{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YMVRHOTCGYWPE4X2IUA6C6QIKS","short_pith_number":"pith:YMVRHOTC","canonical_record":{"source":{"id":"1107.1995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-11T11:14:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"43c2aec7c109d1b0dfdd2d851db4f7b17fb1a24d44598b8d141b9e91d0406960","abstract_canon_sha256":"9644a81307c847b246f2c1c1c12f52b1a3e0560e7f368aca78d833cfe178aadf"},"schema_version":"1.0"},"canonical_sha256":"c32b13ba62362cf272fa4501e17a0854a45153f150261547cfbb0aa7def61964","source":{"kind":"arxiv","id":"1107.1995","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1995","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1995v1","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1995","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"YMVRHOTCGYWP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YMVRHOTCGYWPE4X2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YMVRHOTC","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YMVRHOTCGYWPE4X2IUA6C6QIKS","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-11T11:14:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"43c2aec7c109d1b0dfdd2d851db4f7b17fb1a24d44598b8d141b9e91d0406960","abstract_canon_sha256":"9644a81307c847b246f2c1c1c12f52b1a3e0560e7f368aca78d833cfe178aadf"},"schema_version":"1.0"},"canonical_sha256":"c32b13ba62362cf272fa4501e17a0854a45153f150261547cfbb0aa7def61964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:33.672726Z","signature_b64":"isEcUTKd0K7n5fvzzmzsYnGp02A1k62NqEJm35eZhmwrUK6XRkxQ/lVDpo+F34qKxAJ5lUmZlcxoXDeSDD3XDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c32b13ba62362cf272fa4501e17a0854a45153f150261547cfbb0aa7def61964","last_reissued_at":"2026-05-18T04:18:33.672244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:33.672244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1995","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3dNhXxvw6wSXBIkEHJdQCegdBjJoh7jeaxbP3rq3o/XKKizQ8UdM8OcoE9rUGN54gAjptdZuvpSy1LzhHpsLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:53:16.097593Z"},"content_sha256":"51c3bd8ff177a1388fe9813132f7e92073361b66af239d1a428bc413ae65277e","schema_version":"1.0","event_id":"sha256:51c3bd8ff177a1388fe9813132f7e92073361b66af239d1a428bc413ae65277e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YMVRHOTCGYWPE4X2IUA6C6QIKS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lusztig's $a$ function for Coxeter groups of rank 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Peipei Zhou","submitted_at":"2011-07-11T11:14:31Z","abstract_excerpt":"We show that Lusztig's $a$-function of a Coxeter group is bounded if the rank of the Coxeter group is 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1995","kind":"arxiv","version":1},"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":"2026-05-18T04:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0h0YVbykaTm0Pjq5hKoxHZGQhayeV2fB1l/x6yLOmRbf8UekhBedcZ2ahvHNhb4ZMGams4n3TQKcsZ8vCZpiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:53:16.097932Z"},"content_sha256":"65a2325e2a781f0a497811035ab2bbddf49bca014854b2f904cceb997ef17fe6","schema_version":"1.0","event_id":"sha256:65a2325e2a781f0a497811035ab2bbddf49bca014854b2f904cceb997ef17fe6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS/bundle.json","state_url":"https://pith.science/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS/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":"2026-06-01T14:53:16Z","links":{"resolver":"https://pith.science/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS","bundle":"https://pith.science/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS/bundle.json","state":"https://pith.science/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMVRHOTCGYWPE4X2IUA6C6QIKS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YMVRHOTCGYWPE4X2IUA6C6QIKS","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":"9644a81307c847b246f2c1c1c12f52b1a3e0560e7f368aca78d833cfe178aadf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-11T11:14:31Z","title_canon_sha256":"43c2aec7c109d1b0dfdd2d851db4f7b17fb1a24d44598b8d141b9e91d0406960"},"schema_version":"1.0","source":{"id":"1107.1995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1995","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1995v1","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1995","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"YMVRHOTCGYWP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YMVRHOTCGYWPE4X2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YMVRHOTC","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:65a2325e2a781f0a497811035ab2bbddf49bca014854b2f904cceb997ef17fe6","target":"graph","created_at":"2026-05-18T04:18:33Z","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 show that Lusztig's $a$-function of a Coxeter group is bounded if the rank of the Coxeter group is 3.","authors_text":"Peipei Zhou","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-11T11:14:31Z","title":"Lusztig's $a$ function for Coxeter groups of rank 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1995","kind":"arxiv","version":1},"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":"sha256:51c3bd8ff177a1388fe9813132f7e92073361b66af239d1a428bc413ae65277e","target":"record","created_at":"2026-05-18T04:18:33Z","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":"9644a81307c847b246f2c1c1c12f52b1a3e0560e7f368aca78d833cfe178aadf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-11T11:14:31Z","title_canon_sha256":"43c2aec7c109d1b0dfdd2d851db4f7b17fb1a24d44598b8d141b9e91d0406960"},"schema_version":"1.0","source":{"id":"1107.1995","kind":"arxiv","version":1}},"canonical_sha256":"c32b13ba62362cf272fa4501e17a0854a45153f150261547cfbb0aa7def61964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c32b13ba62362cf272fa4501e17a0854a45153f150261547cfbb0aa7def61964","first_computed_at":"2026-05-18T04:18:33.672244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:33.672244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"isEcUTKd0K7n5fvzzmzsYnGp02A1k62NqEJm35eZhmwrUK6XRkxQ/lVDpo+F34qKxAJ5lUmZlcxoXDeSDD3XDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:33.672726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51c3bd8ff177a1388fe9813132f7e92073361b66af239d1a428bc413ae65277e","sha256:65a2325e2a781f0a497811035ab2bbddf49bca014854b2f904cceb997ef17fe6"],"state_sha256":"226dedebf75bbcb20d87380433daa2c30f27934d91e96fa5bb001536af1382dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQGETUYItBepFlBEf+ADlO+rx56qqdFIshndNByxQZ/Tz9LecfBxMlr/AI7XhCbooN281Jz0xhrDgkSzO5GVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:53:16.099799Z","bundle_sha256":"261c34abb414a431eba950ae706dd2fd286c795a99a26851b5a9e6a6873fe0e8"}}