{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2C3A57A6R7AEWMN3YUTUKMGZ6A","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":"2f1db5e0b8ab46d051fa00b3897b6c65cb93e37f090eba2ff3b29ad3fef32743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-26T02:40:35Z","title_canon_sha256":"2112e508440225d9f738650655daef98d5ec11b9288821497ffd1401e3d9ad35"},"schema_version":"1.0","source":{"id":"1511.08274","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08274","created_at":"2026-05-18T01:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08274v3","created_at":"2026-05-18T01:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08274","created_at":"2026-05-18T01:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"2C3A57A6R7AE","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2C3A57A6R7AEWMN3","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2C3A57A6","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:65c7328723c06e2fbaecd71e3150769933d3cf40bc22f87b6711c1516145c9f2","target":"graph","created_at":"2026-05-18T01:15:06Z","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 consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to definable infinite discrete sets. We also provide a range of examples of strong expansions of ordered abelian groups which demonstrate the great variety of such theories.","authors_text":"Alfred Dolich, John Goodrick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-26T02:40:35Z","title":"Strong theories of ordered abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08274","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":"sha256:4aadbeb21cd1b1cf73d0ba8c115c77dcc79128314e4e1eac21d639bec634eb87","target":"record","created_at":"2026-05-18T01:15:06Z","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":"2f1db5e0b8ab46d051fa00b3897b6c65cb93e37f090eba2ff3b29ad3fef32743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-26T02:40:35Z","title_canon_sha256":"2112e508440225d9f738650655daef98d5ec11b9288821497ffd1401e3d9ad35"},"schema_version":"1.0","source":{"id":"1511.08274","kind":"arxiv","version":3}},"canonical_sha256":"d0b60efc1e8fc04b31bbc5274530d9f022afe6bcbfa3a1e88ac37b62186c6a19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0b60efc1e8fc04b31bbc5274530d9f022afe6bcbfa3a1e88ac37b62186c6a19","first_computed_at":"2026-05-18T01:15:06.509625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:06.509625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UaIPP1eZp2gBmWrZ0gF1ACorB2HfnONw3ae+rIBncf1om3aJ8kTZWASOsLI/J/I+axfDxzWdPqw5V7kqxfOrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:06.510121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08274","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aadbeb21cd1b1cf73d0ba8c115c77dcc79128314e4e1eac21d639bec634eb87","sha256:65c7328723c06e2fbaecd71e3150769933d3cf40bc22f87b6711c1516145c9f2"],"state_sha256":"429efefb5ca24ef85f65d6f3827838abe725b7c25c82afaf7f5cb18d922b26c3"}