{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JMGQMJHAPZUUHSGZ6TABUIEMEM","short_pith_number":"pith:JMGQMJHA","canonical_record":{"source":{"id":"1807.01494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-04T09:24:45Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2ade15993c170958deb4412bd13eb31d1c278f5717414f6027f6d8074c710909","abstract_canon_sha256":"65ac6340bc0608cadcdaf497ae96be84f619c7e40e05822fe8d6216733e701fc"},"schema_version":"1.0"},"canonical_sha256":"4b0d0624e07e6943c8d9f4c01a208c233de060336b24ef20a29846f5673e546d","source":{"kind":"arxiv","id":"1807.01494","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01494","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01494v2","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01494","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"pith_short_12","alias_value":"JMGQMJHAPZUU","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JMGQMJHAPZUUHSGZ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JMGQMJHA","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JMGQMJHAPZUUHSGZ6TABUIEMEM","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-04T09:24:45Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2ade15993c170958deb4412bd13eb31d1c278f5717414f6027f6d8074c710909","abstract_canon_sha256":"65ac6340bc0608cadcdaf497ae96be84f619c7e40e05822fe8d6216733e701fc"},"schema_version":"1.0"},"canonical_sha256":"4b0d0624e07e6943c8d9f4c01a208c233de060336b24ef20a29846f5673e546d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:22.563098Z","signature_b64":"SWehniCW/7zjNESnyco8cih80ipzo1q1waQUS+P8SLAdnc8603v1kAY9/vWCo/Wb0C+L39g9yxFP22a1cvb9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0d0624e07e6943c8d9f4c01a208c233de060336b24ef20a29846f5673e546d","last_reissued_at":"2026-05-17T23:59:22.562759Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:22.562759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01494","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/S8Xoo7gvDHucw5AVyaAVy8YocfNmyVXloVzsIwakydadtSTYMPFbHlxBzBM5gf7t5L9U7kB1dujVZwdCgkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:34:11.803588Z"},"content_sha256":"a2fd92d633556509a7001791157d047563c6a1f3513f1739bc159a03ee061c38","schema_version":"1.0","event_id":"sha256:a2fd92d633556509a7001791157d047563c6a1f3513f1739bc159a03ee061c38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JMGQMJHAPZUUHSGZ6TABUIEMEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A complete system of deduction for Sigma formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Andre Kornell","submitted_at":"2018-07-04T09:24:45Z","abstract_excerpt":"The Sigma formulas of the language of arithmetic express semidecidable relations on the natural numbers. More generally, whenever a totality of objects is regarded as incomplete, the Sigma formulas express relations that are witnessed in a completed portion of that totality when they hold. In this sense, the Sigma formulas are more concrete semantically than other first-order formulas.\n  We describe a system of deduction that uses only Sigma formulas. Each axiom, an implication between two Sigma formulas, is implemented as a rewriting rule for subformulas. We exhibit a complete class of logica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01494","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmCTRlRLaA+3270hdvz36LuzmqAEUHCwIySImJ/kmDqubW1F6BTrQnPjzPD39h+CPnC2C8PFqJNfZxoj+A7kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:34:11.803941Z"},"content_sha256":"eab87205b9b564afbd940c67598e3eab1c5c5636e9397cf76ea362893566a603","schema_version":"1.0","event_id":"sha256:eab87205b9b564afbd940c67598e3eab1c5c5636e9397cf76ea362893566a603"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM/bundle.json","state_url":"https://pith.science/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T13:34:11Z","links":{"resolver":"https://pith.science/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM","bundle":"https://pith.science/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM/bundle.json","state":"https://pith.science/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMGQMJHAPZUUHSGZ6TABUIEMEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JMGQMJHAPZUUHSGZ6TABUIEMEM","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":"65ac6340bc0608cadcdaf497ae96be84f619c7e40e05822fe8d6216733e701fc","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-04T09:24:45Z","title_canon_sha256":"2ade15993c170958deb4412bd13eb31d1c278f5717414f6027f6d8074c710909"},"schema_version":"1.0","source":{"id":"1807.01494","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01494","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01494v2","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01494","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"pith_short_12","alias_value":"JMGQMJHAPZUU","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JMGQMJHAPZUUHSGZ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JMGQMJHA","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:eab87205b9b564afbd940c67598e3eab1c5c5636e9397cf76ea362893566a603","target":"graph","created_at":"2026-05-17T23:59:22Z","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":"The Sigma formulas of the language of arithmetic express semidecidable relations on the natural numbers. More generally, whenever a totality of objects is regarded as incomplete, the Sigma formulas express relations that are witnessed in a completed portion of that totality when they hold. In this sense, the Sigma formulas are more concrete semantically than other first-order formulas.\n  We describe a system of deduction that uses only Sigma formulas. Each axiom, an implication between two Sigma formulas, is implemented as a rewriting rule for subformulas. We exhibit a complete class of logica","authors_text":"Andre Kornell","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-04T09:24:45Z","title":"A complete system of deduction for Sigma formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01494","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:a2fd92d633556509a7001791157d047563c6a1f3513f1739bc159a03ee061c38","target":"record","created_at":"2026-05-17T23:59:22Z","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":"65ac6340bc0608cadcdaf497ae96be84f619c7e40e05822fe8d6216733e701fc","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-04T09:24:45Z","title_canon_sha256":"2ade15993c170958deb4412bd13eb31d1c278f5717414f6027f6d8074c710909"},"schema_version":"1.0","source":{"id":"1807.01494","kind":"arxiv","version":2}},"canonical_sha256":"4b0d0624e07e6943c8d9f4c01a208c233de060336b24ef20a29846f5673e546d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0d0624e07e6943c8d9f4c01a208c233de060336b24ef20a29846f5673e546d","first_computed_at":"2026-05-17T23:59:22.562759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:22.562759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SWehniCW/7zjNESnyco8cih80ipzo1q1waQUS+P8SLAdnc8603v1kAY9/vWCo/Wb0C+L39g9yxFP22a1cvb9Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:22.563098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01494","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2fd92d633556509a7001791157d047563c6a1f3513f1739bc159a03ee061c38","sha256:eab87205b9b564afbd940c67598e3eab1c5c5636e9397cf76ea362893566a603"],"state_sha256":"41f420b15f29b55098c82b1214897e39caa9238f0db4be7db70202dbee2b4d77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"byfZ1mtg/DlMSTcLi4nr5Fq25q9tzC7YwgBWX2LyEu0ZpVR8ndeAezk6YxoqAdoSuTrHf/1WfSoPRgmBxKHvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:34:11.805981Z","bundle_sha256":"4b91a77ac2eec99a98e40ef812a7d36eb1967dd66cdb98ffcee15546305327e7"}}