{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QQDSWI3HLABVOC6GHGKWPSGWIU","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":"539dcae1507b076061295a228d18bbe8d6aa2608ca539faed68b6594bb4328c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-02-09T17:20:29Z","title_canon_sha256":"62705398d9702c73c1ca637bab7fd223242fe9988ef0f7242cf9657c4ddaf5ad"},"schema_version":"1.0","source":{"id":"1602.03083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03083","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03083v2","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03083","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"QQDSWI3HLABV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QQDSWI3HLABVOC6G","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QQDSWI3H","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:d0ff63b343f0c3e06b8bd81712c52d5bfce3fa8af2aea84ad4e525f7668f8864","target":"graph","created_at":"2026-05-18T00:53:15Z","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":"Linear arithmetics are extensions of Presburger arithmetic (Pr) by one or more unary functions, each intended as multiplication by a fixed element (scalar), and containing the full induction schemes for their respective languages. In this paper we construct a model M of the 2-linear arithmetic LA_2 (linear arithmetic with two scalars) in which an infinitely long initial segment of \"Peano multiplication\" on M is 0-definable. This shows, in particular, that LA_2 is not model complete in contrast to theories LA_1 and LA_0=Pr that are known to satisfy quantifier elimination up to disjunctions of p","authors_text":"Pavel Pudl\\'ak, Petr Glivick\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-02-09T17:20:29Z","title":"A wild model of linear arithmetic and discretely ordered modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03083","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":"sha256:266798c59842fad75829af9e80d433ddef63b0556e5880b0514bcc963c784426","target":"record","created_at":"2026-05-18T00:53:15Z","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":"539dcae1507b076061295a228d18bbe8d6aa2608ca539faed68b6594bb4328c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-02-09T17:20:29Z","title_canon_sha256":"62705398d9702c73c1ca637bab7fd223242fe9988ef0f7242cf9657c4ddaf5ad"},"schema_version":"1.0","source":{"id":"1602.03083","kind":"arxiv","version":2}},"canonical_sha256":"84072b23675803570bc6399567c8d6453428a44aa6c4fdbde119ebf15bc09aa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84072b23675803570bc6399567c8d6453428a44aa6c4fdbde119ebf15bc09aa8","first_computed_at":"2026-05-18T00:53:15.775532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:15.775532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UI+LU7fwEGBzOYtyInmRS+DzAhFkv3MBekDmvp+ZqqcWc2RHLEZNIGYqTAezlvEF0Mbwct/Tk72HsuhqaCTjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:15.775925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:266798c59842fad75829af9e80d433ddef63b0556e5880b0514bcc963c784426","sha256:d0ff63b343f0c3e06b8bd81712c52d5bfce3fa8af2aea84ad4e525f7668f8864"],"state_sha256":"8269d7e03571fa3b096e2bd9dd4c2e5165ad2895ab5c25fdc6d509c3c2e2004b"}