{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KX73OYWFXZG33S7EKYINCFNDXC","short_pith_number":"pith:KX73OYWF","canonical_record":{"source":{"id":"1006.1315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-06-07T18:21:10Z","cross_cats_sorted":[],"title_canon_sha256":"ad4e0785fbe36c9fd4efae3821ad14982661744720e0a6ce00f5a2a4a12d9186","abstract_canon_sha256":"d5439a8a9c2db771e9120b2d812173329685b48fd353af1bb130ca53d2a96009"},"schema_version":"1.0"},"canonical_sha256":"55ffb762c5be4dbdcbe45610d115a3b89882c99c12e2897e6776b961e82fedf5","source":{"kind":"arxiv","id":"1006.1315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1315","created_at":"2026-05-18T02:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1315v1","created_at":"2026-05-18T02:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1315","created_at":"2026-05-18T02:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"KX73OYWFXZG3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KX73OYWFXZG33S7E","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KX73OYWF","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KX73OYWFXZG33S7EKYINCFNDXC","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-06-07T18:21:10Z","cross_cats_sorted":[],"title_canon_sha256":"ad4e0785fbe36c9fd4efae3821ad14982661744720e0a6ce00f5a2a4a12d9186","abstract_canon_sha256":"d5439a8a9c2db771e9120b2d812173329685b48fd353af1bb130ca53d2a96009"},"schema_version":"1.0"},"canonical_sha256":"55ffb762c5be4dbdcbe45610d115a3b89882c99c12e2897e6776b961e82fedf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:56.571828Z","signature_b64":"ktZPUcuLpa792x4XzCG9aEwIpXklL1k34q8DaW3LhX5eysDmjubUvGhPbQGVlDY3mKS34Goh0w5aN4i6uuXkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55ffb762c5be4dbdcbe45610d115a3b89882c99c12e2897e6776b961e82fedf5","last_reissued_at":"2026-05-18T02:06:56.571045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:56.571045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1315","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":"2026-05-18T02:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"klsS1eqZTy4UvDomMsuVG7+0o4T5zruwQZ43NcqSr4YntDsCaVAxOMc0YQu0i7WyBHxCq/F1BZ03V8FI5uS9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:32:21.122238Z"},"content_sha256":"aff72168999e2bafe053dbf13802d82aa04a03e455a6e7e7c617f72f3ef23590","schema_version":"1.0","event_id":"sha256:aff72168999e2bafe053dbf13802d82aa04a03e455a6e7e7c617f72f3ef23590"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KX73OYWFXZG33S7EKYINCFNDXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting dependent and independent strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marius Zimand","submitted_at":"2010-06-07T18:21:10Z","abstract_excerpt":"The paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \\alpha independent, (3) the set of strings that are mutually \\alpha independent. The relevant definitions are as follows: C(x) is the Kolmogorov complexity of the string x. A string y has \\alpha -dependency with a string x if C(y) - C(y|x) \\geq \\alpha. A set of strings {x_1, \\ldots, x_t} is pairwise \\alpha-independent if for all i different from j, C(x_i) - C(x_i | x_j) \\leq \\alpha. A tuple of strings (x_1, \\ldots"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1315","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":"2026-05-18T02:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IV7rK6/hJVgKlzlv60fQCTiA2mEVvBJRFTW0ry600I4iB11JVMjvrrwwBH3U6jea1RbhJUDk4DyBcqI7M/j0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:32:21.122612Z"},"content_sha256":"66f5e18b7b865ac9b985e9fcf22e5672395c5e4fff36ecd244d5323587aeedc7","schema_version":"1.0","event_id":"sha256:66f5e18b7b865ac9b985e9fcf22e5672395c5e4fff36ecd244d5323587aeedc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KX73OYWFXZG33S7EKYINCFNDXC/bundle.json","state_url":"https://pith.science/pith/KX73OYWFXZG33S7EKYINCFNDXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KX73OYWFXZG33S7EKYINCFNDXC/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":"2026-06-21T20:32:21Z","links":{"resolver":"https://pith.science/pith/KX73OYWFXZG33S7EKYINCFNDXC","bundle":"https://pith.science/pith/KX73OYWFXZG33S7EKYINCFNDXC/bundle.json","state":"https://pith.science/pith/KX73OYWFXZG33S7EKYINCFNDXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KX73OYWFXZG33S7EKYINCFNDXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KX73OYWFXZG33S7EKYINCFNDXC","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":"d5439a8a9c2db771e9120b2d812173329685b48fd353af1bb130ca53d2a96009","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-06-07T18:21:10Z","title_canon_sha256":"ad4e0785fbe36c9fd4efae3821ad14982661744720e0a6ce00f5a2a4a12d9186"},"schema_version":"1.0","source":{"id":"1006.1315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1315","created_at":"2026-05-18T02:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1315v1","created_at":"2026-05-18T02:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1315","created_at":"2026-05-18T02:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"KX73OYWFXZG3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KX73OYWFXZG33S7E","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KX73OYWF","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:66f5e18b7b865ac9b985e9fcf22e5672395c5e4fff36ecd244d5323587aeedc7","target":"graph","created_at":"2026-05-18T02:06:56Z","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 paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \\alpha independent, (3) the set of strings that are mutually \\alpha independent. The relevant definitions are as follows: C(x) is the Kolmogorov complexity of the string x. A string y has \\alpha -dependency with a string x if C(y) - C(y|x) \\geq \\alpha. A set of strings {x_1, \\ldots, x_t} is pairwise \\alpha-independent if for all i different from j, C(x_i) - C(x_i | x_j) \\leq \\alpha. A tuple of strings (x_1, \\ldots","authors_text":"Marius Zimand","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-06-07T18:21:10Z","title":"Counting dependent and independent strings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1315","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:aff72168999e2bafe053dbf13802d82aa04a03e455a6e7e7c617f72f3ef23590","target":"record","created_at":"2026-05-18T02:06:56Z","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":"d5439a8a9c2db771e9120b2d812173329685b48fd353af1bb130ca53d2a96009","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-06-07T18:21:10Z","title_canon_sha256":"ad4e0785fbe36c9fd4efae3821ad14982661744720e0a6ce00f5a2a4a12d9186"},"schema_version":"1.0","source":{"id":"1006.1315","kind":"arxiv","version":1}},"canonical_sha256":"55ffb762c5be4dbdcbe45610d115a3b89882c99c12e2897e6776b961e82fedf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55ffb762c5be4dbdcbe45610d115a3b89882c99c12e2897e6776b961e82fedf5","first_computed_at":"2026-05-18T02:06:56.571045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:56.571045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ktZPUcuLpa792x4XzCG9aEwIpXklL1k34q8DaW3LhX5eysDmjubUvGhPbQGVlDY3mKS34Goh0w5aN4i6uuXkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:56.571828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aff72168999e2bafe053dbf13802d82aa04a03e455a6e7e7c617f72f3ef23590","sha256:66f5e18b7b865ac9b985e9fcf22e5672395c5e4fff36ecd244d5323587aeedc7"],"state_sha256":"e9f848b07e917af1febe6f61aede339ea374fa6b9be7ef1561417f2c2a0351a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"66o5aganQ63+kVKk+sBMsuth97rrVORdfo00f3+bgU8d/F03ogXLNnKdK2hG7yOPlJ4ganxme6WftJSls9WjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:32:21.124705Z","bundle_sha256":"db6a9174f728eac9d0841713100332a97b99babdf6da265bd1164810db8c69b9"}}