{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SWJO7GOAEHA2U6UPI5ONILIL5C","short_pith_number":"pith:SWJO7GOA","canonical_record":{"source":{"id":"1706.00145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-01T01:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"5d6983ab64eb581d77522803c4f8b0708c57065f4b7e60e4d373a6a59b1358ac","abstract_canon_sha256":"da397decae56edbe8fc1dc68be32303baf1ba95ec84dea5cb2873489bf2234dd"},"schema_version":"1.0"},"canonical_sha256":"9592ef99c021c1aa7a8f475cd42d0be89ed3e08d4494185b4b4594675cee5e3e","source":{"kind":"arxiv","id":"1706.00145","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00145","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00145v2","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00145","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"SWJO7GOAEHA2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SWJO7GOAEHA2U6UP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SWJO7GOA","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SWJO7GOAEHA2U6UPI5ONILIL5C","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-01T01:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"5d6983ab64eb581d77522803c4f8b0708c57065f4b7e60e4d373a6a59b1358ac","abstract_canon_sha256":"da397decae56edbe8fc1dc68be32303baf1ba95ec84dea5cb2873489bf2234dd"},"schema_version":"1.0"},"canonical_sha256":"9592ef99c021c1aa7a8f475cd42d0be89ed3e08d4494185b4b4594675cee5e3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:31.118165Z","signature_b64":"1copt1fKK4P14BgYeV5Yls0mlLWEMCbSm9aDYRSU/tbt/mLPLkaH1nq9hOMx7e+ndLwMwueM4Bwu6C5tf3kXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9592ef99c021c1aa7a8f475cd42d0be89ed3e08d4494185b4b4594675cee5e3e","last_reissued_at":"2026-05-17T23:46:31.117439Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:31.117439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00145","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":"2026-05-17T23:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5jRj8fICca3TnsNHFAlBT+XlLn1+aZTuqgn5X/xT08vIL55JRhE0nWPGpoA3bilEmNndzEUY4bkd5l/C/FtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:56:23.266353Z"},"content_sha256":"cd6d6cceb81096f338d9b1a693bba3cf8a9ce23a7b7855f981560be84383aa97","schema_version":"1.0","event_id":"sha256:cd6d6cceb81096f338d9b1a693bba3cf8a9ce23a7b7855f981560be84383aa97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SWJO7GOAEHA2U6UPI5ONILIL5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bases for local Weyl modules for the hyper and truncated current $\\mathfrak{sl}_2$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Angelo Bianchi, Evan Wilson","submitted_at":"2017-06-01T01:44:21Z","abstract_excerpt":"We use the theory of Gr\\\"obner-Shirshov bases for ideals to construct linear bases for graded local Weyl modules for the (hyper) current and the truncated current algebras associated to the finite-dimensional complex simple Lie algebra $\\mathfrak{sl}_2$. The main result is a characteristic-free construction of bases for this important family of modules for the hyper current $\\mathfrak{sl}_2$-algebra. In the positive characteristic setting this work represents the first construction in the literature. In the characteristic zero setting, the method provides a different construction of the Chari-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00145","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":"2026-05-17T23:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vUwcgvm4j+bFOtffhVkYL0UkfLZMNS/vSmRtEWdpXiA26VMAqYcr0DNsFcpHh0M+mXNm3Ztb8X7ehC7OrI+WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:56:23.266704Z"},"content_sha256":"80ba5ee2b24f3ca4eee0955508c418aa3f0c47bea0c894898d9c6f3587a5a431","schema_version":"1.0","event_id":"sha256:80ba5ee2b24f3ca4eee0955508c418aa3f0c47bea0c894898d9c6f3587a5a431"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWJO7GOAEHA2U6UPI5ONILIL5C/bundle.json","state_url":"https://pith.science/pith/SWJO7GOAEHA2U6UPI5ONILIL5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWJO7GOAEHA2U6UPI5ONILIL5C/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":"2026-06-03T00:56:23Z","links":{"resolver":"https://pith.science/pith/SWJO7GOAEHA2U6UPI5ONILIL5C","bundle":"https://pith.science/pith/SWJO7GOAEHA2U6UPI5ONILIL5C/bundle.json","state":"https://pith.science/pith/SWJO7GOAEHA2U6UPI5ONILIL5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWJO7GOAEHA2U6UPI5ONILIL5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SWJO7GOAEHA2U6UPI5ONILIL5C","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":"da397decae56edbe8fc1dc68be32303baf1ba95ec84dea5cb2873489bf2234dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-01T01:44:21Z","title_canon_sha256":"5d6983ab64eb581d77522803c4f8b0708c57065f4b7e60e4d373a6a59b1358ac"},"schema_version":"1.0","source":{"id":"1706.00145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00145","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00145v2","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00145","created_at":"2026-05-17T23:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"SWJO7GOAEHA2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SWJO7GOAEHA2U6UP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SWJO7GOA","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:80ba5ee2b24f3ca4eee0955508c418aa3f0c47bea0c894898d9c6f3587a5a431","target":"graph","created_at":"2026-05-17T23:46:31Z","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 use the theory of Gr\\\"obner-Shirshov bases for ideals to construct linear bases for graded local Weyl modules for the (hyper) current and the truncated current algebras associated to the finite-dimensional complex simple Lie algebra $\\mathfrak{sl}_2$. The main result is a characteristic-free construction of bases for this important family of modules for the hyper current $\\mathfrak{sl}_2$-algebra. In the positive characteristic setting this work represents the first construction in the literature. In the characteristic zero setting, the method provides a different construction of the Chari-","authors_text":"Angelo Bianchi, Evan Wilson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-01T01:44:21Z","title":"Bases for local Weyl modules for the hyper and truncated current $\\mathfrak{sl}_2$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00145","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:cd6d6cceb81096f338d9b1a693bba3cf8a9ce23a7b7855f981560be84383aa97","target":"record","created_at":"2026-05-17T23:46:31Z","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":"da397decae56edbe8fc1dc68be32303baf1ba95ec84dea5cb2873489bf2234dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-01T01:44:21Z","title_canon_sha256":"5d6983ab64eb581d77522803c4f8b0708c57065f4b7e60e4d373a6a59b1358ac"},"schema_version":"1.0","source":{"id":"1706.00145","kind":"arxiv","version":2}},"canonical_sha256":"9592ef99c021c1aa7a8f475cd42d0be89ed3e08d4494185b4b4594675cee5e3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9592ef99c021c1aa7a8f475cd42d0be89ed3e08d4494185b4b4594675cee5e3e","first_computed_at":"2026-05-17T23:46:31.117439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:31.117439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1copt1fKK4P14BgYeV5Yls0mlLWEMCbSm9aDYRSU/tbt/mLPLkaH1nq9hOMx7e+ndLwMwueM4Bwu6C5tf3kXAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:31.118165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd6d6cceb81096f338d9b1a693bba3cf8a9ce23a7b7855f981560be84383aa97","sha256:80ba5ee2b24f3ca4eee0955508c418aa3f0c47bea0c894898d9c6f3587a5a431"],"state_sha256":"4ab3203ddd3f6ccab581e5cb7e1321b2582b6da6ab4fb04db58fc60093528095"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5TslEj9xjhlRDUjaaFzreOXxJeLWSInoiyjuqndacV/z4xWrdQQPAIkGSas1m+Pr19OVInxDHakBYyTKM4HMDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:56:23.268606Z","bundle_sha256":"9e365d92a99d36156ab242bf1a9f0329aa16b39ddd7f784f5851b4d37134a4a4"}}