{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SBMTRWWDMMVLUBMYGRRXCCN3PA","short_pith_number":"pith:SBMTRWWD","canonical_record":{"source":{"id":"1804.01421","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-03T07:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"28a4f202cc847a115642cd1ef9437fdb1f71ec78f3cf8485b0c84e522991278a","abstract_canon_sha256":"f3e5a91aee1977a06aeaa9b8032c840625ce84bfb5969e5790c650c91b0a15d8"},"schema_version":"1.0"},"canonical_sha256":"905938dac3632aba059834637109bb783b425b60d6fe374c7b0ed966126620e6","source":{"kind":"arxiv","id":"1804.01421","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01421","created_at":"2026-05-18T00:02:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01421v3","created_at":"2026-05-18T00:02:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01421","created_at":"2026-05-18T00:02:10Z"},{"alias_kind":"pith_short_12","alias_value":"SBMTRWWDMMVL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SBMTRWWDMMVLUBMY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SBMTRWWD","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SBMTRWWDMMVLUBMYGRRXCCN3PA","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01421","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-03T07:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"28a4f202cc847a115642cd1ef9437fdb1f71ec78f3cf8485b0c84e522991278a","abstract_canon_sha256":"f3e5a91aee1977a06aeaa9b8032c840625ce84bfb5969e5790c650c91b0a15d8"},"schema_version":"1.0"},"canonical_sha256":"905938dac3632aba059834637109bb783b425b60d6fe374c7b0ed966126620e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:10.247740Z","signature_b64":"SfLAodC7eqAVTt38VrIET5J8A3Xp7LHi0stuHIB16nz0pWDjfkrlyRI+B29fm1SGo85Wqf3OOXm8ML696tT9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"905938dac3632aba059834637109bb783b425b60d6fe374c7b0ed966126620e6","last_reissued_at":"2026-05-18T00:02:10.246963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:10.246963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01421","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pK/8GgX+pSm0G76/8IdMcPIwOT506fyWSzLkApoYOczeHTo2gl4VoDAhmVcppx+4EuTIYsqHrk9fIsMruXXvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:30:04.778329Z"},"content_sha256":"be61d9cb72501e6392ff470bfd4f027dd66eae48b5c899073544ae602131510b","schema_version":"1.0","event_id":"sha256:be61d9cb72501e6392ff470bfd4f027dd66eae48b5c899073544ae602131510b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SBMTRWWDMMVLUBMYGRRXCCN3PA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Model completion of scaled lattices and co-Heyting algebras of p-adic semi-algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Luck Darni\\`ere (LAREMA)","submitted_at":"2018-04-03T07:32:20Z","abstract_excerpt":"Let p be prime number, K be a p-adically closed field, X $\\subseteq$ K^m a semi-algebraic set defined over K and L(X) the lattice of semi-algebraic subsets of X which are closed in X. We prove that the complete theory of L(X) eliminates the quantifiers in a certain language LASC, the LASC-structure on L(X) being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field. We classify these LASC-structures up to elementary equivalence, and get in particular that the complete theory of L(K^m) only depends on m, not on K nor eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01421","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YLMGUIPIa8w2uajvrVN4ZwTTj+KMBm5bPM96Ny0e51R4zF0jTIlfOqrwCXe9Stf1r0MPbSDvYvo9WuEyp2ACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:30:04.778672Z"},"content_sha256":"e7f0b1ec44954805a948543ab66e6185943c75605125b335f1f26ac3e6dc5c89","schema_version":"1.0","event_id":"sha256:e7f0b1ec44954805a948543ab66e6185943c75605125b335f1f26ac3e6dc5c89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA/bundle.json","state_url":"https://pith.science/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T23:30:04Z","links":{"resolver":"https://pith.science/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA","bundle":"https://pith.science/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA/bundle.json","state":"https://pith.science/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBMTRWWDMMVLUBMYGRRXCCN3PA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SBMTRWWDMMVLUBMYGRRXCCN3PA","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":"f3e5a91aee1977a06aeaa9b8032c840625ce84bfb5969e5790c650c91b0a15d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-03T07:32:20Z","title_canon_sha256":"28a4f202cc847a115642cd1ef9437fdb1f71ec78f3cf8485b0c84e522991278a"},"schema_version":"1.0","source":{"id":"1804.01421","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01421","created_at":"2026-05-18T00:02:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01421v3","created_at":"2026-05-18T00:02:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01421","created_at":"2026-05-18T00:02:10Z"},{"alias_kind":"pith_short_12","alias_value":"SBMTRWWDMMVL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SBMTRWWDMMVLUBMY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SBMTRWWD","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:e7f0b1ec44954805a948543ab66e6185943c75605125b335f1f26ac3e6dc5c89","target":"graph","created_at":"2026-05-18T00:02:10Z","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":"Let p be prime number, K be a p-adically closed field, X $\\subseteq$ K^m a semi-algebraic set defined over K and L(X) the lattice of semi-algebraic subsets of X which are closed in X. We prove that the complete theory of L(X) eliminates the quantifiers in a certain language LASC, the LASC-structure on L(X) being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field. We classify these LASC-structures up to elementary equivalence, and get in particular that the complete theory of L(K^m) only depends on m, not on K nor eve","authors_text":"Luck Darni\\`ere (LAREMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-03T07:32:20Z","title":"Model completion of scaled lattices and co-Heyting algebras of p-adic semi-algebraic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01421","kind":"arxiv","version":3},"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:be61d9cb72501e6392ff470bfd4f027dd66eae48b5c899073544ae602131510b","target":"record","created_at":"2026-05-18T00:02:10Z","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":"f3e5a91aee1977a06aeaa9b8032c840625ce84bfb5969e5790c650c91b0a15d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-03T07:32:20Z","title_canon_sha256":"28a4f202cc847a115642cd1ef9437fdb1f71ec78f3cf8485b0c84e522991278a"},"schema_version":"1.0","source":{"id":"1804.01421","kind":"arxiv","version":3}},"canonical_sha256":"905938dac3632aba059834637109bb783b425b60d6fe374c7b0ed966126620e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"905938dac3632aba059834637109bb783b425b60d6fe374c7b0ed966126620e6","first_computed_at":"2026-05-18T00:02:10.246963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:10.246963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SfLAodC7eqAVTt38VrIET5J8A3Xp7LHi0stuHIB16nz0pWDjfkrlyRI+B29fm1SGo85Wqf3OOXm8ML696tT9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:10.247740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01421","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be61d9cb72501e6392ff470bfd4f027dd66eae48b5c899073544ae602131510b","sha256:e7f0b1ec44954805a948543ab66e6185943c75605125b335f1f26ac3e6dc5c89"],"state_sha256":"48345b592e02ff03382b6fc8b05af514656c0d44e49133c9949459d304536252"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jmospqMWKI0XkOmi329xVJfrG0k4D9UA9Ayr7kXJF2Lw5bYKseq8rl51GqvOUQ/+X8lkyAuE/hQxIbwQHtxfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:30:04.780559Z","bundle_sha256":"1566acd93f62e09be99f2376a15a1461597a034385b280f3e0b201e63cf4ea41"}}