{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J3HVUTQVQBR72FGP5AQAZW4FAH","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":"1d9330fbe6e419d4e5e4da76b9f31fcc6b837d0596b172b4083990ac756e8f13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-05T11:35:20Z","title_canon_sha256":"102945fa049c1961a7070aabf3a3891c139bc3091e88131538201a60e1b3d851"},"schema_version":"1.0","source":{"id":"2606.07166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07166","created_at":"2026-06-08T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07166v1","created_at":"2026-06-08T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07166","created_at":"2026-06-08T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"J3HVUTQVQBR7","created_at":"2026-06-08T01:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"J3HVUTQVQBR72FGP","created_at":"2026-06-08T01:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"J3HVUTQV","created_at":"2026-06-08T01:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:25a6dd143c3c857bfe2020d4bde3daec6026dc8ee8f0cc6dcb6e31f90170a6ca","target":"graph","created_at":"2026-06-08T01:04:50Z","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/2606.07166/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this brief note, we present a cyclic proof system developed specifically for the equational version of Primitive recursive arithmetic and establish the equivalence of the two systems. A distinctive feature of our approach is that it does not rely on automata-theoretic methods but is implemented primarily using the tools of structural proof theory.","authors_text":"Daniyar Shamkanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-05T11:35:20Z","title":"Cyclic proofs in the equational version of Primitive recursive arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07166","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:f0e46b2b0570e4d1ea206f110d3e3ba2975b34bc49bbcf7d6f79f058b5e03d5c","target":"record","created_at":"2026-06-08T01:04:50Z","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":"1d9330fbe6e419d4e5e4da76b9f31fcc6b837d0596b172b4083990ac756e8f13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-05T11:35:20Z","title_canon_sha256":"102945fa049c1961a7070aabf3a3891c139bc3091e88131538201a60e1b3d851"},"schema_version":"1.0","source":{"id":"2606.07166","kind":"arxiv","version":1}},"canonical_sha256":"4ecf5a4e158063fd14cfe8200cdb8501eed97c247fff445ae7e6a3840ecb1c7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ecf5a4e158063fd14cfe8200cdb8501eed97c247fff445ae7e6a3840ecb1c7c","first_computed_at":"2026-06-08T01:04:50.326497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:04:50.326497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RpN0nZPTv7BZwV9PKd/5+o7wM6EJLxNLxnJmQziw+FKvzuNichQ4Zf4oQkfKs5+vR5nHdlei7eFvxnZsbRyJBw==","signature_status":"signed_v1","signed_at":"2026-06-08T01:04:50.327264Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0e46b2b0570e4d1ea206f110d3e3ba2975b34bc49bbcf7d6f79f058b5e03d5c","sha256:25a6dd143c3c857bfe2020d4bde3daec6026dc8ee8f0cc6dcb6e31f90170a6ca"],"state_sha256":"b901bb0b815e818e1a31f9555cde1380d8bca9fc960ab8a671b3e0c98089c3a3"}