bc17da764d2ba5fe83f93fefd3","target":"graph","created_at":"2026-05-18T01:09:44Z","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":"We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and apparent singularities at a finite set $Q$ (disjoint from $P$) determine a linear system of maximal rank. In addition, we show that certain auxiliary parameters can also be fixed. This enables us to conclude that the family of such differential equations is of the expected dimension and to define a birational map between an open subset of the moduli space of loga","authors_text":"Szilard Szabo","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-18T15:47:18Z","title":"The dimension of the space of Garnier equations with fixed locus of apparent singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3858","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":"sha256:7d4f442e475e033360b1a7b2a123a98832c500d86316f858d8ce9b3b20dcf5bd","target":"record","created_at":"2026-05-18T01:09:44Z","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":"053f9c262f0ea922f128ba1167896af690d2622035de0f48616655178d9ce7b4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-18T15:47:18Z","title_canon_sha256":"21507cb52342b14049a65e05dadd86298201038700a4a7efc6ae97dfc8def919"},"schema_version":"1.0","source":{"id":"1102.3858","kind":"arxiv","version":2}},"canonical_sha256":"29a249e766cd39e0f157037fe7d69d2807cb9090f95bc4229cca1cbcfa18c1dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29a249e766cd39e0f157037fe7d69d2807cb9090f95bc4229cca1cbcfa18c1dc","first_computed_at":"2026-05-18T01:09:44.029203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:44.029203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l9GWwkLiNERq6wN+BJhLiL40uCB5IVcoT3y4RCY8krPuRljJk2IcaOzyvjlO8NjnEYmB1cvoyppQN0GWZ6tTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:44.029805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3858","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d4f442e475e033360b1a7b2a123a98832c500d86316f858d8ce9b3b20dcf5bd","sha256:6b14be693e0d25871e193710e4f3ab86a71944bc17da764d2ba5fe83f93fefd3"],"state_sha256":"0dc5bd56c4bd327b084d96f3d0b4a769f75d175d1d144de60d6a01569c1c9bbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v1ocrek3o9eNHbpg26UD9nfYkhRMb36P6NFbLpDJ+xVaDaObvwkXbW09xd3P0Nb70t5OEvEXfjB5tR20YGlCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T03:17:50.193586Z","bundle_sha256":"fd23daf05172623fd261bae19aa47c9c28e4339f5a322b9fb8d334a7ac4d8fd4"}}