{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IBA2SFGAWAYYU52SFQ6YWWSGRO","short_pith_number":"pith:IBA2SFGA","canonical_record":{"source":{"id":"1610.02194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-07T09:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"d5edb22277fb4930f2db4b32b400fc238b139744b069fe043b038f07d3d3043d","abstract_canon_sha256":"f6de2bdf090d2b616a72493362fe929e190b8423ccfb8e9534925e7eaa43461d"},"schema_version":"1.0"},"canonical_sha256":"4041a914c0b0318a77522c3d8b5a468ba1e2bec00013b16c9dcd5ca908a1baa0","source":{"kind":"arxiv","id":"1610.02194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02194","created_at":"2026-05-18T01:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02194v1","created_at":"2026-05-18T01:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02194","created_at":"2026-05-18T01:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"IBA2SFGAWAYY","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IBA2SFGAWAYYU52S","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IBA2SFGA","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IBA2SFGAWAYYU52SFQ6YWWSGRO","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-07T09:06:36Z","cross_cats_sorted":[],"title_canon_sha256":"d5edb22277fb4930f2db4b32b400fc238b139744b069fe043b038f07d3d3043d","abstract_canon_sha256":"f6de2bdf090d2b616a72493362fe929e190b8423ccfb8e9534925e7eaa43461d"},"schema_version":"1.0"},"canonical_sha256":"4041a914c0b0318a77522c3d8b5a468ba1e2bec00013b16c9dcd5ca908a1baa0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:58.138420Z","signature_b64":"l4oI0QXDdlCwQO604bluaFTGQD66F3h3YxK50sLkKfLDdTfUzNvG8Cj/weHTjV5WAIJiel8xjm9kCpqP2OgsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4041a914c0b0318a77522c3d8b5a468ba1e2bec00013b16c9dcd5ca908a1baa0","last_reissued_at":"2026-05-18T01:02:58.137684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:58.137684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02194","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":"2026-05-18T01:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swdgd/lPgLBdvlaXR7oG0TgPZV8tEvpnzYKKJIghSt7PYMZl8p2mfkwpimgZfSbUGncP2gmN8tU90xA9lbsYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:27:17.851987Z"},"content_sha256":"64e872b90516171b1b44227c7c373e470bbcf139a0abf1c61cbc4953597ed4f0","schema_version":"1.0","event_id":"sha256:64e872b90516171b1b44227c7c373e470bbcf139a0abf1c61cbc4953597ed4f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IBA2SFGAWAYYU52SFQ6YWWSGRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying the provably total set functions of KP and KP(P)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jacob Cook, Michael Rathjen","submitted_at":"2016-10-07T09:06:36Z","abstract_excerpt":"This article is concerned with classifying the provably total set-functions of Kripke-Platek set theory, KP, and Power Kripke-Platek set theory, KP(P), as well as proving several (partial) conservativity results. The main technical tool used in this paper is a relativisation technique where ordinal analysis is carried out relative to an arbitrary but fixed set x. A classic result from ordinal analysis is the characterisation of the provably recursive functions of Peano Arithmetic, PA, by means of the fast growing hierarchy [10]. Whilst it is possible to formulate the natural numbers within KP,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02194","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":"2026-05-18T01:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZv8nwvwBdFp1qWdIdzu2hwvRvw9/XR05BQPzQZ0NQgIbWrqS2DIhGkf9/91SBcfyu+teI5mOBKkDxBWwvQyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:27:17.852440Z"},"content_sha256":"c5c7dd9556bb56a74f93a59c2e8e969b924d05d947a79d31799e0ca638587661","schema_version":"1.0","event_id":"sha256:c5c7dd9556bb56a74f93a59c2e8e969b924d05d947a79d31799e0ca638587661"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO/bundle.json","state_url":"https://pith.science/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO/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":"2026-05-24T16:27:17Z","links":{"resolver":"https://pith.science/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO","bundle":"https://pith.science/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO/bundle.json","state":"https://pith.science/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBA2SFGAWAYYU52SFQ6YWWSGRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IBA2SFGAWAYYU52SFQ6YWWSGRO","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":"f6de2bdf090d2b616a72493362fe929e190b8423ccfb8e9534925e7eaa43461d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-07T09:06:36Z","title_canon_sha256":"d5edb22277fb4930f2db4b32b400fc238b139744b069fe043b038f07d3d3043d"},"schema_version":"1.0","source":{"id":"1610.02194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02194","created_at":"2026-05-18T01:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02194v1","created_at":"2026-05-18T01:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02194","created_at":"2026-05-18T01:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"IBA2SFGAWAYY","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IBA2SFGAWAYYU52S","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IBA2SFGA","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:c5c7dd9556bb56a74f93a59c2e8e969b924d05d947a79d31799e0ca638587661","target":"graph","created_at":"2026-05-18T01:02:58Z","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":"This article is concerned with classifying the provably total set-functions of Kripke-Platek set theory, KP, and Power Kripke-Platek set theory, KP(P), as well as proving several (partial) conservativity results. The main technical tool used in this paper is a relativisation technique where ordinal analysis is carried out relative to an arbitrary but fixed set x. A classic result from ordinal analysis is the characterisation of the provably recursive functions of Peano Arithmetic, PA, by means of the fast growing hierarchy [10]. Whilst it is possible to formulate the natural numbers within KP,","authors_text":"Jacob Cook, Michael Rathjen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-07T09:06:36Z","title":"Classifying the provably total set functions of KP and KP(P)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02194","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":"sha256:64e872b90516171b1b44227c7c373e470bbcf139a0abf1c61cbc4953597ed4f0","target":"record","created_at":"2026-05-18T01:02:58Z","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":"f6de2bdf090d2b616a72493362fe929e190b8423ccfb8e9534925e7eaa43461d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-07T09:06:36Z","title_canon_sha256":"d5edb22277fb4930f2db4b32b400fc238b139744b069fe043b038f07d3d3043d"},"schema_version":"1.0","source":{"id":"1610.02194","kind":"arxiv","version":1}},"canonical_sha256":"4041a914c0b0318a77522c3d8b5a468ba1e2bec00013b16c9dcd5ca908a1baa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4041a914c0b0318a77522c3d8b5a468ba1e2bec00013b16c9dcd5ca908a1baa0","first_computed_at":"2026-05-18T01:02:58.137684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:58.137684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l4oI0QXDdlCwQO604bluaFTGQD66F3h3YxK50sLkKfLDdTfUzNvG8Cj/weHTjV5WAIJiel8xjm9kCpqP2OgsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:58.138420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64e872b90516171b1b44227c7c373e470bbcf139a0abf1c61cbc4953597ed4f0","sha256:c5c7dd9556bb56a74f93a59c2e8e969b924d05d947a79d31799e0ca638587661"],"state_sha256":"4db0d0e24436de6357c3956c0e4291cd250c2c716c7ea0f158f02d0a4d9430a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXuBSvYekRqwFONA+62TPngMXbFklw6/RwdzHNFUsgf2RHcYNftCQcayt7eCMH4zI0p2h7lQDYtMEdEz3EktAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T16:27:17.855458Z","bundle_sha256":"da1e22c01dd2404685a5900f60c1a75ebaaae37fdda3206abe11435a9e5a3372"}}