{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TPQMXDBBOH5PVZE7YF5K7VNWK3","short_pith_number":"pith:TPQMXDBB","canonical_record":{"source":{"id":"1012.2095","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-09T19:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"f9553878dff1a945032f2dbe751c549a14fbf8847ce83f62d750382b26c25e6f","abstract_canon_sha256":"b0682dcde796be37c8338f00f9cfd19c6c0b83745a134341ed88118625d8d20a"},"schema_version":"1.0"},"canonical_sha256":"9be0cb8c2171fafae49fc17aafd5b656c967f655187afb7faeb749c01b21257a","source":{"kind":"arxiv","id":"1012.2095","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2095","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2095v3","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2095","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"TPQMXDBBOH5P","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TPQMXDBBOH5PVZE7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TPQMXDBB","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TPQMXDBBOH5PVZE7YF5K7VNWK3","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2095","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-09T19:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"f9553878dff1a945032f2dbe751c549a14fbf8847ce83f62d750382b26c25e6f","abstract_canon_sha256":"b0682dcde796be37c8338f00f9cfd19c6c0b83745a134341ed88118625d8d20a"},"schema_version":"1.0"},"canonical_sha256":"9be0cb8c2171fafae49fc17aafd5b656c967f655187afb7faeb749c01b21257a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:01.432479Z","signature_b64":"fBK/Otj8Q6PulOYRxM4CuvWbVDpwPI5yv/eTGs7UjkUnoycXpc4XHj3Wqq6VFlidyG9+sdsBuKuJVWBe5W4pDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9be0cb8c2171fafae49fc17aafd5b656c967f655187afb7faeb749c01b21257a","last_reissued_at":"2026-05-18T02:26:01.431995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:01.431995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2095","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":"2026-05-18T02:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Mt1+/Emq65u7rZdxQrYUU5dH1gqP0uxdoCxQ/cvEalamNyH7uTlRuMp2kok322X8+hLDd4FPp3qWMw3WPwSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:38:10.106376Z"},"content_sha256":"f3900b21dc7bc16b1ddf741917b76ac4cd36a9c11a8f5fc3a157780c56ea9fc5","schema_version":"1.0","event_id":"sha256:f3900b21dc7bc16b1ddf741917b76ac4cd36a9c11a8f5fc3a157780c56ea9fc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TPQMXDBBOH5PVZE7YF5K7VNWK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Brylinski filtration for affine Kac-Moody algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"William Slofstra","submitted_at":"2010-12-09T19:44:33Z","abstract_excerpt":"Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac-Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac-Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2095","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":"2026-05-18T02:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cagb3F4RdI265pO7FxQM+gObISG4vsprtrP9BmJiq1+BJUI9IC31sEHZFYI8gdg13FavdlX+QP3nFuqWBcebCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:38:10.106725Z"},"content_sha256":"08f1f8a8f864e07277a9e2a82708849612bba51eeecad59ffd83fa5479532d8d","schema_version":"1.0","event_id":"sha256:08f1f8a8f864e07277a9e2a82708849612bba51eeecad59ffd83fa5479532d8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3/bundle.json","state_url":"https://pith.science/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3/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":"2026-06-03T10:38:10Z","links":{"resolver":"https://pith.science/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3","bundle":"https://pith.science/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3/bundle.json","state":"https://pith.science/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPQMXDBBOH5PVZE7YF5K7VNWK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TPQMXDBBOH5PVZE7YF5K7VNWK3","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":"b0682dcde796be37c8338f00f9cfd19c6c0b83745a134341ed88118625d8d20a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-09T19:44:33Z","title_canon_sha256":"f9553878dff1a945032f2dbe751c549a14fbf8847ce83f62d750382b26c25e6f"},"schema_version":"1.0","source":{"id":"1012.2095","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2095","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2095v3","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2095","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"TPQMXDBBOH5P","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TPQMXDBBOH5PVZE7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TPQMXDBB","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:08f1f8a8f864e07277a9e2a82708849612bba51eeecad59ffd83fa5479532d8d","target":"graph","created_at":"2026-05-18T02:26:01Z","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":"Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac-Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac-Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra ","authors_text":"William Slofstra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-09T19:44:33Z","title":"A Brylinski filtration for affine Kac-Moody algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2095","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:f3900b21dc7bc16b1ddf741917b76ac4cd36a9c11a8f5fc3a157780c56ea9fc5","target":"record","created_at":"2026-05-18T02:26:01Z","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":"b0682dcde796be37c8338f00f9cfd19c6c0b83745a134341ed88118625d8d20a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-09T19:44:33Z","title_canon_sha256":"f9553878dff1a945032f2dbe751c549a14fbf8847ce83f62d750382b26c25e6f"},"schema_version":"1.0","source":{"id":"1012.2095","kind":"arxiv","version":3}},"canonical_sha256":"9be0cb8c2171fafae49fc17aafd5b656c967f655187afb7faeb749c01b21257a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9be0cb8c2171fafae49fc17aafd5b656c967f655187afb7faeb749c01b21257a","first_computed_at":"2026-05-18T02:26:01.431995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:01.431995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fBK/Otj8Q6PulOYRxM4CuvWbVDpwPI5yv/eTGs7UjkUnoycXpc4XHj3Wqq6VFlidyG9+sdsBuKuJVWBe5W4pDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:01.432479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2095","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3900b21dc7bc16b1ddf741917b76ac4cd36a9c11a8f5fc3a157780c56ea9fc5","sha256:08f1f8a8f864e07277a9e2a82708849612bba51eeecad59ffd83fa5479532d8d"],"state_sha256":"320ca7af56b8f99794edec393d240cce02b84950b06ad47db68a4bd9b2f9d6b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0HYM1mQFKejocvGPPq3EAl4l21VI58gV1S1a8HZOofgcXXiIcJzCZmv/AD6+U+fXvF4vs3F1FlL+XzfqGpLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:38:10.108669Z","bundle_sha256":"d34665af84b6a0644e47c1cd5d9c0d0fdb6920a0e9973e29e58d2aa401aea8bf"}}