{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:WTTV22A4NS2ZJXMCNZYJVDLLH5","short_pith_number":"pith:WTTV22A4","canonical_record":{"source":{"id":"math/0409292","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2004-09-16T22:03:18Z","cross_cats_sorted":[],"title_canon_sha256":"2cd5f991d1d876e8ed589afa401d133b6e77f974ec922b0a030b6daf62dbce77","abstract_canon_sha256":"2cf39bd71852d3cfa2fc272a09babf8262ee85606f3e8c2daa7acc68ee8d660a"},"schema_version":"1.0"},"canonical_sha256":"b4e75d681c6cb594dd826e709a8d6b3f5fd3a82f046ffeffdaa1b26c450f8c80","source":{"kind":"arxiv","id":"math/0409292","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409292","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409292v1","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409292","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"WTTV22A4NS2Z","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"pith_short_16","alias_value":"WTTV22A4NS2ZJXMC","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"pith_short_8","alias_value":"WTTV22A4","created_at":"2026-07-04T14:39:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:WTTV22A4NS2ZJXMCNZYJVDLLH5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0409292","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2004-09-16T22:03:18Z","cross_cats_sorted":[],"title_canon_sha256":"2cd5f991d1d876e8ed589afa401d133b6e77f974ec922b0a030b6daf62dbce77","abstract_canon_sha256":"2cf39bd71852d3cfa2fc272a09babf8262ee85606f3e8c2daa7acc68ee8d660a"},"schema_version":"1.0"},"canonical_sha256":"b4e75d681c6cb594dd826e709a8d6b3f5fd3a82f046ffeffdaa1b26c450f8c80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:04.498271Z","signature_b64":"BOUb3qNqLSjb9P9xx8fHwEpgln6C3h/NAGdpCmDly9pc+IzJlOUuQu3OdI+LPw0rb3+LCDknaDq/ppNCJITmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4e75d681c6cb594dd826e709a8d6b3f5fd3a82f046ffeffdaa1b26c450f8c80","last_reissued_at":"2026-07-04T14:39:04.497856Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:04.497856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0409292","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":"2026-07-04T14:39:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7NQ5tssy3ZA0RD20k9jSnCJlMpy5HHPtZx5KRrFee43q2nS4tlbophnccPYOm/VzsoaRfIH+pnKmlEwcZYbCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:29:15.617141Z"},"content_sha256":"85f7b998c53473c631cf0506947cd77964f130927769ddfd1862dc46f0de8422","schema_version":"1.0","event_id":"sha256:85f7b998c53473c631cf0506947cd77964f130927769ddfd1862dc46f0de8422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:WTTV22A4NS2ZJXMCNZYJVDLLH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A character formula for compact elements (the rank one case)","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Korman","submitted_at":"2004-09-16T22:03:18Z","abstract_excerpt":"In their 1997 paper, Schneider and Stuhler gave a formula relating the value of an admissible character of a $p$-adic group at an elliptic element to the fixed point set of this element on the Bruhat-Tits building. Here we give a similar formula which works for compact elements. Elliptic elements have finitely many fixed facets in the building but compact elements can have infinitely many. In order to deal with the compact case we truncate the building so that we only look at a bounded piece of it. We show that for compact elements the (finite) information contained in the truncated building i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0409292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:39:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8989vGYW14QbYzEKhsVRQEAcY1Vs0Ntek4c4ZsMSsbAenmUH/A8E1cGDVU4wxrcb+ULPAf1uy/QvkJlfxOL0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:29:15.617522Z"},"content_sha256":"df7adda32893fe4e4d8a76088321e673d0bcf054a690b92992125ba13447e121","schema_version":"1.0","event_id":"sha256:df7adda32893fe4e4d8a76088321e673d0bcf054a690b92992125ba13447e121"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5/bundle.json","state_url":"https://pith.science/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5/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":"2026-07-04T20:29:15Z","links":{"resolver":"https://pith.science/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5","bundle":"https://pith.science/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5/bundle.json","state":"https://pith.science/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTTV22A4NS2ZJXMCNZYJVDLLH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WTTV22A4NS2ZJXMCNZYJVDLLH5","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":"2cf39bd71852d3cfa2fc272a09babf8262ee85606f3e8c2daa7acc68ee8d660a","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2004-09-16T22:03:18Z","title_canon_sha256":"2cd5f991d1d876e8ed589afa401d133b6e77f974ec922b0a030b6daf62dbce77"},"schema_version":"1.0","source":{"id":"math/0409292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409292","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409292v1","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409292","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"WTTV22A4NS2Z","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"pith_short_16","alias_value":"WTTV22A4NS2ZJXMC","created_at":"2026-07-04T14:39:04Z"},{"alias_kind":"pith_short_8","alias_value":"WTTV22A4","created_at":"2026-07-04T14:39:04Z"}],"graph_snapshots":[{"event_id":"sha256:df7adda32893fe4e4d8a76088321e673d0bcf054a690b92992125ba13447e121","target":"graph","created_at":"2026-07-04T14:39:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0409292/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In their 1997 paper, Schneider and Stuhler gave a formula relating the value of an admissible character of a $p$-adic group at an elliptic element to the fixed point set of this element on the Bruhat-Tits building. Here we give a similar formula which works for compact elements. Elliptic elements have finitely many fixed facets in the building but compact elements can have infinitely many. In order to deal with the compact case we truncate the building so that we only look at a bounded piece of it. We show that for compact elements the (finite) information contained in the truncated building i","authors_text":"Jonathan Korman","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2004-09-16T22:03:18Z","title":"A character formula for compact elements (the rank one case)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409292","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":"sha256:85f7b998c53473c631cf0506947cd77964f130927769ddfd1862dc46f0de8422","target":"record","created_at":"2026-07-04T14:39:04Z","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":"2cf39bd71852d3cfa2fc272a09babf8262ee85606f3e8c2daa7acc68ee8d660a","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"2004-09-16T22:03:18Z","title_canon_sha256":"2cd5f991d1d876e8ed589afa401d133b6e77f974ec922b0a030b6daf62dbce77"},"schema_version":"1.0","source":{"id":"math/0409292","kind":"arxiv","version":1}},"canonical_sha256":"b4e75d681c6cb594dd826e709a8d6b3f5fd3a82f046ffeffdaa1b26c450f8c80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4e75d681c6cb594dd826e709a8d6b3f5fd3a82f046ffeffdaa1b26c450f8c80","first_computed_at":"2026-07-04T14:39:04.497856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:04.497856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BOUb3qNqLSjb9P9xx8fHwEpgln6C3h/NAGdpCmDly9pc+IzJlOUuQu3OdI+LPw0rb3+LCDknaDq/ppNCJITmBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:04.498271Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0409292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85f7b998c53473c631cf0506947cd77964f130927769ddfd1862dc46f0de8422","sha256:df7adda32893fe4e4d8a76088321e673d0bcf054a690b92992125ba13447e121"],"state_sha256":"85533147b8e38b36f5b0d68c60067704745590d4557af84acb747b211e73c5ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7RupjygyY3HMDBWaWNgOTDjWBAsQfOQPajRy/fFHc+6Jgrth5ShgL2uAbGv8A4Yf/lpmJh4q+Oo0y3ZYgbgxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T20:29:15.619410Z","bundle_sha256":"01e5ff09c87ae025632d2cabf018c8e2f35b678995f8541127f0b22be5047d13"}}