{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NJR2KKN5HCDOX3B67VGQND33PU","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":"d0897743a8c3e85c275a34c594a824b91aec2b5c82bb7d4afa61e0b8e12b629b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-07-27T08:28:27Z","title_canon_sha256":"2bd98090444dde79f72463cd688c93773a760e96f847789a452d672afdf134a7"},"schema_version":"1.0","source":{"id":"0907.4560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4560","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4560v2","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4560","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"NJR2KKN5HCDO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NJR2KKN5HCDOX3B6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NJR2KKN5","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:0d9d77f5e1aa75f8f3a196bcba349db07be7bf4176a673000ebd77a739c31a38","target":"graph","created_at":"2026-05-18T03:26:23Z","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 study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field $(K,|{\\cdot}|)$ directly, but rather the associated projective spaces $K\\bP^n$, as bounded metric structures. We show that the class of (projective spaces over) metric valued fields is elementary, with theory $MVF$, and that the projective spaces $\\bP^n$ and $\\bP^m$ are bi\\\"interpretable for every $n,m \\geq 1$. The theory $MVF$ admits a model completion $ACMVF$, ","authors_text":"Ita\\\"i Ben Yaacov (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-07-27T08:28:27Z","title":"Model theoretic properties of metric valued fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4560","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:f76921d5ed3755dbe4222c633d73e213f4171e49705a48b8df850cfc279f1ccf","target":"record","created_at":"2026-05-18T03:26:23Z","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":"d0897743a8c3e85c275a34c594a824b91aec2b5c82bb7d4afa61e0b8e12b629b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-07-27T08:28:27Z","title_canon_sha256":"2bd98090444dde79f72463cd688c93773a760e96f847789a452d672afdf134a7"},"schema_version":"1.0","source":{"id":"0907.4560","kind":"arxiv","version":2}},"canonical_sha256":"6a63a529bd3886ebec3efd4d068f7b7d0655588708476ddb1a20e4cb0bf1c052","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a63a529bd3886ebec3efd4d068f7b7d0655588708476ddb1a20e4cb0bf1c052","first_computed_at":"2026-05-18T03:26:23.535871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:23.535871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDVE7lzzmhxUw5c/UhrrIDP2nHCj2h8X94NUVL2yMWbpj1xM4ZNeADp7+C3mJiAKYz2uxxUYsB4v4W+/0NgpCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:23.536610Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f76921d5ed3755dbe4222c633d73e213f4171e49705a48b8df850cfc279f1ccf","sha256:0d9d77f5e1aa75f8f3a196bcba349db07be7bf4176a673000ebd77a739c31a38"],"state_sha256":"5027bd1b63b5a53e6b47139650f11b835f2b08abef8d9f85957c1fc8ba8219de"}