{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OZT6KB2EHHU4XSDUQMRGPVFOAX","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":"e0999cc9e916500f86f8b97a62e0682576aa579cc8f6a17c2b57c11c912738cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-20T17:28:49Z","title_canon_sha256":"cb9d09861753413e6e55b8118d21ad77ea84457f433a869baca74aeacbc4b6b7"},"schema_version":"1.0","source":{"id":"1409.5906","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5906","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5906v3","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5906","created_at":"2026-05-18T02:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"OZT6KB2EHHU4","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OZT6KB2EHHU4XSDU","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OZT6KB2E","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:58c8b7f699ac016ac806dca146070c4b45265c17991b7a4fdaf40d5e44b4cee0","target":"graph","created_at":"2026-05-18T02:38:38Z","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":"Let $\\{\\phi_p\\}$ be an optimal G\\\"odel numbering of the family of computable functions (in Schnorr's sense), where $p$ ranges over binary strings. Assume that a list of strings $L(p)$ is computable from $p$ and for all $p$ contains a $\\phi$-program for $\\phi_p$ whose length is at most $\\varepsilon$ bits larger that the length of the shortest $\\phi$-program for $\\phi_p$. We show that for infinitely many $p$ the list $L(p)$ must have $2^{|p|-\\varepsilon-O(1)}$ strings. Here $\\varepsilon$ is an arbitrary function of $p$.","authors_text":"Nikolay Vereshchagin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-20T17:28:49Z","title":"Short lists with short programs for functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5906","kind":"arxiv","version":3},"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":"sha256:3530c19a399efc82fa614d4eb13e71b8f1323f7c3df7328eb5c8bbaa16280b70","target":"record","created_at":"2026-05-18T02:38:38Z","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":"e0999cc9e916500f86f8b97a62e0682576aa579cc8f6a17c2b57c11c912738cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-20T17:28:49Z","title_canon_sha256":"cb9d09861753413e6e55b8118d21ad77ea84457f433a869baca74aeacbc4b6b7"},"schema_version":"1.0","source":{"id":"1409.5906","kind":"arxiv","version":3}},"canonical_sha256":"7667e5074439e9cbc874832267d4ae05f9affd28ac5a1bc60e5fca1842bc38c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7667e5074439e9cbc874832267d4ae05f9affd28ac5a1bc60e5fca1842bc38c4","first_computed_at":"2026-05-18T02:38:38.651624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:38.651624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1G7oE8ZS8C4SxJKTd/tA4QWLiz++NtdQSQb3rZfI9P7w2QEmbI/09e+Z/huwNmUnY4+AfCThRfFSW+YMhP4TCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:38.652040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5906","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3530c19a399efc82fa614d4eb13e71b8f1323f7c3df7328eb5c8bbaa16280b70","sha256:58c8b7f699ac016ac806dca146070c4b45265c17991b7a4fdaf40d5e44b4cee0"],"state_sha256":"0d469acce9fe4d8f575e62d06771626c9bc066bfb276c72a1b6c3e53831adaec"}