{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JPHY3OJVX3QIBDKLO2UWXUGHKD","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":"460985900a3a63697aa4908b4387d18614380eac8e85c35edbf5145e6aeed623","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-28T19:21:45Z","title_canon_sha256":"6afac18b5399058d672adb5be5dd30cbaebfa1ab90f9230f1bc9073e2f88eaf5"},"schema_version":"1.0","source":{"id":"1808.09504","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09504","created_at":"2026-05-17T23:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09504v5","created_at":"2026-05-17T23:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09504","created_at":"2026-05-17T23:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"JPHY3OJVX3QI","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JPHY3OJVX3QIBDKL","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JPHY3OJV","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:d1d685f0659325943282db2148175f55d04c31cc55cb8b1c84d6d7c2e46c94a9","target":"graph","created_at":"2026-05-17T23:41:53Z","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":"We give a short and purely bilinear proof of the fact that two chains of $p$-elementary lattices with quadratic form or alternating bilinear form over the $p$-adic integers ore more generally over a complete discrete valuation ring have common hyperbolic bases. This fact, which is useful for the study of Bruhat-Tits buildings, has been proven before with different methods by Abramenko and Nebe and by Frisch.","authors_text":"Rainer Schulze-Pillot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-28T19:21:45Z","title":"Common hyperbolic bases for chains of alternating or quadratic lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09504","kind":"arxiv","version":5},"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:f5463d2a0e47c33a427a2283d9f77843ab32fd3b398f3d04285a7659bc12fb96","target":"record","created_at":"2026-05-17T23:41:53Z","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":"460985900a3a63697aa4908b4387d18614380eac8e85c35edbf5145e6aeed623","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-28T19:21:45Z","title_canon_sha256":"6afac18b5399058d672adb5be5dd30cbaebfa1ab90f9230f1bc9073e2f88eaf5"},"schema_version":"1.0","source":{"id":"1808.09504","kind":"arxiv","version":5}},"canonical_sha256":"4bcf8db935bee0808d4b76a96bd0c750f49270121d43a9b08eec2e91167838e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bcf8db935bee0808d4b76a96bd0c750f49270121d43a9b08eec2e91167838e7","first_computed_at":"2026-05-17T23:41:53.883934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:53.883934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rHnNZrV5lwqcjyk3yfqdtF6BPa9GR6+BhDgWgDJT75EATzdEN68vgqdjWjBQJxvEyYt9cU7kov6xAcbTxn3MBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:53.884360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09504","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5463d2a0e47c33a427a2283d9f77843ab32fd3b398f3d04285a7659bc12fb96","sha256:d1d685f0659325943282db2148175f55d04c31cc55cb8b1c84d6d7c2e46c94a9"],"state_sha256":"aa07674044c9f5e45e1d4d97ced05d490a461e2019b36afbff63c06faa67cdb1"}