{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AE32SEEUOYJJ6O4HDWCFCTXGRY","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":"40014015d717ea9a3bf3432e00529f14258c91ac9af1325073e18eb19d822c0d","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-01-18T15:20:39Z","title_canon_sha256":"daf678dfdc123602ada698848d2429d91f1f5dacec8f9950e6a967575babe3d6"},"schema_version":"1.0","source":{"id":"1701.05094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05094","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05094v1","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05094","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"AE32SEEUOYJJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AE32SEEUOYJJ6O4H","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AE32SEEU","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:e337f76247f59e843fee7fc5eff157951695e82575500bc77013b64c9abd879d","target":"graph","created_at":"2026-05-18T00:52:33Z","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":"In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R^n with n >= 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot detect topological dimension in the frame of all open sets of a Euclidean space. By contrast, we consider the lattice of open subpolyhedra of a given compact polyhedron P \\subseteq R^n, prove that it is a locally finite Heyting subalgebra of the (non-locally-finite) algebra of a","authors_text":"Andrea Pedrini, Daniel McNeill, Nick Bezhanishvili, Vincenzo Marra","cross_cats":["math.GN","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-01-18T15:20:39Z","title":"Tarski's Theorem on Intuitionistic logic, for polyhedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05094","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:bac6f4cef29df23d800ded9b5b5046b7e53ee3075dba5a8cd0f7cb4952c90929","target":"record","created_at":"2026-05-18T00:52:33Z","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":"40014015d717ea9a3bf3432e00529f14258c91ac9af1325073e18eb19d822c0d","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-01-18T15:20:39Z","title_canon_sha256":"daf678dfdc123602ada698848d2429d91f1f5dacec8f9950e6a967575babe3d6"},"schema_version":"1.0","source":{"id":"1701.05094","kind":"arxiv","version":1}},"canonical_sha256":"0137a9109476129f3b871d84514ee68e02f8c91666461a79304d67200cd25f86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0137a9109476129f3b871d84514ee68e02f8c91666461a79304d67200cd25f86","first_computed_at":"2026-05-18T00:52:33.193914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:33.193914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iU8qDN0s77DZ61H1apV84yjvWCQE33X8e0oBN8+8P7JMLOcO3HGiP6XCY1ZV3GuxejijWi4d06m5cXI4G732Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:33.194310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bac6f4cef29df23d800ded9b5b5046b7e53ee3075dba5a8cd0f7cb4952c90929","sha256:e337f76247f59e843fee7fc5eff157951695e82575500bc77013b64c9abd879d"],"state_sha256":"d7bac96a668e93ea3786f2830e957a7e86eca13f5f39b88b0c80978d201933e1"}