{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PSJNDBISUAIJR5T7STYNADBIC4","short_pith_number":"pith:PSJNDBIS","canonical_record":{"source":{"id":"1403.4539","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-02-27T18:56:40Z","cross_cats_sorted":[],"title_canon_sha256":"f4e8d0ebf663f1c83ca32501573633b8e1b05b8ee6c5b9164b1e649c037ae3f0","abstract_canon_sha256":"bdad5e15a1b79de2536ca7115ade889b9f861c89f54ceff82e51acbc7048d67c"},"schema_version":"1.0"},"canonical_sha256":"7c92d18512a01098f67f94f0d00c28170b34a67de6a82244ac7fa514fce0e194","source":{"kind":"arxiv","id":"1403.4539","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4539","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4539v2","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4539","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"PSJNDBISUAIJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PSJNDBISUAIJR5T7","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PSJNDBIS","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PSJNDBISUAIJR5T7STYNADBIC4","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4539","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-02-27T18:56:40Z","cross_cats_sorted":[],"title_canon_sha256":"f4e8d0ebf663f1c83ca32501573633b8e1b05b8ee6c5b9164b1e649c037ae3f0","abstract_canon_sha256":"bdad5e15a1b79de2536ca7115ade889b9f861c89f54ceff82e51acbc7048d67c"},"schema_version":"1.0"},"canonical_sha256":"7c92d18512a01098f67f94f0d00c28170b34a67de6a82244ac7fa514fce0e194","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:33.539433Z","signature_b64":"llp2Ckiq9Crik6jnytBbmWO78ajgKenADMO2BBWS5fwPpjcD6Afj1o6kPvCqeC7BOqKzicPHZybJ4KxSEqYaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c92d18512a01098f67f94f0d00c28170b34a67de6a82244ac7fa514fce0e194","last_reissued_at":"2026-05-17T23:59:33.538861Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:33.538861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4539","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zMRIm8ex831RaFJKNp+44dLF3h8/UDMbKjRBJvwPWTzUQB44mvG6NVa/hYY2tqVbavtF4aWPKbbPlSmUXviBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:45:10.929815Z"},"content_sha256":"9c44585fd4b0d4e9c6278b1d54ee9509cea891bd29e07207b5391a0d71586dbd","schema_version":"1.0","event_id":"sha256:9c44585fd4b0d4e9c6278b1d54ee9509cea891bd29e07207b5391a0d71586dbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PSJNDBISUAIJR5T7STYNADBIC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Occam Bound on Lowest Complexity of Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Leonid A. Levin","submitted_at":"2014-02-27T18:56:40Z","abstract_excerpt":"The combined universal probability M(D) of strings x in sets D is close to max_{x \\in D} M({x}): their ~ logs differ by at most D's information j = I(D:H) about the halting sequence H. Thus if all x have complexity K(x) > k, D carries > i bits of information on each x where i+j ~ k. Note, there are no ways (whether natural or artificial) to generate D with significant I(D:H)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4539","kind":"arxiv","version":2},"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":"2026-05-17T23:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBP6Hdz6bNTykitbomgCvwZLBfnpVYpi0fUYlEVuoi2CCyJTlyTdJPn6kPVL6Hqowpwn2kuXvlOwyEKv1PiEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:45:10.930150Z"},"content_sha256":"e9efc580186a89845bdde932d0e4dc3c15f1cfd7d247ee2adb64ce271d890c9c","schema_version":"1.0","event_id":"sha256:e9efc580186a89845bdde932d0e4dc3c15f1cfd7d247ee2adb64ce271d890c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSJNDBISUAIJR5T7STYNADBIC4/bundle.json","state_url":"https://pith.science/pith/PSJNDBISUAIJR5T7STYNADBIC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSJNDBISUAIJR5T7STYNADBIC4/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":"2026-06-27T20:45:10Z","links":{"resolver":"https://pith.science/pith/PSJNDBISUAIJR5T7STYNADBIC4","bundle":"https://pith.science/pith/PSJNDBISUAIJR5T7STYNADBIC4/bundle.json","state":"https://pith.science/pith/PSJNDBISUAIJR5T7STYNADBIC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSJNDBISUAIJR5T7STYNADBIC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PSJNDBISUAIJR5T7STYNADBIC4","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":"bdad5e15a1b79de2536ca7115ade889b9f861c89f54ceff82e51acbc7048d67c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-02-27T18:56:40Z","title_canon_sha256":"f4e8d0ebf663f1c83ca32501573633b8e1b05b8ee6c5b9164b1e649c037ae3f0"},"schema_version":"1.0","source":{"id":"1403.4539","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4539","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4539v2","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4539","created_at":"2026-05-17T23:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"PSJNDBISUAIJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PSJNDBISUAIJR5T7","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PSJNDBIS","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e9efc580186a89845bdde932d0e4dc3c15f1cfd7d247ee2adb64ce271d890c9c","target":"graph","created_at":"2026-05-17T23:59:33Z","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":"The combined universal probability M(D) of strings x in sets D is close to max_{x \\in D} M({x}): their ~ logs differ by at most D's information j = I(D:H) about the halting sequence H. Thus if all x have complexity K(x) > k, D carries > i bits of information on each x where i+j ~ k. Note, there are no ways (whether natural or artificial) to generate D with significant I(D:H).","authors_text":"Leonid A. Levin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-02-27T18:56:40Z","title":"Occam Bound on Lowest Complexity of Elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4539","kind":"arxiv","version":2},"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":"sha256:9c44585fd4b0d4e9c6278b1d54ee9509cea891bd29e07207b5391a0d71586dbd","target":"record","created_at":"2026-05-17T23:59:33Z","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":"bdad5e15a1b79de2536ca7115ade889b9f861c89f54ceff82e51acbc7048d67c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-02-27T18:56:40Z","title_canon_sha256":"f4e8d0ebf663f1c83ca32501573633b8e1b05b8ee6c5b9164b1e649c037ae3f0"},"schema_version":"1.0","source":{"id":"1403.4539","kind":"arxiv","version":2}},"canonical_sha256":"7c92d18512a01098f67f94f0d00c28170b34a67de6a82244ac7fa514fce0e194","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c92d18512a01098f67f94f0d00c28170b34a67de6a82244ac7fa514fce0e194","first_computed_at":"2026-05-17T23:59:33.538861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:33.538861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"llp2Ckiq9Crik6jnytBbmWO78ajgKenADMO2BBWS5fwPpjcD6Afj1o6kPvCqeC7BOqKzicPHZybJ4KxSEqYaBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:33.539433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4539","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c44585fd4b0d4e9c6278b1d54ee9509cea891bd29e07207b5391a0d71586dbd","sha256:e9efc580186a89845bdde932d0e4dc3c15f1cfd7d247ee2adb64ce271d890c9c"],"state_sha256":"51f85399d5669d2a2538f1304b4e410938375591e4989e9c9fd453fa47c954fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKmXX3FvqtY5CuJ1ll/K2dcCfeuBe+2RV1tpmm9QoPXSYjFL0dbbZ05L1wSccLCRTtdsoz/rhzsOYByJpU47Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:45:10.932148Z","bundle_sha256":"731b6b871c1fb78e55e01512276df839e20b74c4079f67ac657065eb343407a9"}}