{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TUYRVJQW3CU2455SCCCALZZSYJ","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":"07d0e55e8b0bfa302bf6e5ffb881f08b2eb8bff4a341e50db290f3ced568e5eb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2021-04-15T02:31:05Z","title_canon_sha256":"5fff42e33f7cd970162b5382e2aad94d0b0dcfc6349182bd3b88ea5130c55e67"},"schema_version":"1.0","source":{"id":"2104.07202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07202","created_at":"2026-07-05T02:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07202v1","created_at":"2026-07-05T02:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07202","created_at":"2026-07-05T02:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"TUYRVJQW3CU2","created_at":"2026-07-05T02:32:18Z"},{"alias_kind":"pith_short_16","alias_value":"TUYRVJQW3CU2455S","created_at":"2026-07-05T02:32:18Z"},{"alias_kind":"pith_short_8","alias_value":"TUYRVJQW","created_at":"2026-07-05T02:32:18Z"}],"graph_snapshots":[{"event_id":"sha256:56077c805e5fd9d8f67b3ae00cc7ac1c861dc00582122a2d38eaf71d72706f30","target":"graph","created_at":"2026-07-05T02:32:18Z","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/2104.07202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Kristiansen and Murwanashyaka recently proved that Robinson arithmetic Q is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings and sets. We also in introduce a \"hybrid\" elementary theory of strings and trees and establish its mutual interpretability with Robinson's weak arithmetic R, the weak theory of binary trees WT","authors_text":"Zlatan Damnjanovic","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2021-04-15T02:31:05Z","title":"Mutual Interpretability of Weak Essentially Undecidable Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07202","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:be5b458fa741a2bc947d7a6c0b70d66af088d6ceca1c323a9932034244c6fdbc","target":"record","created_at":"2026-07-05T02:32:18Z","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":"07d0e55e8b0bfa302bf6e5ffb881f08b2eb8bff4a341e50db290f3ced568e5eb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2021-04-15T02:31:05Z","title_canon_sha256":"5fff42e33f7cd970162b5382e2aad94d0b0dcfc6349182bd3b88ea5130c55e67"},"schema_version":"1.0","source":{"id":"2104.07202","kind":"arxiv","version":1}},"canonical_sha256":"9d311aa616d8a9ae77b2108405e732c259fabad2700df06e0f6ed80cb2b6ce4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d311aa616d8a9ae77b2108405e732c259fabad2700df06e0f6ed80cb2b6ce4a","first_computed_at":"2026-07-05T02:32:18.990900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:32:18.990900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csrhL9m+LmeLw5FID2iX5YbsNNIXejD7q18jzTCms4LUbtDp7XJbKG7KJrUCHBnuJ2ACS/ODO3m54TjuCkLBDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:32:18.991380Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.07202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5b458fa741a2bc947d7a6c0b70d66af088d6ceca1c323a9932034244c6fdbc","sha256:56077c805e5fd9d8f67b3ae00cc7ac1c861dc00582122a2d38eaf71d72706f30"],"state_sha256":"61e05635881d0b74537581e1ed3971c58988c6ce32f4e36e098c5f36621df583"}