{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KIRL47EQBEPLGU2Q64WFB7DQIZ","short_pith_number":"pith:KIRL47EQ","canonical_record":{"source":{"id":"1207.5780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-24T19:30:20Z","cross_cats_sorted":[],"title_canon_sha256":"f06f968bbecc43e14e5248547ae85d2c62830f0eae4f3607ba66396ab51669f5","abstract_canon_sha256":"9468c6b2aefabf41703614538a89efbd69c3b30547c4abd4ccafac599f7b37c2"},"schema_version":"1.0"},"canonical_sha256":"5222be7c90091eb35350f72c50fc70467384614de7a140d034001e91deeea093","source":{"kind":"arxiv","id":"1207.5780","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5780","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5780v2","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5780","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"KIRL47EQBEPL","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KIRL47EQBEPLGU2Q","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KIRL47EQ","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KIRL47EQBEPLGU2Q64WFB7DQIZ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-24T19:30:20Z","cross_cats_sorted":[],"title_canon_sha256":"f06f968bbecc43e14e5248547ae85d2c62830f0eae4f3607ba66396ab51669f5","abstract_canon_sha256":"9468c6b2aefabf41703614538a89efbd69c3b30547c4abd4ccafac599f7b37c2"},"schema_version":"1.0"},"canonical_sha256":"5222be7c90091eb35350f72c50fc70467384614de7a140d034001e91deeea093","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:45.979110Z","signature_b64":"07WUWXYJl4NeM7jTdwIjYVsgTB/EYgOrGARAU8zGPo5apNQWQNbUQHEnsMKi7wkPjxR/gMtC8TXn3SCsRQQRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5222be7c90091eb35350f72c50fc70467384614de7a140d034001e91deeea093","last_reissued_at":"2026-05-18T03:42:45.978651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:45.978651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5780","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ahoe/T+JUQ+Q7sINiWlSnRaMBR+8fxY7+BCvm02AXbP5HRVfyiCNCylQbe4dY96oD+n3SaMErvFetBHhs6rQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:43:19.290675Z"},"content_sha256":"5a725ea79fe82e279eaad75c06f4681050070d8cc21a921083bc893d4c40d46c","schema_version":"1.0","event_id":"sha256:5a725ea79fe82e279eaad75c06f4681050070d8cc21a921083bc893d4c40d46c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KIRL47EQBEPLGU2Q64WFB7DQIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weight modules over infinite dimensional Weyl algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dimitar Grantcharov, Volodymyr Mazorchuk, Vyacheslav Futorny","submitted_at":"2012-07-24T19:30:20Z","abstract_excerpt":"We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from this a description of blocks of the category of weight modules by quivers and relations. As a corollary we establish Koszulity for all blocks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5780","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSEasgIFrxrJU4o/GRcVXvcOpRSxS9a6j8glNXRO+Bmvn4tR8/JvPwxPbLcZxLg8BNb71pcvBtN4SO3daqTEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:43:19.291184Z"},"content_sha256":"1478b837beb08774b3bbbb0fc3071f3fa8275a3969ce392bc0f727cf1e0b9756","schema_version":"1.0","event_id":"sha256:1478b837beb08774b3bbbb0fc3071f3fa8275a3969ce392bc0f727cf1e0b9756"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ/bundle.json","state_url":"https://pith.science/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ/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":"2026-05-31T08:43:19Z","links":{"resolver":"https://pith.science/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ","bundle":"https://pith.science/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ/bundle.json","state":"https://pith.science/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIRL47EQBEPLGU2Q64WFB7DQIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KIRL47EQBEPLGU2Q64WFB7DQIZ","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":"9468c6b2aefabf41703614538a89efbd69c3b30547c4abd4ccafac599f7b37c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-24T19:30:20Z","title_canon_sha256":"f06f968bbecc43e14e5248547ae85d2c62830f0eae4f3607ba66396ab51669f5"},"schema_version":"1.0","source":{"id":"1207.5780","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5780","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5780v2","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5780","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"KIRL47EQBEPL","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KIRL47EQBEPLGU2Q","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KIRL47EQ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:1478b837beb08774b3bbbb0fc3071f3fa8275a3969ce392bc0f727cf1e0b9756","target":"graph","created_at":"2026-05-18T03:42:45Z","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 classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from this a description of blocks of the category of weight modules by quivers and relations. As a corollary we establish Koszulity for all blocks.","authors_text":"Dimitar Grantcharov, Volodymyr Mazorchuk, Vyacheslav Futorny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-24T19:30:20Z","title":"Weight modules over infinite dimensional Weyl algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5780","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":"sha256:5a725ea79fe82e279eaad75c06f4681050070d8cc21a921083bc893d4c40d46c","target":"record","created_at":"2026-05-18T03:42:45Z","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":"9468c6b2aefabf41703614538a89efbd69c3b30547c4abd4ccafac599f7b37c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-24T19:30:20Z","title_canon_sha256":"f06f968bbecc43e14e5248547ae85d2c62830f0eae4f3607ba66396ab51669f5"},"schema_version":"1.0","source":{"id":"1207.5780","kind":"arxiv","version":2}},"canonical_sha256":"5222be7c90091eb35350f72c50fc70467384614de7a140d034001e91deeea093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5222be7c90091eb35350f72c50fc70467384614de7a140d034001e91deeea093","first_computed_at":"2026-05-18T03:42:45.978651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:45.978651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"07WUWXYJl4NeM7jTdwIjYVsgTB/EYgOrGARAU8zGPo5apNQWQNbUQHEnsMKi7wkPjxR/gMtC8TXn3SCsRQQRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:45.979110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5780","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a725ea79fe82e279eaad75c06f4681050070d8cc21a921083bc893d4c40d46c","sha256:1478b837beb08774b3bbbb0fc3071f3fa8275a3969ce392bc0f727cf1e0b9756"],"state_sha256":"08c2ebd198b034e2ca7fbaf5d83899abf8e80f66a6c31017612902f35de6a078"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sr9Hiwad0hmBc6KuW0FZtGZFsi6pe4z67M+NzgRYFYb+ugV+ogRRfz/89GhI+Wi1F4MhfwjnMfSVSb7gxcP7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:43:19.294132Z","bundle_sha256":"7fa2d63cb2ef7831bca10c3cb04504425e389404f13ba2ab2d703862078c0610"}}