{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TDA6Z3QTVYGTDVJF64FXFJ5UI4","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":"d849a62b338655cf8bc86b6fe041327dfebdca2504696d0ac7a781bf9647485a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-12-16T13:22:27Z","title_canon_sha256":"221071c10587e14071f53b313373c6753547ced3c0a0ed47878c358e8fb2e925"},"schema_version":"1.0","source":{"id":"1612.05457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05457","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05457v2","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05457","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"TDA6Z3QTVYGT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDA6Z3QTVYGTDVJF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDA6Z3QT","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:4160f3e2ebfe849c4540ae808418179744caa2d514ceef35a4465d63e6a7c95d","target":"graph","created_at":"2026-05-18T00:01:10Z","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":"Intuitionistic first-order logic extended with a restricted form of Markov's principle is constructive and admits a Curry-Howard correspondence, as shown by Herbelin. We provide a simpler proof of that result and then we study intuitionistic first-order logic extended with unrestricted Markov's principle. Starting from classical natural deduction, we restrict the excluded middle and we obtain a natural deduction system and a parallel Curry-Howard isomorphism for the logic. We show that proof terms for existentially quantified formulas reduce to a list of individual terms representing all possi","authors_text":"Federico Aschieri, Matteo Manighetti","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-12-16T13:22:27Z","title":"On Natural Deduction for Herbrand Constructive Logics II: Curry-Howard Correspondence for Markov's Principle in First-Order Logic and Arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05457","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:bad7fc60c7dc91757ee8a31eaf61e871af91df49262f832ceefa46dd3f14f3bd","target":"record","created_at":"2026-05-18T00:01:10Z","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":"d849a62b338655cf8bc86b6fe041327dfebdca2504696d0ac7a781bf9647485a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-12-16T13:22:27Z","title_canon_sha256":"221071c10587e14071f53b313373c6753547ced3c0a0ed47878c358e8fb2e925"},"schema_version":"1.0","source":{"id":"1612.05457","kind":"arxiv","version":2}},"canonical_sha256":"98c1ecee13ae0d31d525f70b72a7b44718f87802521917190716b7f714858854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98c1ecee13ae0d31d525f70b72a7b44718f87802521917190716b7f714858854","first_computed_at":"2026-05-18T00:01:10.645571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:10.645571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qo8JBLyX+8tRp085p6RBq4fAwMq7K06CEezSIHYkENzgSscpU0xi5X9KUZ+XTNAtuxv7bi8QwkespGG3espaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:10.646252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bad7fc60c7dc91757ee8a31eaf61e871af91df49262f832ceefa46dd3f14f3bd","sha256:4160f3e2ebfe849c4540ae808418179744caa2d514ceef35a4465d63e6a7c95d"],"state_sha256":"d887204b408cb3ec200e89724521fbcf1923b90d2f0f11001cd8d74558d30294"}