{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LTSW22T3PJTUNTDAYQ6AHN2IAZ","short_pith_number":"pith:LTSW22T3","canonical_record":{"source":{"id":"1107.1179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-06T16:35:36Z","cross_cats_sorted":[],"title_canon_sha256":"b03d012f1fbddc86836b5c75845a945b7494426543550085265a6a9640f960a7","abstract_canon_sha256":"b402816e1190ae5195c931118fcf2b3ad906722de2748acde945c34582b44d83"},"schema_version":"1.0"},"canonical_sha256":"5ce56d6a7b7a6746cc60c43c03b748065268da9e1899a52a75fd2d6d07832cd7","source":{"kind":"arxiv","id":"1107.1179","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1179","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1179v2","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1179","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"LTSW22T3PJTU","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LTSW22T3PJTUNTDA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LTSW22T3","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LTSW22T3PJTUNTDAYQ6AHN2IAZ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-06T16:35:36Z","cross_cats_sorted":[],"title_canon_sha256":"b03d012f1fbddc86836b5c75845a945b7494426543550085265a6a9640f960a7","abstract_canon_sha256":"b402816e1190ae5195c931118fcf2b3ad906722de2748acde945c34582b44d83"},"schema_version":"1.0"},"canonical_sha256":"5ce56d6a7b7a6746cc60c43c03b748065268da9e1899a52a75fd2d6d07832cd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:02.381442Z","signature_b64":"a9HjpJVITAvhAHUrhXNxJnJZUtWI+o54Dgwu230y8vC8cHMvUbjJ0q6oDI2GILGet70ehyJDxnL+8H2zKueaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ce56d6a7b7a6746cc60c43c03b748065268da9e1899a52a75fd2d6d07832cd7","last_reissued_at":"2026-05-18T03:51:02.380824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:02.380824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1179","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":"2026-05-18T03:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5mRijhEQYDQJOAOo3jakZ+yWSs6AYEQJVNHizmilNomPzKYtWtVdu0DP1VO2O9mUK9APyBF1LPuFrNKZ1HqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:53:24.267032Z"},"content_sha256":"dd4561da963d64ed970365241aa114a81774fa7a701f76872de583c985aaf04f","schema_version":"1.0","event_id":"sha256:dd4561da963d64ed970365241aa114a81774fa7a701f76872de583c985aaf04f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LTSW22T3PJTUNTDAYQ6AHN2IAZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solution algebras of differential equations and quasi-homogeneous varieties: a new differential Galois correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yves Andre","submitted_at":"2011-07-06T16:35:36Z","abstract_excerpt":"We develop a new connection between Differential Algebra and Geometric Invariant Theory, based on an anti-equivalence of categories between solution algebras associated to a linear differential equation (i.e. differential algebras generated by finitely many polynomials in a fundamental set of solutions), and affine quasi-homogeneous varieties (over the constant field) for the differential Galois group of the equation.\n  Solution algebras can be associated to any connection over a smooth affine variety. It turns out that he spectrum of a solution algebra is an algebraic fiber space over the bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1179","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":"2026-05-18T03:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOk/UMND0cvS2U+JVM8EO5M5cEgt48aA9oUx9AjZ3r/RJuGj7Zz5CQXSOArzQu5WNe4YohUP5Tp4PzNso69tAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:53:24.267749Z"},"content_sha256":"6cf3e1b85286c90eaef9aa9275d959831b76e4c3f87a12ba369662078c9308af","schema_version":"1.0","event_id":"sha256:6cf3e1b85286c90eaef9aa9275d959831b76e4c3f87a12ba369662078c9308af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ/bundle.json","state_url":"https://pith.science/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ/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":"2026-05-26T17:53:24Z","links":{"resolver":"https://pith.science/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ","bundle":"https://pith.science/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ/bundle.json","state":"https://pith.science/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTSW22T3PJTUNTDAYQ6AHN2IAZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LTSW22T3PJTUNTDAYQ6AHN2IAZ","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":"b402816e1190ae5195c931118fcf2b3ad906722de2748acde945c34582b44d83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-06T16:35:36Z","title_canon_sha256":"b03d012f1fbddc86836b5c75845a945b7494426543550085265a6a9640f960a7"},"schema_version":"1.0","source":{"id":"1107.1179","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1179","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1179v2","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1179","created_at":"2026-05-18T03:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"LTSW22T3PJTU","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LTSW22T3PJTUNTDA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LTSW22T3","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:6cf3e1b85286c90eaef9aa9275d959831b76e4c3f87a12ba369662078c9308af","target":"graph","created_at":"2026-05-18T03:51:02Z","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 develop a new connection between Differential Algebra and Geometric Invariant Theory, based on an anti-equivalence of categories between solution algebras associated to a linear differential equation (i.e. differential algebras generated by finitely many polynomials in a fundamental set of solutions), and affine quasi-homogeneous varieties (over the constant field) for the differential Galois group of the equation.\n  Solution algebras can be associated to any connection over a smooth affine variety. It turns out that he spectrum of a solution algebra is an algebraic fiber space over the bas","authors_text":"Yves Andre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-06T16:35:36Z","title":"Solution algebras of differential equations and quasi-homogeneous varieties: a new differential Galois correspondence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1179","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:dd4561da963d64ed970365241aa114a81774fa7a701f76872de583c985aaf04f","target":"record","created_at":"2026-05-18T03:51:02Z","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":"b402816e1190ae5195c931118fcf2b3ad906722de2748acde945c34582b44d83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-06T16:35:36Z","title_canon_sha256":"b03d012f1fbddc86836b5c75845a945b7494426543550085265a6a9640f960a7"},"schema_version":"1.0","source":{"id":"1107.1179","kind":"arxiv","version":2}},"canonical_sha256":"5ce56d6a7b7a6746cc60c43c03b748065268da9e1899a52a75fd2d6d07832cd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ce56d6a7b7a6746cc60c43c03b748065268da9e1899a52a75fd2d6d07832cd7","first_computed_at":"2026-05-18T03:51:02.380824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:02.380824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a9HjpJVITAvhAHUrhXNxJnJZUtWI+o54Dgwu230y8vC8cHMvUbjJ0q6oDI2GILGet70ehyJDxnL+8H2zKueaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:02.381442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1179","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd4561da963d64ed970365241aa114a81774fa7a701f76872de583c985aaf04f","sha256:6cf3e1b85286c90eaef9aa9275d959831b76e4c3f87a12ba369662078c9308af"],"state_sha256":"9fe9fe08079e0ce11def50ed44d65a102da63461cefe477a948b8c33c08de1fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"thDD1GRtS8ZrhxCSBzXKHt0p/BTMwMoVnq9zjzfi/l+P3+eMzodaQAzX4Wqfo3Z5i6ASN+48iWISDAMVJ9vwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:53:24.271215Z","bundle_sha256":"48831405b9aa155e6931e1b99cfab51668dc502078641537cecfdb3e5965e20a"}}