{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Q3OOMYUJYZ5AVFS5QA6LFVXLXS","short_pith_number":"pith:Q3OOMYUJ","canonical_record":{"source":{"id":"1204.5582","kind":"arxiv","version":10},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-25T08:21:11Z","cross_cats_sorted":[],"title_canon_sha256":"6d91c4e5eb6599675b2b3d94c189386f0b197ff25418f4b78ae391fb1838d5b1","abstract_canon_sha256":"45338f311f42997df1fcc6d9e3639083f15a98be742fefca77d3e6c181d7293e"},"schema_version":"1.0"},"canonical_sha256":"86dce66289c67a0a965d803cb2d6ebbc8a36dc36213d9a0db808298e3ec7af28","source":{"kind":"arxiv","id":"1204.5582","version":10},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5582","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5582v10","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5582","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"Q3OOMYUJYZ5A","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q3OOMYUJYZ5AVFS5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q3OOMYUJ","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Q3OOMYUJYZ5AVFS5QA6LFVXLXS","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5582","kind":"arxiv","version":10},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-25T08:21:11Z","cross_cats_sorted":[],"title_canon_sha256":"6d91c4e5eb6599675b2b3d94c189386f0b197ff25418f4b78ae391fb1838d5b1","abstract_canon_sha256":"45338f311f42997df1fcc6d9e3639083f15a98be742fefca77d3e6c181d7293e"},"schema_version":"1.0"},"canonical_sha256":"86dce66289c67a0a965d803cb2d6ebbc8a36dc36213d9a0db808298e3ec7af28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:46.597403Z","signature_b64":"SzHMiziWMCbX30H2PsyeTuPVsOyMrC6ptwcGHHwCzQ4u0X1K+sDwfrvbzeHMqAVxRrpmM3wrKjK5JouXNuQfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86dce66289c67a0a965d803cb2d6ebbc8a36dc36213d9a0db808298e3ec7af28","last_reissued_at":"2026-05-18T02:32:46.596967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:46.596967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5582","source_version":10,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUXdZOnimqYHG8OMePudkM6ijCTL09qc/73QW1jpMEa03XzZ+Dyiq4DeD/NvyQ0jYQm7Chbf79TAW/vQTV2MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:38:07.898940Z"},"content_sha256":"609b281a79d1098379c5884b4603ea2a1131a38828f0dd4f54763b094a183936","schema_version":"1.0","event_id":"sha256:609b281a79d1098379c5884b4603ea2a1131a38828f0dd4f54763b094a183936"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Q3OOMYUJYZ5AVFS5QA6LFVXLXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Predicatively computable functions on sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Toshiyasu Arai","submitted_at":"2012-04-25T08:21:11Z","abstract_excerpt":"Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable functions. Each function in this class is polynomial time computable when we restrict to finite binary strings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5582","kind":"arxiv","version":10},"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":"2026-05-18T02:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUmeRO4wFo28HArHTbSmbbmEl2tSaEXk5fkRMBAeR6lXdiT/o5il1o8TdRAqREnzoDhLE3VkHy8+uGAkXObsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:38:07.899280Z"},"content_sha256":"de7c60e2280afbb06ccc7dd027f7d9499ef2fb763666cf07c738756639f5f85e","schema_version":"1.0","event_id":"sha256:de7c60e2280afbb06ccc7dd027f7d9499ef2fb763666cf07c738756639f5f85e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS/bundle.json","state_url":"https://pith.science/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS/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":"2026-06-26T09:38:07Z","links":{"resolver":"https://pith.science/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS","bundle":"https://pith.science/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS/bundle.json","state":"https://pith.science/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3OOMYUJYZ5AVFS5QA6LFVXLXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q3OOMYUJYZ5AVFS5QA6LFVXLXS","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":"45338f311f42997df1fcc6d9e3639083f15a98be742fefca77d3e6c181d7293e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-25T08:21:11Z","title_canon_sha256":"6d91c4e5eb6599675b2b3d94c189386f0b197ff25418f4b78ae391fb1838d5b1"},"schema_version":"1.0","source":{"id":"1204.5582","kind":"arxiv","version":10}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5582","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5582v10","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5582","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"Q3OOMYUJYZ5A","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q3OOMYUJYZ5AVFS5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q3OOMYUJ","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:de7c60e2280afbb06ccc7dd027f7d9499ef2fb763666cf07c738756639f5f85e","target":"graph","created_at":"2026-05-18T02:32:46Z","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":"Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable functions. Each function in this class is polynomial time computable when we restrict to finite binary strings.","authors_text":"Toshiyasu Arai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-25T08:21:11Z","title":"Predicatively computable functions on sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5582","kind":"arxiv","version":10},"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":"sha256:609b281a79d1098379c5884b4603ea2a1131a38828f0dd4f54763b094a183936","target":"record","created_at":"2026-05-18T02:32:46Z","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":"45338f311f42997df1fcc6d9e3639083f15a98be742fefca77d3e6c181d7293e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-25T08:21:11Z","title_canon_sha256":"6d91c4e5eb6599675b2b3d94c189386f0b197ff25418f4b78ae391fb1838d5b1"},"schema_version":"1.0","source":{"id":"1204.5582","kind":"arxiv","version":10}},"canonical_sha256":"86dce66289c67a0a965d803cb2d6ebbc8a36dc36213d9a0db808298e3ec7af28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86dce66289c67a0a965d803cb2d6ebbc8a36dc36213d9a0db808298e3ec7af28","first_computed_at":"2026-05-18T02:32:46.596967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:46.596967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SzHMiziWMCbX30H2PsyeTuPVsOyMrC6ptwcGHHwCzQ4u0X1K+sDwfrvbzeHMqAVxRrpmM3wrKjK5JouXNuQfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:46.597403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5582","source_kind":"arxiv","source_version":10}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:609b281a79d1098379c5884b4603ea2a1131a38828f0dd4f54763b094a183936","sha256:de7c60e2280afbb06ccc7dd027f7d9499ef2fb763666cf07c738756639f5f85e"],"state_sha256":"f99cd1a9ab381b5a33249b344db85d6e4a80b4fa8f4e7c256aca60d72d189736"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3gnWsRW1iM7Np8wsSoixSY3Lorc5vclc65+a6RThoh1E/isMg1PIFkPG/vBbJj6mLxyTI30xqAZNBzsmsCfBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:38:07.901241Z","bundle_sha256":"3d4e70ea3cd7f052cf780380ec31f1fc3b39388d71009fc977915cdaae467060"}}