{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:2OD6OBDMCNDO46MW7CPVWDAYCY","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":"4eb29b6a6b2f8960c24062f57901599e377a0e51c046344615d7ce2233fa2559","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-11-28T15:08:28Z","title_canon_sha256":"e61c733a4538a75ad914382c6ab2490b95113d71352eb28d4f836e8a7cc97996"},"schema_version":"1.0","source":{"id":"math/0611867","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611867","created_at":"2026-05-18T04:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611867v2","created_at":"2026-05-18T04:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611867","created_at":"2026-05-18T04:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"2OD6OBDMCNDO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"2OD6OBDMCNDO46MW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"2OD6OBDM","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:2f0d681d8d43fe25318dbf96a89fa61641d0f250d4ed7357c5d3bc4cc41ad170","target":"graph","created_at":"2026-05-18T04:00:14Z","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 $k$ be a non-Archimedean field, $X$ a $k$-affinoid space and $f$ an analytic function over $X$. We precisely describe how the geometric connected components of the spaces $\\{x \\in X, |f(x)| \\ge \\varepsilon\\}$ behave with regards to $\\varepsilon$. We also obtain a result concerning privileged neighbourhoods and adapt a theorem from complex analytic geometry about Noetherianity for germs of analytic functions.","authors_text":"J\\'er\\^ome Poineau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-11-28T15:08:28Z","title":"Un r\\'esultat de connexit\\'e pour les vari\\'et\\'es analytiques p-adiques. Privil\\`ege et noeth\\'erianit\\'e"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611867","kind":"arxiv","version":2},"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":"sha256:8903cafafda2fabe0842036b3bbb7b3ecf4e3ddb49a3b78b4ef2719d1da2ff87","target":"record","created_at":"2026-05-18T04:00:14Z","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":"4eb29b6a6b2f8960c24062f57901599e377a0e51c046344615d7ce2233fa2559","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-11-28T15:08:28Z","title_canon_sha256":"e61c733a4538a75ad914382c6ab2490b95113d71352eb28d4f836e8a7cc97996"},"schema_version":"1.0","source":{"id":"math/0611867","kind":"arxiv","version":2}},"canonical_sha256":"d387e7046c1346ee7996f89f5b0c18162203e74bf2d200c2913a408ec3ca1dfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d387e7046c1346ee7996f89f5b0c18162203e74bf2d200c2913a408ec3ca1dfd","first_computed_at":"2026-05-18T04:00:14.178789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:14.178789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z/W8IV3W3zNyGZA4w4CR649U/otid2weemYEQvQ7syvS6Q0N3XapZUg94b3Fx0B1l6R/FLXWieP3uQ+JFM7aDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:14.179678Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611867","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8903cafafda2fabe0842036b3bbb7b3ecf4e3ddb49a3b78b4ef2719d1da2ff87","sha256:2f0d681d8d43fe25318dbf96a89fa61641d0f250d4ed7357c5d3bc4cc41ad170"],"state_sha256":"74269516413bb3e3c0aa75815eef02caa011021ac0980cad9bf56f19f66b9417"}