{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GMKE6C3B4OF6CVMG7M2GLRX7YY","short_pith_number":"pith:GMKE6C3B","canonical_record":{"source":{"id":"1201.5566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-26T16:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"2d916de5da74e8aceb919d842794e65c3eb4cfdd3c9f1b4b7b37e65b2a43f39d","abstract_canon_sha256":"4dfb17a4c55e5b332cb085b18562d00644259620ac1c3853e537c058088e45ee"},"schema_version":"1.0"},"canonical_sha256":"33144f0b61e38be15586fb3465c6ffc6309ab6dfe9d24653e24ece7e85b624ad","source":{"kind":"arxiv","id":"1201.5566","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5566","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5566v2","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5566","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"GMKE6C3B4OF6","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GMKE6C3B4OF6CVMG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GMKE6C3B","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GMKE6C3B4OF6CVMG7M2GLRX7YY","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-26T16:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"2d916de5da74e8aceb919d842794e65c3eb4cfdd3c9f1b4b7b37e65b2a43f39d","abstract_canon_sha256":"4dfb17a4c55e5b332cb085b18562d00644259620ac1c3853e537c058088e45ee"},"schema_version":"1.0"},"canonical_sha256":"33144f0b61e38be15586fb3465c6ffc6309ab6dfe9d24653e24ece7e85b624ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.979749Z","signature_b64":"x8ekzlzAGDt+7eQswTO4o1IUPaHvmh6gGxDEWqJoX2k08F/2toHEXV7XvK8CkBiC56qAM38fH5swWvnqeS4UDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33144f0b61e38be15586fb3465c6ffc6309ab6dfe9d24653e24ece7e85b624ad","last_reissued_at":"2026-05-17T23:53:18.979154Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.979154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5566","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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F1uri87DF/C/MKMTH6LkaeXtAbjOv43WnCIvoEMxABt+oPtRcJ7mofFWGxNqptJyZ1ldT/iK/qdxNfCTCHn6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:49:09.045594Z"},"content_sha256":"ef293a691e4f8859e040cbcdcbd99a94e8efb651745c3dc8b7e86d98922c523a","schema_version":"1.0","event_id":"sha256:ef293a691e4f8859e040cbcdcbd99a94e8efb651745c3dc8b7e86d98922c523a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GMKE6C3B4OF6CVMG7M2GLRX7YY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PyCox: Computing with (finite) Coxeter groups and Iwahori-Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Meinolf Geck","submitted_at":"2012-01-26T16:12:10Z","abstract_excerpt":"We introduce the computer algebra package {\\sf PyCox}, written entirely in the {\\sf Python} language. It implements a set of algorithms - in a spirit similar to the older {\\sf CHEVIE} system - for working with Coxeter groups and Hecke algebras. This includes a new variation of the traditional algorithm for computing Kazhdan--Lusztig cells and $W$-graphs, which works efficiently for all finite groups of rank $\\leq 8$ (except $E_8$). We also discuss the computation of Lusztig's leading coefficients of character values and distinguished involutions (which works for $E_8$ as well). Our experiments"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5566","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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6d0Hf5cwk61oNWkxAFv8UvS/20JbS5w8tEenyRMfnDPhhQRue/2GqOVlG3LbnD16/8+ahI6o75SnRWwBPjdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:49:09.046244Z"},"content_sha256":"b28ae62581f80668d7178e6b6dc13781e6a3b0df8c52b60284afac8714330188","schema_version":"1.0","event_id":"sha256:b28ae62581f80668d7178e6b6dc13781e6a3b0df8c52b60284afac8714330188"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY/bundle.json","state_url":"https://pith.science/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY/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":"2026-05-28T16:49:09Z","links":{"resolver":"https://pith.science/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY","bundle":"https://pith.science/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY/bundle.json","state":"https://pith.science/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMKE6C3B4OF6CVMG7M2GLRX7YY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GMKE6C3B4OF6CVMG7M2GLRX7YY","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":"4dfb17a4c55e5b332cb085b18562d00644259620ac1c3853e537c058088e45ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-26T16:12:10Z","title_canon_sha256":"2d916de5da74e8aceb919d842794e65c3eb4cfdd3c9f1b4b7b37e65b2a43f39d"},"schema_version":"1.0","source":{"id":"1201.5566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5566","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5566v2","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5566","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"GMKE6C3B4OF6","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GMKE6C3B4OF6CVMG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GMKE6C3B","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:b28ae62581f80668d7178e6b6dc13781e6a3b0df8c52b60284afac8714330188","target":"graph","created_at":"2026-05-17T23:53:18Z","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 introduce the computer algebra package {\\sf PyCox}, written entirely in the {\\sf Python} language. It implements a set of algorithms - in a spirit similar to the older {\\sf CHEVIE} system - for working with Coxeter groups and Hecke algebras. This includes a new variation of the traditional algorithm for computing Kazhdan--Lusztig cells and $W$-graphs, which works efficiently for all finite groups of rank $\\leq 8$ (except $E_8$). We also discuss the computation of Lusztig's leading coefficients of character values and distinguished involutions (which works for $E_8$ as well). Our experiments","authors_text":"Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-26T16:12:10Z","title":"PyCox: Computing with (finite) Coxeter groups and Iwahori-Hecke algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5566","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:ef293a691e4f8859e040cbcdcbd99a94e8efb651745c3dc8b7e86d98922c523a","target":"record","created_at":"2026-05-17T23:53:18Z","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":"4dfb17a4c55e5b332cb085b18562d00644259620ac1c3853e537c058088e45ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-26T16:12:10Z","title_canon_sha256":"2d916de5da74e8aceb919d842794e65c3eb4cfdd3c9f1b4b7b37e65b2a43f39d"},"schema_version":"1.0","source":{"id":"1201.5566","kind":"arxiv","version":2}},"canonical_sha256":"33144f0b61e38be15586fb3465c6ffc6309ab6dfe9d24653e24ece7e85b624ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33144f0b61e38be15586fb3465c6ffc6309ab6dfe9d24653e24ece7e85b624ad","first_computed_at":"2026-05-17T23:53:18.979154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.979154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8ekzlzAGDt+7eQswTO4o1IUPaHvmh6gGxDEWqJoX2k08F/2toHEXV7XvK8CkBiC56qAM38fH5swWvnqeS4UDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.979749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef293a691e4f8859e040cbcdcbd99a94e8efb651745c3dc8b7e86d98922c523a","sha256:b28ae62581f80668d7178e6b6dc13781e6a3b0df8c52b60284afac8714330188"],"state_sha256":"5e57a7a7eef415936bf1ce656faf668e3fcaa7621545724f2a792e67a993b6f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kab4FTSVTd4umFT/NUgadUHjVNWycHAcl1Qs7EAQ39D46bd0UGWvv7pNE+XnYNrs3ya3+BLEOXmhM9aCwaefBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:49:09.049761Z","bundle_sha256":"12673d290d4158374cf79b9f65bc8d727400202b30939e392d0f60215c28f485"}}