{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TO2VZQGYVYIXYHYYNZRPUJ4PKV","short_pith_number":"pith:TO2VZQGY","canonical_record":{"source":{"id":"1106.3654","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-18T14:57:47Z","cross_cats_sorted":[],"title_canon_sha256":"8116a8caf626ced624b06a8917e50f9dfed74ac4e32b6f8293059bdefb394f47","abstract_canon_sha256":"4c80899bc38366062ebe41cbc0d9d4b9f9baae16fdd5aa7d5a9e2e3bcc0a21eb"},"schema_version":"1.0"},"canonical_sha256":"9bb55cc0d8ae117c1f186e62fa278f555d541447dcb564753f56fefb173ed793","source":{"kind":"arxiv","id":"1106.3654","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3654","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3654v3","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3654","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"TO2VZQGYVYIX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO2VZQGYVYIXYHYY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO2VZQGY","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TO2VZQGYVYIXYHYYNZRPUJ4PKV","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3654","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-18T14:57:47Z","cross_cats_sorted":[],"title_canon_sha256":"8116a8caf626ced624b06a8917e50f9dfed74ac4e32b6f8293059bdefb394f47","abstract_canon_sha256":"4c80899bc38366062ebe41cbc0d9d4b9f9baae16fdd5aa7d5a9e2e3bcc0a21eb"},"schema_version":"1.0"},"canonical_sha256":"9bb55cc0d8ae117c1f186e62fa278f555d541447dcb564753f56fefb173ed793","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:11.321124Z","signature_b64":"cj3JsywqpaVJdVzeEBoUtumxhZG2+LgW+Vndixt7ECILCj+7nXwLcGljpT7xkfDCTKneAmczKXfBi1xH9O7ACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bb55cc0d8ae117c1f186e62fa278f555d541447dcb564753f56fefb173ed793","last_reissued_at":"2026-05-18T01:10:11.320693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:11.320693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3654","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":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5RNr7/uoZBbXj8yjCJolTVo6jk/uBvY5GTB4y2UtUm4TuFpHjd41o6IULU/f6ATcE9GVm6eYGblge1sZOqeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:47:14.639399Z"},"content_sha256":"49cc3c4b5f6ff1be8c5d5ecbb23b23b42b96de005bc092131a1e9d6a96bfc8ee","schema_version":"1.0","event_id":"sha256:49cc3c4b5f6ff1be8c5d5ecbb23b23b42b96de005bc092131a1e9d6a96bfc8ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TO2VZQGYVYIXYHYYNZRPUJ4PKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Nanhua XI","submitted_at":"2011-06-18T14:57:47Z","abstract_excerpt":"We give some discussions to the relations between canonical left cells and the lowest two-sided cell of an affine Weyl group. In particular, we use the relations to construct irreducible modules attached to the lowest two-sided cell and some one dimensional representations of an affine Hecke algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3654","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":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OICF4JjJGv24GRzE+qy96QeGJIw588vYZgcm9n5o8BHaZl1EmBRpnQsdDvLUBgHX6X75LpY4cKCAWfcg5gM+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:47:14.640182Z"},"content_sha256":"5bb63fed17ef8b6b875cb654d29be256d24e2bfaa6a25b309e684bec5b866c5f","schema_version":"1.0","event_id":"sha256:5bb63fed17ef8b6b875cb654d29be256d24e2bfaa6a25b309e684bec5b866c5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV/bundle.json","state_url":"https://pith.science/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV/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":"2026-05-31T09:47:14Z","links":{"resolver":"https://pith.science/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV","bundle":"https://pith.science/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV/bundle.json","state":"https://pith.science/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TO2VZQGYVYIXYHYYNZRPUJ4PKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TO2VZQGYVYIXYHYYNZRPUJ4PKV","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":"4c80899bc38366062ebe41cbc0d9d4b9f9baae16fdd5aa7d5a9e2e3bcc0a21eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-18T14:57:47Z","title_canon_sha256":"8116a8caf626ced624b06a8917e50f9dfed74ac4e32b6f8293059bdefb394f47"},"schema_version":"1.0","source":{"id":"1106.3654","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3654","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3654v3","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3654","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"TO2VZQGYVYIX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO2VZQGYVYIXYHYY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO2VZQGY","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:5bb63fed17ef8b6b875cb654d29be256d24e2bfaa6a25b309e684bec5b866c5f","target":"graph","created_at":"2026-05-18T01:10:11Z","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 give some discussions to the relations between canonical left cells and the lowest two-sided cell of an affine Weyl group. In particular, we use the relations to construct irreducible modules attached to the lowest two-sided cell and some one dimensional representations of an affine Hecke algebra.","authors_text":"Nanhua XI","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-18T14:57:47Z","title":"Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3654","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":"sha256:49cc3c4b5f6ff1be8c5d5ecbb23b23b42b96de005bc092131a1e9d6a96bfc8ee","target":"record","created_at":"2026-05-18T01:10:11Z","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":"4c80899bc38366062ebe41cbc0d9d4b9f9baae16fdd5aa7d5a9e2e3bcc0a21eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-18T14:57:47Z","title_canon_sha256":"8116a8caf626ced624b06a8917e50f9dfed74ac4e32b6f8293059bdefb394f47"},"schema_version":"1.0","source":{"id":"1106.3654","kind":"arxiv","version":3}},"canonical_sha256":"9bb55cc0d8ae117c1f186e62fa278f555d541447dcb564753f56fefb173ed793","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bb55cc0d8ae117c1f186e62fa278f555d541447dcb564753f56fefb173ed793","first_computed_at":"2026-05-18T01:10:11.320693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:11.320693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cj3JsywqpaVJdVzeEBoUtumxhZG2+LgW+Vndixt7ECILCj+7nXwLcGljpT7xkfDCTKneAmczKXfBi1xH9O7ACw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:11.321124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3654","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49cc3c4b5f6ff1be8c5d5ecbb23b23b42b96de005bc092131a1e9d6a96bfc8ee","sha256:5bb63fed17ef8b6b875cb654d29be256d24e2bfaa6a25b309e684bec5b866c5f"],"state_sha256":"c92083ffaf000351d7c46f0786611e29df25257e69d4a8fd8449480b50f95d49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fK/F/fYLh2fZHxNDER506m2mNc9SmDJBEijSb+V/r5BiSBwR7TS0C351NL+zMqyCuRgFKH9QvKjSg1YIYpvaAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:47:14.644934Z","bundle_sha256":"6c17eab9fbb80575e1248734073b6bc40a503e8f04b15584b66dda355d779c36"}}