{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5CTBEWC5MYLWYRKHNNFQBLB6S6","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":"d146908a68bd889359ba0953feae379b6843e259f4afcfc70dd542e55cb4ad0a","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-01T14:28:41Z","title_canon_sha256":"7b017735cb6da2e80091933f67a2531d103b90d90ee833bcc2705c7844f39634"},"schema_version":"1.0","source":{"id":"1708.00357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00357","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00357v1","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00357","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"5CTBEWC5MYLW","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5CTBEWC5MYLWYRKH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5CTBEWC5","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:e90f75626e985f2e3fae8ac083ef06838fd7595f0286f6df2e254ae290702ae4","target":"graph","created_at":"2026-05-17T23:47:40Z","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":"Let $V$ be a complete discrete valuation ring with residue field $k$ and with fraction field $K$ of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completion of a commutative $V$-algebra using spectral radius estimates for bounded subsets in complete bornological $V$-algebras. This leads us to a functorial chain complex for commutative $k$-algebras that computes Berthelot's rigid cohomology. This chain complex is related to the periodic cyclic homology of certain complete bornological $V$-algebras.","authors_text":"Georg Tamme, Guillermo Corti\\~nas, Joachim Cuntz, Ralf Meyer","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-01T14:28:41Z","title":"Nonarchimedean bornologies, cyclic homology and rigid cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00357","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":"sha256:097dd1ca629940e46da39183930ccbb626ea5e7263add29e4bce3a07c7ea0890","target":"record","created_at":"2026-05-17T23:47:40Z","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":"d146908a68bd889359ba0953feae379b6843e259f4afcfc70dd542e55cb4ad0a","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-01T14:28:41Z","title_canon_sha256":"7b017735cb6da2e80091933f67a2531d103b90d90ee833bcc2705c7844f39634"},"schema_version":"1.0","source":{"id":"1708.00357","kind":"arxiv","version":1}},"canonical_sha256":"e8a612585d66176c45476b4b00ac3e97ac7391593a332c0ee4589bb87aa813ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8a612585d66176c45476b4b00ac3e97ac7391593a332c0ee4589bb87aa813ef","first_computed_at":"2026-05-17T23:47:40.266063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:40.266063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hc+9/b6WO9FFzzyr1DdGbXco3rSudukRotuWiDFt3ii53xO17Y7UZyFa0xmyfEFCyQn4vT7gXtZ/9TDqsJPBBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:40.266475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:097dd1ca629940e46da39183930ccbb626ea5e7263add29e4bce3a07c7ea0890","sha256:e90f75626e985f2e3fae8ac083ef06838fd7595f0286f6df2e254ae290702ae4"],"state_sha256":"1ac4248559ba65b0f8d5e895f894a407d62e68bb000381dee89de0412e405f50"}