{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YSZAGM2JLXRNFTMKEWX4TFKOFG","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":"413bed2f772db27282fcef01b3e21003650cb259b82319051b9bfe6bb1c1abf6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-01-28T23:18:39Z","title_canon_sha256":"253d575f31c4eaadd428eda62239096b4d85ab8da988d67375de2cfacad01543"},"schema_version":"1.0","source":{"id":"2601.21118","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.21118","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"2601.21118v3","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.21118","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"YSZAGM2JLXRN","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"pith_short_16","alias_value":"YSZAGM2JLXRNFTMK","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"pith_short_8","alias_value":"YSZAGM2J","created_at":"2026-06-19T16:10:54Z"}],"graph_snapshots":[{"event_id":"sha256:0db63b281ecd6e789923258383f7dcd48a23a5c4d4a4068b3fa08df5b3831c35","target":"graph","created_at":"2026-06-19T16:10:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.21118/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We take two approaches to classifying the complexity of Presburger models: Scott analysis and degree spectra. In particular, we investigate the possible Scott sentence complexities and possible degree spectra of models of Presburger arithmetic. Many of our results will be achieved by showing how given a linear order $\\mathcal{L}$, we can construct a Presburger group $P_\\mathcal{L}$ that maintains much of the structure of $\\mathcal{L}$.","authors_text":"Jason Block","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-01-28T23:18:39Z","title":"Measuring the Complexity of Countable Presburger Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.21118","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":"sha256:6497905504027e3c1969a15fe2b3a6d60f9a535b40c664f1cba0577d3300a44b","target":"record","created_at":"2026-06-19T16:10:54Z","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":"413bed2f772db27282fcef01b3e21003650cb259b82319051b9bfe6bb1c1abf6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-01-28T23:18:39Z","title_canon_sha256":"253d575f31c4eaadd428eda62239096b4d85ab8da988d67375de2cfacad01543"},"schema_version":"1.0","source":{"id":"2601.21118","kind":"arxiv","version":3}},"canonical_sha256":"c4b20333495de2d2cd8a25afc9954e29a88c9b3a1dcab540b0ba566633c5a8f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4b20333495de2d2cd8a25afc9954e29a88c9b3a1dcab540b0ba566633c5a8f6","first_computed_at":"2026-06-19T16:10:54.467635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:54.467635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GikImTdf7G7GSUvfVRXsDvCx+1AGhOWFnHv9LiXP/Gg+8qz+4Mzkw8MtMS8URRtQ6DNsIdOsAHTURFMJ/fGEAw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:54.468113Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.21118","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6497905504027e3c1969a15fe2b3a6d60f9a535b40c664f1cba0577d3300a44b","sha256:0db63b281ecd6e789923258383f7dcd48a23a5c4d4a4068b3fa08df5b3831c35"],"state_sha256":"6bbd36d55027b44278b86a081a301ce24ce530232fc6566c7e3b00dfb97b4df7"}