{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ABXQ6PZZUQPPR45HY4QMY4JERF","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":"29cd85f4c26a52a7fee04fa5b9450c717e2a9ac327cf51311cdf4523d7b5e513","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-06-06T08:46:52Z","title_canon_sha256":"19ea068c1a47f61aa625d84f1da84dda280720db74da18a26cadea1105136fb7"},"schema_version":"1.0","source":{"id":"2406.03860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03860","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03860v3","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03860","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"ABXQ6PZZUQPP","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"ABXQ6PZZUQPPR45H","created_at":"2026-06-02T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"ABXQ6PZZ","created_at":"2026-06-02T02:04:44Z"}],"graph_snapshots":[{"event_id":"sha256:888294ab236c9dd33d3a7f42a0c0c2be1d82f96f9dc35b2bd1a8f9c219cef36d","target":"graph","created_at":"2026-06-02T02:04:44Z","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/2406.03860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications due to a general syntax used in the formal systems. For our models we present a new proof of the downward L\\\"owenheim-Skolem Theorem for elementary submodels.","authors_text":"Matthias Kunik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-06-06T08:46:52Z","title":"On the downward L\\\"owenheim-Skolem Theorem for elementary submodels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03860","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:c0538f238def4fe45e8ec5a3bf4d878b94f70d24660f8ed6fdbdf2ff272f89da","target":"record","created_at":"2026-06-02T02:04:44Z","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":"29cd85f4c26a52a7fee04fa5b9450c717e2a9ac327cf51311cdf4523d7b5e513","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-06-06T08:46:52Z","title_canon_sha256":"19ea068c1a47f61aa625d84f1da84dda280720db74da18a26cadea1105136fb7"},"schema_version":"1.0","source":{"id":"2406.03860","kind":"arxiv","version":3}},"canonical_sha256":"006f0f3f39a41ef8f3a7c720cc7124897526988a553fd2e20866e0d0133cfe71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"006f0f3f39a41ef8f3a7c720cc7124897526988a553fd2e20866e0d0133cfe71","first_computed_at":"2026-06-02T02:04:44.865553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:44.865553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RZmSZZvowurgNyj1v3pN5DnUIoElzdOlJ7CJEeZa/lcF0LlqH67w4H9SmSKFEWlFcxzrKV5VFCjnJE9FT488AA==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:44.866050Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0538f238def4fe45e8ec5a3bf4d878b94f70d24660f8ed6fdbdf2ff272f89da","sha256:888294ab236c9dd33d3a7f42a0c0c2be1d82f96f9dc35b2bd1a8f9c219cef36d"],"state_sha256":"1787451a19e6b6683ff3629e42a7afd3a0c296fa92eda6ed24847954a0fa3060"}