{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7NXLJKKKPZAQVMUKCCH56BN63Y","short_pith_number":"pith:7NXLJKKK","canonical_record":{"source":{"id":"1805.00381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-01T15:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"9b23c21143fee3c56627dff9b496c5708f19455e25e66e5cfb041a40bb267947","abstract_canon_sha256":"8a4fd3a686e6d3507916b480bf87ba91e1b661ee0a8104d58703fd550d9a02b2"},"schema_version":"1.0"},"canonical_sha256":"fb6eb4a94a7e410ab28a108fdf05bede3104e3ee54a6226155cc43915251958d","source":{"kind":"arxiv","id":"1805.00381","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00381","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00381v1","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00381","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"7NXLJKKKPZAQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7NXLJKKKPZAQVMUK","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7NXLJKKK","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7NXLJKKKPZAQVMUKCCH56BN63Y","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-01T15:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"9b23c21143fee3c56627dff9b496c5708f19455e25e66e5cfb041a40bb267947","abstract_canon_sha256":"8a4fd3a686e6d3507916b480bf87ba91e1b661ee0a8104d58703fd550d9a02b2"},"schema_version":"1.0"},"canonical_sha256":"fb6eb4a94a7e410ab28a108fdf05bede3104e3ee54a6226155cc43915251958d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:41.820001Z","signature_b64":"2sl2IKj7sydYZq2wcJvXcLYTE5YNBpXpeV5o/+s8C9WCmX7fZ/y2V+v9n5nJYsaDk/0ozicnKHcq6GFsh+5yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb6eb4a94a7e410ab28a108fdf05bede3104e3ee54a6226155cc43915251958d","last_reissued_at":"2026-05-17T23:40:41.819371Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:41.819371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00381","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N8EMVRWC2Pmj6XqhpiZEbmuxEXIub/aAqAHUKSa8CAULCAZeS6nLEZZdbzJZZXxJ0bkX+UgksIoCy3wiHu4kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:33:52.310605Z"},"content_sha256":"5cabfc84e737aa3f022d24d45cccb8bbec25c3f54704bc5d7166247957db2332","schema_version":"1.0","event_id":"sha256:5cabfc84e737aa3f022d24d45cccb8bbec25c3f54704bc5d7166247957db2332"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7NXLJKKKPZAQVMUKCCH56BN63Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Axiomatizing provable $n$-provability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Evgeny Kolmakov, Lev Beklemishev","submitted_at":"2018-05-01T15:04:02Z","abstract_excerpt":"A formula $\\phi$ is called \\emph{$n$-provable} in a formal arithmetical theory $S$ if $\\phi$ is provable in $S$ together with all true arithmetical $\\Pi_{n}$-sentences taken as additional axioms. While in general the set of all $n$-provable formulas, for a fixed $n>0$, is not recursively enumerable, the set of formulas $\\phi$ whose $n$-provability is provable in a given r.e.\\ metatheory $T$ is r.e. This set is deductively closed and will be, in general, an extension of $S$. We prove that these theories can be naturally axiomatized in terms of progressions of iterated local reflection principle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00381","kind":"arxiv","version":1},"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":"2026-05-17T23:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgAGEPSNdkDJICdCCcR2VhVeVi9g1RazJrktFjRC+wtx1QfRTggo9z9vBWf5kvRmFWuB9431ij1895jroeZrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:33:52.310946Z"},"content_sha256":"140a77227aa9427d11cd319fa7217763f21de7cd51eaa131ee2ba207f1f92472","schema_version":"1.0","event_id":"sha256:140a77227aa9427d11cd319fa7217763f21de7cd51eaa131ee2ba207f1f92472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NXLJKKKPZAQVMUKCCH56BN63Y/bundle.json","state_url":"https://pith.science/pith/7NXLJKKKPZAQVMUKCCH56BN63Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NXLJKKKPZAQVMUKCCH56BN63Y/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":"2026-06-27T03:33:52Z","links":{"resolver":"https://pith.science/pith/7NXLJKKKPZAQVMUKCCH56BN63Y","bundle":"https://pith.science/pith/7NXLJKKKPZAQVMUKCCH56BN63Y/bundle.json","state":"https://pith.science/pith/7NXLJKKKPZAQVMUKCCH56BN63Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NXLJKKKPZAQVMUKCCH56BN63Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7NXLJKKKPZAQVMUKCCH56BN63Y","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":"8a4fd3a686e6d3507916b480bf87ba91e1b661ee0a8104d58703fd550d9a02b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-01T15:04:02Z","title_canon_sha256":"9b23c21143fee3c56627dff9b496c5708f19455e25e66e5cfb041a40bb267947"},"schema_version":"1.0","source":{"id":"1805.00381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00381","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00381v1","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00381","created_at":"2026-05-17T23:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"7NXLJKKKPZAQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7NXLJKKKPZAQVMUK","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7NXLJKKK","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:140a77227aa9427d11cd319fa7217763f21de7cd51eaa131ee2ba207f1f92472","target":"graph","created_at":"2026-05-17T23:40:41Z","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":"A formula $\\phi$ is called \\emph{$n$-provable} in a formal arithmetical theory $S$ if $\\phi$ is provable in $S$ together with all true arithmetical $\\Pi_{n}$-sentences taken as additional axioms. While in general the set of all $n$-provable formulas, for a fixed $n>0$, is not recursively enumerable, the set of formulas $\\phi$ whose $n$-provability is provable in a given r.e.\\ metatheory $T$ is r.e. This set is deductively closed and will be, in general, an extension of $S$. We prove that these theories can be naturally axiomatized in terms of progressions of iterated local reflection principle","authors_text":"Evgeny Kolmakov, Lev Beklemishev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-01T15:04:02Z","title":"Axiomatizing provable $n$-provability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00381","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":"sha256:5cabfc84e737aa3f022d24d45cccb8bbec25c3f54704bc5d7166247957db2332","target":"record","created_at":"2026-05-17T23:40:41Z","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":"8a4fd3a686e6d3507916b480bf87ba91e1b661ee0a8104d58703fd550d9a02b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-01T15:04:02Z","title_canon_sha256":"9b23c21143fee3c56627dff9b496c5708f19455e25e66e5cfb041a40bb267947"},"schema_version":"1.0","source":{"id":"1805.00381","kind":"arxiv","version":1}},"canonical_sha256":"fb6eb4a94a7e410ab28a108fdf05bede3104e3ee54a6226155cc43915251958d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb6eb4a94a7e410ab28a108fdf05bede3104e3ee54a6226155cc43915251958d","first_computed_at":"2026-05-17T23:40:41.819371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:41.819371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2sl2IKj7sydYZq2wcJvXcLYTE5YNBpXpeV5o/+s8C9WCmX7fZ/y2V+v9n5nJYsaDk/0ozicnKHcq6GFsh+5yDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:41.820001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cabfc84e737aa3f022d24d45cccb8bbec25c3f54704bc5d7166247957db2332","sha256:140a77227aa9427d11cd319fa7217763f21de7cd51eaa131ee2ba207f1f92472"],"state_sha256":"7594e2113d80b35384c53040d3951f27e795d12b55d81869c4d910668ecffb6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YhMuc86wM/7LbnfU/2J4BBCMpjnF2BhQpvgEFGnvlcFJlK5TYhKr1yTeEP49tWyE4rOigGuOaZx/md8yWKCsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:33:52.312875Z","bundle_sha256":"1ee5a60894db1600cb606ba61f8459f536ef2bfead25c18a0b1a21c123959b06"}}