{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TW3I2K63AO2N6SWCYS4CLBADE3","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":"cafa7e72e71105c1fc122bed5cb4e27d446bef39ab95db1e1d35764ea52c0269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-06T20:50:57Z","title_canon_sha256":"8d835cb516f611481529d4bb94eac717bb9545a27fa7c90b0325b3c6d6af134a"},"schema_version":"1.0","source":{"id":"1106.1196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1196","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1196v1","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1196","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"TW3I2K63AO2N","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TW3I2K63AO2N6SWC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TW3I2K63","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:e63d2e5c76b088f3f6da9f76af19b55146837f3af292779161277153c35d54ca","target":"graph","created_at":"2026-05-18T02:44:23Z","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":"An ordered structure is called o-minimalistic if it has all the first-order features of an o-minimal structure. We propose a theory, DCTC (Definable Completeness/Type Completeness), that describes many properties of o-minimalistic structures (dimension theory, monotonicity, Hardy structures, quasi-cell decomposition). Failure of cell decomposition leads to the related notion of a tame structure, and we give a criterium for an o-minimalistic structure to be tame. To any o-minimalistic structure, we can associate its Grothendieck ring, which in the non-o-minimal case is a non-trivial invariant. ","authors_text":"Hans Schoutens","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-06T20:50:57Z","title":"O-minimalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1196","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":"sha256:8451f3a31868cb548aedbc91d8dc6825f87f3704180d3d06100364dc9bf0f060","target":"record","created_at":"2026-05-18T02:44:23Z","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":"cafa7e72e71105c1fc122bed5cb4e27d446bef39ab95db1e1d35764ea52c0269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-06T20:50:57Z","title_canon_sha256":"8d835cb516f611481529d4bb94eac717bb9545a27fa7c90b0325b3c6d6af134a"},"schema_version":"1.0","source":{"id":"1106.1196","kind":"arxiv","version":1}},"canonical_sha256":"9db68d2bdb03b4df4ac2c4b825840326ecf5ab6acf73b92ae8b51c7331afefc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9db68d2bdb03b4df4ac2c4b825840326ecf5ab6acf73b92ae8b51c7331afefc3","first_computed_at":"2026-05-18T02:44:23.774162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:23.774162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6dJfkv0CeVZJq5vzgXvOfBIlUQtRX+QXWCcjK3gz/ziDHdqpew0re3zBrhQIETcbzy4VujUXCU9fO6+wWaiHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:23.774591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8451f3a31868cb548aedbc91d8dc6825f87f3704180d3d06100364dc9bf0f060","sha256:e63d2e5c76b088f3f6da9f76af19b55146837f3af292779161277153c35d54ca"],"state_sha256":"0dfaf21170367488ea37edffd243abac0a78ac9c6cfbcdd8646153859c11d683"}