{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YUTTQFO7EISCWDONWWDWUR2HN7","short_pith_number":"pith:YUTTQFO7","canonical_record":{"source":{"id":"1310.4681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-17T12:57:54Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e47ee13600c51176c931e554774a754de1837888093b829216e3cedb9d814449","abstract_canon_sha256":"9f82852e095185f399c2ec96967f87e0cc9e0b5df42960af1014af54c0912701"},"schema_version":"1.0"},"canonical_sha256":"c5273815df22242b0dcdb5876a47476fe38fc93591b3ef33d2f6b2bf9e71e366","source":{"kind":"arxiv","id":"1310.4681","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4681","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4681v1","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4681","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"YUTTQFO7EISC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YUTTQFO7EISCWDON","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YUTTQFO7","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YUTTQFO7EISCWDONWWDWUR2HN7","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-17T12:57:54Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e47ee13600c51176c931e554774a754de1837888093b829216e3cedb9d814449","abstract_canon_sha256":"9f82852e095185f399c2ec96967f87e0cc9e0b5df42960af1014af54c0912701"},"schema_version":"1.0"},"canonical_sha256":"c5273815df22242b0dcdb5876a47476fe38fc93591b3ef33d2f6b2bf9e71e366","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:13.230718Z","signature_b64":"hvG7Ne60vM0gBCEsX/9teKeyrBdfVVQNE7PFlgAXh+oFtxXLK7eASljYxpiaExqcNjJixHYkN0k1h1cjF2JsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5273815df22242b0dcdb5876a47476fe38fc93591b3ef33d2f6b2bf9e71e366","last_reissued_at":"2026-05-18T03:10:13.230203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:13.230203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4681","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":"2026-05-18T03:10:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zLsO+dpk/2r5D0wiONLX8dZ9STPJcfB9NnCFqrMB8HZ22TqBFljIHL3w5zA2q1QK8NVYFnvl15tpYWY7TDYyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:09:07.791985Z"},"content_sha256":"194aa6e368038b7fe20d39bd786c0792bc4d8f3ea55bde9a5c4361b6e5e2cb5a","schema_version":"1.0","event_id":"sha256:194aa6e368038b7fe20d39bd786c0792bc4d8f3ea55bde9a5c4361b6e5e2cb5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YUTTQFO7EISCWDONWWDWUR2HN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random index of codivisibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Jos\\'e L. Fern\\'andez, Pablo Fern\\'andez","submitted_at":"2013-10-17T12:57:54Z","abstract_excerpt":"The index of codivisibility of a set of integers is the size of its largest subset with a common prime divisor. For large random samples of integers, the index of codivisibility is approximately normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4681","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":"2026-05-18T03:10:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9REFGn0ayc5rDIkc4nc4do9MsBr0gmgXPPcegCgS4TGg+D3A9xtormYiWy7urer8TdXidRRl1HGDxWctXbaUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:09:07.792335Z"},"content_sha256":"00b6ecdbe560f3f7b15bc0422fbbcba61a5ebf63a55c52548eedbebda4cb9a05","schema_version":"1.0","event_id":"sha256:00b6ecdbe560f3f7b15bc0422fbbcba61a5ebf63a55c52548eedbebda4cb9a05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUTTQFO7EISCWDONWWDWUR2HN7/bundle.json","state_url":"https://pith.science/pith/YUTTQFO7EISCWDONWWDWUR2HN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUTTQFO7EISCWDONWWDWUR2HN7/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":"2026-05-28T02:09:07Z","links":{"resolver":"https://pith.science/pith/YUTTQFO7EISCWDONWWDWUR2HN7","bundle":"https://pith.science/pith/YUTTQFO7EISCWDONWWDWUR2HN7/bundle.json","state":"https://pith.science/pith/YUTTQFO7EISCWDONWWDWUR2HN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUTTQFO7EISCWDONWWDWUR2HN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YUTTQFO7EISCWDONWWDWUR2HN7","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":"9f82852e095185f399c2ec96967f87e0cc9e0b5df42960af1014af54c0912701","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-17T12:57:54Z","title_canon_sha256":"e47ee13600c51176c931e554774a754de1837888093b829216e3cedb9d814449"},"schema_version":"1.0","source":{"id":"1310.4681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4681","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4681v1","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4681","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"YUTTQFO7EISC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YUTTQFO7EISCWDON","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YUTTQFO7","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:00b6ecdbe560f3f7b15bc0422fbbcba61a5ebf63a55c52548eedbebda4cb9a05","target":"graph","created_at":"2026-05-18T03:10:13Z","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 index of codivisibility of a set of integers is the size of its largest subset with a common prime divisor. For large random samples of integers, the index of codivisibility is approximately normal.","authors_text":"Jos\\'e L. Fern\\'andez, Pablo Fern\\'andez","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-17T12:57:54Z","title":"Random index of codivisibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4681","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":"sha256:194aa6e368038b7fe20d39bd786c0792bc4d8f3ea55bde9a5c4361b6e5e2cb5a","target":"record","created_at":"2026-05-18T03:10:13Z","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":"9f82852e095185f399c2ec96967f87e0cc9e0b5df42960af1014af54c0912701","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-17T12:57:54Z","title_canon_sha256":"e47ee13600c51176c931e554774a754de1837888093b829216e3cedb9d814449"},"schema_version":"1.0","source":{"id":"1310.4681","kind":"arxiv","version":1}},"canonical_sha256":"c5273815df22242b0dcdb5876a47476fe38fc93591b3ef33d2f6b2bf9e71e366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5273815df22242b0dcdb5876a47476fe38fc93591b3ef33d2f6b2bf9e71e366","first_computed_at":"2026-05-18T03:10:13.230203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:13.230203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvG7Ne60vM0gBCEsX/9teKeyrBdfVVQNE7PFlgAXh+oFtxXLK7eASljYxpiaExqcNjJixHYkN0k1h1cjF2JsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:13.230718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:194aa6e368038b7fe20d39bd786c0792bc4d8f3ea55bde9a5c4361b6e5e2cb5a","sha256:00b6ecdbe560f3f7b15bc0422fbbcba61a5ebf63a55c52548eedbebda4cb9a05"],"state_sha256":"e9085fafff35e0f75e012c7cf15a855f28b84bd53e11f273d643c9321a40f947"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wn7VD4aLtm4JUzDZn4HL9ug9DV+/I1TBAdW1FKZvDsKq+FGtrwBO51CWmwACaOOX4vOT6mJZ4D9UlODGPS+9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:09:07.794382Z","bundle_sha256":"41aa28793bb2fee60f87fb6c28ad2407251d4c889d81ecf69052f3283a85309b"}}