{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3UJG5F2LR5V7IQADR2SBONXH5X","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":"ae24c2c1156c2b448b1520bd888e65c85f42bc93525ef7b147b36630a522a033","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-02T23:55:26Z","title_canon_sha256":"6d10ada459e03128dc5a68b543fd3ba2539499a9cd2d6ed84862ff2281ec9fa8"},"schema_version":"1.0","source":{"id":"1006.0527","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0527","created_at":"2026-05-18T04:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0527v2","created_at":"2026-05-18T04:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0527","created_at":"2026-05-18T04:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"3UJG5F2LR5V7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3UJG5F2LR5V7IQAD","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3UJG5F2L","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:c0e71876670eec823191b2c459ae30b7a68be7c811e7db33f42164f6e8e0c031","target":"graph","created_at":"2026-05-18T04:39:10Z","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 express some basic properties of Deninger's conjectural dynamical system in terms of morphisms of topoi. Then we show that the current definition of the Weil-\\'etale topos satisfies these properties. In particular, the flow, the closed orbits, the fixed points of the flow and the foliation in characteristic $p$ are well defined on the Weil-\\'etale topos. This analogy extends to arithmetic schemes. Over a prime number $p$ and over the archimedean place of $\\mathbb{Q}$, we define a morphism from a topos associated to Deninger's dynamical system to the Weil-\\'etale topos. This morphism is comp","authors_text":"Baptiste Morin","cross_cats":["math.AG","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-02T23:55:26Z","title":"Sur l'analogie entre le syst\\`eme dynamique de Deninger et le topos Weil-\\'etale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0527","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":"sha256:40b14e644df604a25148d96f8bc75b2a5b3107f936f5c2d1ff24137bdc2bf7de","target":"record","created_at":"2026-05-18T04:39:10Z","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":"ae24c2c1156c2b448b1520bd888e65c85f42bc93525ef7b147b36630a522a033","cross_cats_sorted":["math.AG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-02T23:55:26Z","title_canon_sha256":"6d10ada459e03128dc5a68b543fd3ba2539499a9cd2d6ed84862ff2281ec9fa8"},"schema_version":"1.0","source":{"id":"1006.0527","kind":"arxiv","version":2}},"canonical_sha256":"dd126e974b8f6bf440038ea41736e7edc42607c1124fc2cc0f59589c06cea3f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd126e974b8f6bf440038ea41736e7edc42607c1124fc2cc0f59589c06cea3f5","first_computed_at":"2026-05-18T04:39:10.009454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:10.009454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JeoQPVepIAvwKsfQV5Uuz5yxETrm+aB3k6MslhBoZFJsY5VLD2oO5dsuyiQO8koD/acS7Lmy6rCF0jqPduIABw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:10.010007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0527","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40b14e644df604a25148d96f8bc75b2a5b3107f936f5c2d1ff24137bdc2bf7de","sha256:c0e71876670eec823191b2c459ae30b7a68be7c811e7db33f42164f6e8e0c031"],"state_sha256":"36ec2b353d2c5d4bb2d51555f5377a2005f46954066db336a73eec39c72f8a9d"}