{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OZT6KB2EHHU4XSDUQMRGPVFOAX","short_pith_number":"pith:OZT6KB2E","canonical_record":{"source":{"id":"1409.5906","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-20T17:28:49Z","cross_cats_sorted":[],"title_canon_sha256":"cb9d09861753413e6e55b8118d21ad77ea84457f433a869baca74aeacbc4b6b7","abstract_canon_sha256":"e0999cc9e916500f86f8b97a62e0682576aa579cc8f6a17c2b57c11c912738cb"},"schema_version":"1.0"},"canonical_sha256":"7667e5074439e9cbc874832267d4ae05f9affd28ac5a1bc60e5fca1842bc38c4","source":{"kind":"arxiv","id":"1409.5906","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OZT6KB2EHHU4XSDUQMRGPVFOAX","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5906","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-20T17:28:49Z","cross_cats_sorted":[],"title_canon_sha256":"cb9d09861753413e6e55b8118d21ad77ea84457f433a869baca74aeacbc4b6b7","abstract_canon_sha256":"e0999cc9e916500f86f8b97a62e0682576aa579cc8f6a17c2b57c11c912738cb"},"schema_version":"1.0"},"canonical_sha256":"7667e5074439e9cbc874832267d4ae05f9affd28ac5a1bc60e5fca1842bc38c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:38.652040Z","signature_b64":"1G7oE8ZS8C4SxJKTd/tA4QWLiz++NtdQSQb3rZfI9P7w2QEmbI/09e+Z/huwNmUnY4+AfCThRfFSW+YMhP4TCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7667e5074439e9cbc874832267d4ae05f9affd28ac5a1bc60e5fca1842bc38c4","last_reissued_at":"2026-05-18T02:38:38.651624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:38.651624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5906","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JojB8IIpepcM3YfNWJ4/AHCDKO+lPJIrIF81SZg+jHdiXwRzSFKNHrs8T54HTM5Pq0bZLyfJpSxfhO2AjbUpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:13:16.078097Z"},"content_sha256":"3530c19a399efc82fa614d4eb13e71b8f1323f7c3df7328eb5c8bbaa16280b70","schema_version":"1.0","event_id":"sha256:3530c19a399efc82fa614d4eb13e71b8f1323f7c3df7328eb5c8bbaa16280b70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OZT6KB2EHHU4XSDUQMRGPVFOAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Short lists with short programs for functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Nikolay Vereshchagin","submitted_at":"2014-09-20T17:28:49Z","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 $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5906","kind":"arxiv","version":3},"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":"2026-05-18T02:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ccg+4whymib9FB2rCCMjAlV8tBKuOr4G88jgAf61KjPVnhTjsOYNjTKTlRlqsd8KEjQFGPnZFxOOzsHZth6LDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:13:16.078791Z"},"content_sha256":"58c8b7f699ac016ac806dca146070c4b45265c17991b7a4fdaf40d5e44b4cee0","schema_version":"1.0","event_id":"sha256:58c8b7f699ac016ac806dca146070c4b45265c17991b7a4fdaf40d5e44b4cee0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX/bundle.json","state_url":"https://pith.science/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX/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":"2026-06-07T06:13:16Z","links":{"resolver":"https://pith.science/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX","bundle":"https://pith.science/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX/bundle.json","state":"https://pith.science/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZT6KB2EHHU4XSDUQMRGPVFOAX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uwLQRJa3AvNZgi0F1ofhZgB6P4VtrjjkD1xYY7HvtRKGECDU/qzngmVl/qobUCeYDa8R0QdRxCbYGYpL/0waDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:13:16.082242Z","bundle_sha256":"66f9587c332bb75be30a46a66290579a33be730619094dbeb83903e3581de56b"}}