{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MLRAEY5IDMBDIRVKBHUWM4OMDF","short_pith_number":"pith:MLRAEY5I","canonical_record":{"source":{"id":"1008.0911","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-05T04:52:21Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d2d6c04bf091b78b34322957430349246464e971afdf2b0d549b60225ad7e693","abstract_canon_sha256":"3af12f0609ea8616b586e23bf242e920b3ce975382076b75c4a2633224ec3ee7"},"schema_version":"1.0"},"canonical_sha256":"62e20263a81b023446aa09e96671cc196bcd0a887826db75804572be3eec2f70","source":{"kind":"arxiv","id":"1008.0911","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0911","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0911v3","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0911","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"MLRAEY5IDMBD","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MLRAEY5IDMBDIRVK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MLRAEY5I","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MLRAEY5IDMBDIRVKBHUWM4OMDF","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0911","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-05T04:52:21Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d2d6c04bf091b78b34322957430349246464e971afdf2b0d549b60225ad7e693","abstract_canon_sha256":"3af12f0609ea8616b586e23bf242e920b3ce975382076b75c4a2633224ec3ee7"},"schema_version":"1.0"},"canonical_sha256":"62e20263a81b023446aa09e96671cc196bcd0a887826db75804572be3eec2f70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:51.040660Z","signature_b64":"EhZDulwaGxoDKxCpr0YwmTj4MWGAA9/jn+Uj3arniaQ2B/B3gwb/tVK8ZiOFwuGtpex3xV9MP37oDBJKmJ/WBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62e20263a81b023446aa09e96671cc196bcd0a887826db75804572be3eec2f70","last_reissued_at":"2026-05-18T01:32:51.040114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:51.040114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0911","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":"2026-05-18T01:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eT572oGRwIyMEEkbJIagmaY2R0+WCFoWsO4GJ+hWbusM+ooeM0r4e/u4MHXnWLkR5aSP8RRHDVgXUKlaif1GCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T05:50:36.060112Z"},"content_sha256":"12b7a7133693854b375d108238ded22272d885096cc8dbc08cf17e2ce4d0ec8c","schema_version":"1.0","event_id":"sha256:12b7a7133693854b375d108238ded22272d885096cc8dbc08cf17e2ce4d0ec8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MLRAEY5IDMBDIRVKBHUWM4OMDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant degenerations of spherical modules for groups of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Bart Van Steirteghem, Stavros Argyrios Papadakis","submitted_at":"2010-08-05T04:52:21Z","abstract_excerpt":"Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G, with unipotent radical U, and a maximal torus T in B with character group X(T). Let S be a submonoid of X(T) generated by finitely many dominant weights. V. Alexeev and M. Brion introduced a moduli scheme M_S which classifies pairs (X,f) where X is an affine G-variety and f is a T-equivariant isomorphism between the categorical quotient of X by U and the toric variety determined by S. In this paper, we prove that M_S is isomorphic to an affine space when S is the weight monoid of a spherical G-module with G of type A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0911","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":"2026-05-18T01:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9la4np92ZsZynxZxjpLfanZiuV/FMeW0Ki92SimyZ2TJ7V7U9/Y8BLmPjd/1KpghIV3wARyVwTLICFkaHQ4fDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T05:50:36.060821Z"},"content_sha256":"c19d941c5e793487abfd93b39e08d286d49c77e2dd522052c96843237b155613","schema_version":"1.0","event_id":"sha256:c19d941c5e793487abfd93b39e08d286d49c77e2dd522052c96843237b155613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF/bundle.json","state_url":"https://pith.science/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF/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":"2026-05-19T05:50:36Z","links":{"resolver":"https://pith.science/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF","bundle":"https://pith.science/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF/bundle.json","state":"https://pith.science/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MLRAEY5IDMBDIRVKBHUWM4OMDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MLRAEY5IDMBDIRVKBHUWM4OMDF","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":"3af12f0609ea8616b586e23bf242e920b3ce975382076b75c4a2633224ec3ee7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-05T04:52:21Z","title_canon_sha256":"d2d6c04bf091b78b34322957430349246464e971afdf2b0d549b60225ad7e693"},"schema_version":"1.0","source":{"id":"1008.0911","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0911","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0911v3","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0911","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"MLRAEY5IDMBD","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MLRAEY5IDMBDIRVK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MLRAEY5I","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:c19d941c5e793487abfd93b39e08d286d49c77e2dd522052c96843237b155613","target":"graph","created_at":"2026-05-18T01:32:51Z","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":"Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G, with unipotent radical U, and a maximal torus T in B with character group X(T). Let S be a submonoid of X(T) generated by finitely many dominant weights. V. Alexeev and M. Brion introduced a moduli scheme M_S which classifies pairs (X,f) where X is an affine G-variety and f is a T-equivariant isomorphism between the categorical quotient of X by U and the toric variety determined by S. In this paper, we prove that M_S is isomorphic to an affine space when S is the weight monoid of a spherical G-module with G of type A.","authors_text":"Bart Van Steirteghem, Stavros Argyrios Papadakis","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-05T04:52:21Z","title":"Equivariant degenerations of spherical modules for groups of type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0911","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":"sha256:12b7a7133693854b375d108238ded22272d885096cc8dbc08cf17e2ce4d0ec8c","target":"record","created_at":"2026-05-18T01:32:51Z","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":"3af12f0609ea8616b586e23bf242e920b3ce975382076b75c4a2633224ec3ee7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-05T04:52:21Z","title_canon_sha256":"d2d6c04bf091b78b34322957430349246464e971afdf2b0d549b60225ad7e693"},"schema_version":"1.0","source":{"id":"1008.0911","kind":"arxiv","version":3}},"canonical_sha256":"62e20263a81b023446aa09e96671cc196bcd0a887826db75804572be3eec2f70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62e20263a81b023446aa09e96671cc196bcd0a887826db75804572be3eec2f70","first_computed_at":"2026-05-18T01:32:51.040114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:51.040114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EhZDulwaGxoDKxCpr0YwmTj4MWGAA9/jn+Uj3arniaQ2B/B3gwb/tVK8ZiOFwuGtpex3xV9MP37oDBJKmJ/WBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:51.040660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0911","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12b7a7133693854b375d108238ded22272d885096cc8dbc08cf17e2ce4d0ec8c","sha256:c19d941c5e793487abfd93b39e08d286d49c77e2dd522052c96843237b155613"],"state_sha256":"327d0a0219130ac20f0aa8d55633ba5d205f755c26fdbd3e0c76c2bab93163fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHpjYAg7+3aSdre8eV6KwYAblUUdQGpbEb8oOmovcMllcTxx6w53My+EZvx/PqxwiSlNvzay6igV/TJeBW3ADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T05:50:36.063092Z","bundle_sha256":"9a6b301189b1a5c01581ecff6806a19cb745bf5760b849e4b0701ca0c4bbfe96"}}