{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DYNNWWXSCCI27VBGYHXTPKEU7Z","short_pith_number":"pith:DYNNWWXS","canonical_record":{"source":{"id":"1101.4470","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-24T09:09:21Z","cross_cats_sorted":[],"title_canon_sha256":"66d1d8d7c236fb1dcada30fef19165f7c37d788a810f10f53691dca06b3e421d","abstract_canon_sha256":"7b2eef9bb84d9eb85053f08fb4ddffc8d50755b8d84ff64e91fc571955c5a6d4"},"schema_version":"1.0"},"canonical_sha256":"1e1adb5af21091afd426c1ef37a894fe571a6d541d3d2812f6783c3c2c0eccff","source":{"kind":"arxiv","id":"1101.4470","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4470","created_at":"2026-05-18T04:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4470v2","created_at":"2026-05-18T04:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4470","created_at":"2026-05-18T04:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"DYNNWWXSCCI2","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DYNNWWXSCCI27VBG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DYNNWWXS","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DYNNWWXSCCI27VBGYHXTPKEU7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4470","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-24T09:09:21Z","cross_cats_sorted":[],"title_canon_sha256":"66d1d8d7c236fb1dcada30fef19165f7c37d788a810f10f53691dca06b3e421d","abstract_canon_sha256":"7b2eef9bb84d9eb85053f08fb4ddffc8d50755b8d84ff64e91fc571955c5a6d4"},"schema_version":"1.0"},"canonical_sha256":"1e1adb5af21091afd426c1ef37a894fe571a6d541d3d2812f6783c3c2c0eccff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:58.893349Z","signature_b64":"YXlUWdx+/NlD+2fP4NJChIMFhUndR8wDmupn3hyepWtkr5E+0Vv1/XYtC4gK7WHHfaTdjrReZ2lN/N2i4YWtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e1adb5af21091afd426c1ef37a894fe571a6d541d3d2812f6783c3c2c0eccff","last_reissued_at":"2026-05-18T04:20:58.892774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:58.892774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4470","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":"2026-05-18T04:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4BVhahH2n2MJVvqs/5Pk8GY0fuHuXKishCtM43++Ncs2n+nDvYgxQdLo8hqUBMn99nosLi8WufBt0Joj1qACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:10:19.848652Z"},"content_sha256":"8fe9f409840335b8290f734ff9aa88cce408675e19efa57a6a459c27877dcb60","schema_version":"1.0","event_id":"sha256:8fe9f409840335b8290f734ff9aa88cce408675e19efa57a6a459c27877dcb60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DYNNWWXSCCI27VBGYHXTPKEU7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sloane's Gap. Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hector Zenil, Jean-Paul Delahaye, Nicolas Gauvrit","submitted_at":"2011-01-24T09:09:21Z","abstract_excerpt":"The Online Encyclopedia of Integer Sequences (OEIS) is made up of thousands of numerical sequences considered particularly interesting by some mathematicians. The graphic representation of the frequency with which a number n as a function of n appears in that database shows that the underlying function decreases fast, and that the points are distributed in a cloud, seemingly split into two by a clear zone that will be referred to here as \"Sloane's Gap\". The decrease and general form are explained by mathematics, but an explanation of the gap requires further considerations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4470","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":"2026-05-18T04:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zRdmDDz2voYQQG54V80ag7yAfpI6V97axOmSlEorV3B4aVm+RgZb8Ua+SYo/XSmQny3hwHODXE9fQBU/9BxmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:10:19.849300Z"},"content_sha256":"a07e5337fc9b5ae75afb3548329bd4d2be9cefc98470bc6abb74677cca31277b","schema_version":"1.0","event_id":"sha256:a07e5337fc9b5ae75afb3548329bd4d2be9cefc98470bc6abb74677cca31277b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z/bundle.json","state_url":"https://pith.science/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z/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":"2026-05-25T23:10:19Z","links":{"resolver":"https://pith.science/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z","bundle":"https://pith.science/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z/bundle.json","state":"https://pith.science/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYNNWWXSCCI27VBGYHXTPKEU7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DYNNWWXSCCI27VBGYHXTPKEU7Z","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":"7b2eef9bb84d9eb85053f08fb4ddffc8d50755b8d84ff64e91fc571955c5a6d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-24T09:09:21Z","title_canon_sha256":"66d1d8d7c236fb1dcada30fef19165f7c37d788a810f10f53691dca06b3e421d"},"schema_version":"1.0","source":{"id":"1101.4470","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4470","created_at":"2026-05-18T04:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4470v2","created_at":"2026-05-18T04:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4470","created_at":"2026-05-18T04:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"DYNNWWXSCCI2","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DYNNWWXSCCI27VBG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DYNNWWXS","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:a07e5337fc9b5ae75afb3548329bd4d2be9cefc98470bc6abb74677cca31277b","target":"graph","created_at":"2026-05-18T04:20:58Z","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 Online Encyclopedia of Integer Sequences (OEIS) is made up of thousands of numerical sequences considered particularly interesting by some mathematicians. The graphic representation of the frequency with which a number n as a function of n appears in that database shows that the underlying function decreases fast, and that the points are distributed in a cloud, seemingly split into two by a clear zone that will be referred to here as \"Sloane's Gap\". The decrease and general form are explained by mathematics, but an explanation of the gap requires further considerations.","authors_text":"Hector Zenil, Jean-Paul Delahaye, Nicolas Gauvrit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-24T09:09:21Z","title":"Sloane's Gap. Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4470","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":"sha256:8fe9f409840335b8290f734ff9aa88cce408675e19efa57a6a459c27877dcb60","target":"record","created_at":"2026-05-18T04:20:58Z","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":"7b2eef9bb84d9eb85053f08fb4ddffc8d50755b8d84ff64e91fc571955c5a6d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-24T09:09:21Z","title_canon_sha256":"66d1d8d7c236fb1dcada30fef19165f7c37d788a810f10f53691dca06b3e421d"},"schema_version":"1.0","source":{"id":"1101.4470","kind":"arxiv","version":2}},"canonical_sha256":"1e1adb5af21091afd426c1ef37a894fe571a6d541d3d2812f6783c3c2c0eccff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e1adb5af21091afd426c1ef37a894fe571a6d541d3d2812f6783c3c2c0eccff","first_computed_at":"2026-05-18T04:20:58.892774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:58.892774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXlUWdx+/NlD+2fP4NJChIMFhUndR8wDmupn3hyepWtkr5E+0Vv1/XYtC4gK7WHHfaTdjrReZ2lN/N2i4YWtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:58.893349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4470","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fe9f409840335b8290f734ff9aa88cce408675e19efa57a6a459c27877dcb60","sha256:a07e5337fc9b5ae75afb3548329bd4d2be9cefc98470bc6abb74677cca31277b"],"state_sha256":"bb2de1a80e2f016fbdccc452afe5e881c5fe89d03336408236580cfd862e4e57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8YbYcyIdetpXyaZPDgXfB7GdE3ucFDACX8wSlKr/O94l4JKpC/TpObBOsue3ZHz0G9KUPmAr+Q4iCuZYTFImDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:10:19.852857Z","bundle_sha256":"db0f53a648ac17aa55fd2e6d8022896275f61fc60ce7ef7ee6e95261f8e7468d"}}