{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5RP6QIWND72KOYI4IQ4KSBCZH7","short_pith_number":"pith:5RP6QIWN","canonical_record":{"source":{"id":"1609.06998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-22T14:38:19Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4bfaff4ad90dbafd13151e6acb0fa23f4a6601f5cee98ca60907065f4946c755","abstract_canon_sha256":"439643c5f21b99e135545444192395f0251b654f28a7050c8e40e94f9dd23122"},"schema_version":"1.0"},"canonical_sha256":"ec5fe822cd1ff4a7611c4438a904593fe3fccfe8ae73214683432cfb40aa30cc","source":{"kind":"arxiv","id":"1609.06998","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06998","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06998v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06998","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"5RP6QIWND72K","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RP6QIWND72KOYI4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RP6QIWN","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5RP6QIWND72KOYI4IQ4KSBCZH7","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-22T14:38:19Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4bfaff4ad90dbafd13151e6acb0fa23f4a6601f5cee98ca60907065f4946c755","abstract_canon_sha256":"439643c5f21b99e135545444192395f0251b654f28a7050c8e40e94f9dd23122"},"schema_version":"1.0"},"canonical_sha256":"ec5fe822cd1ff4a7611c4438a904593fe3fccfe8ae73214683432cfb40aa30cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:04.678184Z","signature_b64":"3SrFMrB8TbR8m2GTWWSE1+YpvbcYyTkzKH8N1a9JU/MJ+rEOJlpf+Oiw3YjIVGnF6UcquqB2BbIGkWei+byuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec5fe822cd1ff4a7611c4438a904593fe3fccfe8ae73214683432cfb40aa30cc","last_reissued_at":"2026-05-18T01:04:04.677780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:04.677780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06998","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":"2026-05-18T01:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"db4KPe/lBB9GqZ6a7nrjge8ydRwL6gJmkKs2hP24F+KaFVEsEjbEAweovkvg6hiiP4bmqc9KJ2JxlYC0dJR1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:55:16.532184Z"},"content_sha256":"ffb04e2d7b3503d41c97964f90a926fb95fd45f91b506037211dc5a0d7846c69","schema_version":"1.0","event_id":"sha256:ffb04e2d7b3503d41c97964f90a926fb95fd45f91b506037211dc5a0d7846c69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5RP6QIWND72KOYI4IQ4KSBCZH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On differential operators on complete symmetric varieties of type $A_1$ and $A_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Beno\\^it Dejoncheere","submitted_at":"2016-09-22T14:38:19Z","abstract_excerpt":"In this paper, we will look at the algebra of global differential operators $D_X$ on wonderful compactifications $X$ of symmetric spaces $G/H$ of type $A_1$ and $A_2$. We will first construct a global differential operator on these varieties that does not come from the infinitesimal action of $\\mathfrak{g}$. We will then focus on type $A_2$, where we will show that $D_X$ is an algebra of finite type, and that for any invertible sheaf ${\\cal L}$ on $X$, $H^{0}(X,{\\cal L})$ is either 0 or a simple left $D_{X,{\\cal L}}$-module. Finally, we will show with the help of local cohomology that this is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06998","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":"2026-05-18T01:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EdH0wUJOgSSEwxT+mye17O28a8YG4dL+a5W/9xcj1Zow8eN1LHixaqGwprBh5BmEs2Ju5w7GmB6oEZ/dlCcyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:55:16.532543Z"},"content_sha256":"477ed90a60f3e90d713db87e54002f8d9fb4cb2846cc0bea1f393ccc265b7580","schema_version":"1.0","event_id":"sha256:477ed90a60f3e90d713db87e54002f8d9fb4cb2846cc0bea1f393ccc265b7580"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RP6QIWND72KOYI4IQ4KSBCZH7/bundle.json","state_url":"https://pith.science/pith/5RP6QIWND72KOYI4IQ4KSBCZH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RP6QIWND72KOYI4IQ4KSBCZH7/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":"2026-06-02T21:55:16Z","links":{"resolver":"https://pith.science/pith/5RP6QIWND72KOYI4IQ4KSBCZH7","bundle":"https://pith.science/pith/5RP6QIWND72KOYI4IQ4KSBCZH7/bundle.json","state":"https://pith.science/pith/5RP6QIWND72KOYI4IQ4KSBCZH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RP6QIWND72KOYI4IQ4KSBCZH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5RP6QIWND72KOYI4IQ4KSBCZH7","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":"439643c5f21b99e135545444192395f0251b654f28a7050c8e40e94f9dd23122","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-22T14:38:19Z","title_canon_sha256":"4bfaff4ad90dbafd13151e6acb0fa23f4a6601f5cee98ca60907065f4946c755"},"schema_version":"1.0","source":{"id":"1609.06998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06998","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06998v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06998","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"5RP6QIWND72K","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5RP6QIWND72KOYI4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5RP6QIWN","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:477ed90a60f3e90d713db87e54002f8d9fb4cb2846cc0bea1f393ccc265b7580","target":"graph","created_at":"2026-05-18T01:04:04Z","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 this paper, we will look at the algebra of global differential operators $D_X$ on wonderful compactifications $X$ of symmetric spaces $G/H$ of type $A_1$ and $A_2$. We will first construct a global differential operator on these varieties that does not come from the infinitesimal action of $\\mathfrak{g}$. We will then focus on type $A_2$, where we will show that $D_X$ is an algebra of finite type, and that for any invertible sheaf ${\\cal L}$ on $X$, $H^{0}(X,{\\cal L})$ is either 0 or a simple left $D_{X,{\\cal L}}$-module. Finally, we will show with the help of local cohomology that this is ","authors_text":"Beno\\^it Dejoncheere","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-22T14:38:19Z","title":"On differential operators on complete symmetric varieties of type $A_1$ and $A_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06998","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:ffb04e2d7b3503d41c97964f90a926fb95fd45f91b506037211dc5a0d7846c69","target":"record","created_at":"2026-05-18T01:04:04Z","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":"439643c5f21b99e135545444192395f0251b654f28a7050c8e40e94f9dd23122","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-22T14:38:19Z","title_canon_sha256":"4bfaff4ad90dbafd13151e6acb0fa23f4a6601f5cee98ca60907065f4946c755"},"schema_version":"1.0","source":{"id":"1609.06998","kind":"arxiv","version":1}},"canonical_sha256":"ec5fe822cd1ff4a7611c4438a904593fe3fccfe8ae73214683432cfb40aa30cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec5fe822cd1ff4a7611c4438a904593fe3fccfe8ae73214683432cfb40aa30cc","first_computed_at":"2026-05-18T01:04:04.677780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:04.677780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3SrFMrB8TbR8m2GTWWSE1+YpvbcYyTkzKH8N1a9JU/MJ+rEOJlpf+Oiw3YjIVGnF6UcquqB2BbIGkWei+byuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:04.678184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffb04e2d7b3503d41c97964f90a926fb95fd45f91b506037211dc5a0d7846c69","sha256:477ed90a60f3e90d713db87e54002f8d9fb4cb2846cc0bea1f393ccc265b7580"],"state_sha256":"f7f388299f8687519f3cb31ce0fbe714b815c2f29c606cae3e6274eea0b276b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uwbU4urrB3LApzWNkWJJkZzFZk6OUAkUNH9+Zr1XjfMdmoKxNVtzdDII+MuS02PY2CQMl/nw17CBDam8HKKWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:55:16.534518Z","bundle_sha256":"ed32c292a34a0e54d21ef20eea45d7ce61d084798f119031bd91991000e3c3f5"}}