{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A4H4RSRM54THXP4JTOJRSXWHFO","short_pith_number":"pith:A4H4RSRM","canonical_record":{"source":{"id":"1611.08400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-11-25T09:44:11Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8d333f22c0b114383b5d4173d5bf50a4328c10e834d94e270355b84ca3b951c3","abstract_canon_sha256":"df3d6e96c7328da06a17444d94a12f26a29177fce50fc1545b75b66e08e5f63f"},"schema_version":"1.0"},"canonical_sha256":"070fc8ca2cef267bbf899b93195ec72b92434cbd96a20b28eecb54182c27e8ff","source":{"kind":"arxiv","id":"1611.08400","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08400","created_at":"2026-05-18T00:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08400v2","created_at":"2026-05-18T00:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08400","created_at":"2026-05-18T00:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"A4H4RSRM54TH","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A4H4RSRM54THXP4J","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A4H4RSRM","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A4H4RSRM54THXP4JTOJRSXWHFO","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-11-25T09:44:11Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8d333f22c0b114383b5d4173d5bf50a4328c10e834d94e270355b84ca3b951c3","abstract_canon_sha256":"df3d6e96c7328da06a17444d94a12f26a29177fce50fc1545b75b66e08e5f63f"},"schema_version":"1.0"},"canonical_sha256":"070fc8ca2cef267bbf899b93195ec72b92434cbd96a20b28eecb54182c27e8ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:00.096133Z","signature_b64":"+QEN4rGk5kTJg2ffVVx26yZo/GZLnirTR0ensmbCAvcswISFKxTbk4KyBQo43RGaxW5LLSfNS2aQnarAbPlkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"070fc8ca2cef267bbf899b93195ec72b92434cbd96a20b28eecb54182c27e8ff","last_reissued_at":"2026-05-18T00:56:00.095481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:00.095481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08400","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":"2026-05-18T00:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hNsdF/LJzY0fuXa+RDX7xsVt3gwTzAnMhIOzLYHhynB5EbDAYVFHrtfdSmT/QLJhLg/t4hvng9kUIE/+jq3yDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:17:55.591161Z"},"content_sha256":"41187ef9684478ac349e852c819c2df3bac28865c7ce0f3b7e99ff6c78c99154","schema_version":"1.0","event_id":"sha256:41187ef9684478ac349e852c819c2df3bac28865c7ce0f3b7e99ff6c78c99154"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A4H4RSRM54THXP4JTOJRSXWHFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nondeterministic Communication Complexity of Random Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DM","authors_text":"Dirk Oliver Theis, Mozhgan Pourmoradnasseri","submitted_at":"2016-11-25T09:44:11Z","abstract_excerpt":"We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\\colon X\\times Y \\to \\{0,1\\}$ where each value is chosen to be 1 independently with probability $p=p(n)$, $n := |X|=|Y|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08400","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":"2026-05-18T00:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RM+IkYIYwiY1MfbRXAKWIuykqKohBZ25A9R9piNtF10QZ0Y+fpeM6V5ia+NvzKDapEOJWDlvLGcDGyXFotbaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:17:55.591529Z"},"content_sha256":"542ed04f5f4887cf29d92fd937d2260d79456efecf18ca5b88b18d4c1f3141eb","schema_version":"1.0","event_id":"sha256:542ed04f5f4887cf29d92fd937d2260d79456efecf18ca5b88b18d4c1f3141eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4H4RSRM54THXP4JTOJRSXWHFO/bundle.json","state_url":"https://pith.science/pith/A4H4RSRM54THXP4JTOJRSXWHFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4H4RSRM54THXP4JTOJRSXWHFO/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":"2026-06-03T02:17:55Z","links":{"resolver":"https://pith.science/pith/A4H4RSRM54THXP4JTOJRSXWHFO","bundle":"https://pith.science/pith/A4H4RSRM54THXP4JTOJRSXWHFO/bundle.json","state":"https://pith.science/pith/A4H4RSRM54THXP4JTOJRSXWHFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4H4RSRM54THXP4JTOJRSXWHFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A4H4RSRM54THXP4JTOJRSXWHFO","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":"df3d6e96c7328da06a17444d94a12f26a29177fce50fc1545b75b66e08e5f63f","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-11-25T09:44:11Z","title_canon_sha256":"8d333f22c0b114383b5d4173d5bf50a4328c10e834d94e270355b84ca3b951c3"},"schema_version":"1.0","source":{"id":"1611.08400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08400","created_at":"2026-05-18T00:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08400v2","created_at":"2026-05-18T00:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08400","created_at":"2026-05-18T00:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"A4H4RSRM54TH","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A4H4RSRM54THXP4J","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A4H4RSRM","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:542ed04f5f4887cf29d92fd937d2260d79456efecf18ca5b88b18d4c1f3141eb","target":"graph","created_at":"2026-05-18T00:56:00Z","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":"We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\\colon X\\times Y \\to \\{0,1\\}$ where each value is chosen to be 1 independently with probability $p=p(n)$, $n := |X|=|Y|$.","authors_text":"Dirk Oliver Theis, Mozhgan Pourmoradnasseri","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-11-25T09:44:11Z","title":"Nondeterministic Communication Complexity of Random Boolean Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08400","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":"sha256:41187ef9684478ac349e852c819c2df3bac28865c7ce0f3b7e99ff6c78c99154","target":"record","created_at":"2026-05-18T00:56:00Z","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":"df3d6e96c7328da06a17444d94a12f26a29177fce50fc1545b75b66e08e5f63f","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-11-25T09:44:11Z","title_canon_sha256":"8d333f22c0b114383b5d4173d5bf50a4328c10e834d94e270355b84ca3b951c3"},"schema_version":"1.0","source":{"id":"1611.08400","kind":"arxiv","version":2}},"canonical_sha256":"070fc8ca2cef267bbf899b93195ec72b92434cbd96a20b28eecb54182c27e8ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"070fc8ca2cef267bbf899b93195ec72b92434cbd96a20b28eecb54182c27e8ff","first_computed_at":"2026-05-18T00:56:00.095481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:00.095481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+QEN4rGk5kTJg2ffVVx26yZo/GZLnirTR0ensmbCAvcswISFKxTbk4KyBQo43RGaxW5LLSfNS2aQnarAbPlkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:00.096133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41187ef9684478ac349e852c819c2df3bac28865c7ce0f3b7e99ff6c78c99154","sha256:542ed04f5f4887cf29d92fd937d2260d79456efecf18ca5b88b18d4c1f3141eb"],"state_sha256":"d31dc3e52def520af825e8a4df76a6fa50affa9bea72671bf9dd74fe9107dc46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oF5X3bpnSNcRonNO8lw+nyuY/DlyjVNU26XdEdtG3u/WFjTduwq7SfWBLCiFjkorgYDSa3nM/9s8EKg68b5/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:17:55.593553Z","bundle_sha256":"298a382f2fbab12d4bdeaaad7c305690fd07e1e337a08a14eb5afabe9cf7456d"}}