{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:OOU7MTQDQZDLAW6QD63NCFJPPW","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":"4f57ae8e921b84b87329f73063181bcee7d6acc2e9cccb6ff81bef4b049c33e5","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.RT","submitted_at":"2003-04-14T13:06:14Z","title_canon_sha256":"141242642e36c07b1accd4fd6ff3be85d6f5a1db1afd84bea66b2c15e028238f"},"schema_version":"1.0","source":{"id":"math/0304172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0304172","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0304172v1","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0304172","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"OOU7MTQDQZDL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OOU7MTQDQZDLAW6Q","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OOU7MTQD","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:2617d1879c0deaa75d6e84dd0a07a65e9369af1e147dac0e8a1a3ab6bd8a0de7","target":"graph","created_at":"2026-05-18T03:39:53Z","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":"For the space $Lat_n$ of all the lattices in a $p$-adic $n$-dimensional linear space we obtain an analog of matrix beta-functions; this beta-function has a degeneration to the Tamagawa zeta-function. We propose an analog of Berezin kernels for $Lat_n$. We obtain conditions of positive definiteness of these kernels and explicit Plancherel formula.","authors_text":"Yurii A. Neretin","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2003-04-14T13:06:14Z","title":"Beta-function of Bruhat--Tits buildings and deformation of $l_2$ on the space of lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304172","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":"sha256:33c49692337b0aa1544d68342bd0575eec0fbb59a631ea1b8863864a5c034b5a","target":"record","created_at":"2026-05-18T03:39:53Z","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":"4f57ae8e921b84b87329f73063181bcee7d6acc2e9cccb6ff81bef4b049c33e5","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.RT","submitted_at":"2003-04-14T13:06:14Z","title_canon_sha256":"141242642e36c07b1accd4fd6ff3be85d6f5a1db1afd84bea66b2c15e028238f"},"schema_version":"1.0","source":{"id":"math/0304172","kind":"arxiv","version":1}},"canonical_sha256":"73a9f64e038646b05bd01fb6d1152f7db1bff3e37d1a50e66a29cceae4e3320a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a9f64e038646b05bd01fb6d1152f7db1bff3e37d1a50e66a29cceae4e3320a","first_computed_at":"2026-05-18T03:39:53.463232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:53.463232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KM2BUKRLKkapr4CGBjYA95EXkYxCM4ESqd545e+LkU+YQ6A7DUtrNORw1fH87gn9YSktVF7NLzPvNdUa+BAJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:53.463778Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0304172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33c49692337b0aa1544d68342bd0575eec0fbb59a631ea1b8863864a5c034b5a","sha256:2617d1879c0deaa75d6e84dd0a07a65e9369af1e147dac0e8a1a3ab6bd8a0de7"],"state_sha256":"a8857420754bad48d0371f54bfe133672866b45b99afd03198f8aa5924da5e0d"}