{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CUGNCX76ZYCBNO6JXI7YCU4DW3","short_pith_number":"pith:CUGNCX76","canonical_record":{"source":{"id":"1411.5782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-21T07:47:09Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"f2417a2c2853cf021c6547ce8ff0d4ab11aded4382d5d6f373934a1d4ba3c603","abstract_canon_sha256":"f5b72f9dad497e8988990e837c701410d23919e7676ff66fe7c073c3a5db8a46"},"schema_version":"1.0"},"canonical_sha256":"150cd15ffece0416bbc9ba3f815383b6efeaa5f865e53f6e7c20e8f49b9de147","source":{"kind":"arxiv","id":"1411.5782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5782","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5782v1","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5782","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"CUGNCX76ZYCB","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CUGNCX76ZYCBNO6J","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CUGNCX76","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CUGNCX76ZYCBNO6JXI7YCU4DW3","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-21T07:47:09Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"f2417a2c2853cf021c6547ce8ff0d4ab11aded4382d5d6f373934a1d4ba3c603","abstract_canon_sha256":"f5b72f9dad497e8988990e837c701410d23919e7676ff66fe7c073c3a5db8a46"},"schema_version":"1.0"},"canonical_sha256":"150cd15ffece0416bbc9ba3f815383b6efeaa5f865e53f6e7c20e8f49b9de147","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:07.109782Z","signature_b64":"D380QYFbMx2tNvQQnttPjVm48L7kfbwULGPHj9ces6JE4mmna23/zcp6xqPY6s9YZrUfNaIkIz0MqTghBJxUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"150cd15ffece0416bbc9ba3f815383b6efeaa5f865e53f6e7c20e8f49b9de147","last_reissued_at":"2026-05-18T02:33:07.109424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:07.109424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5782","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":"2026-05-18T02:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2YXmkWWtOO+3y0ohNrF+VDeWtg7VYs98HmPWIKxbDhEokclW74fL4IFDMnXdnweaMHrLvIIsPBU2SRJOKx6XCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:28:22.869014Z"},"content_sha256":"26e44c2d41a10b4eda92e275db303236f3ee12eccaca199c7b251a7dd69e0b18","schema_version":"1.0","event_id":"sha256:26e44c2d41a10b4eda92e275db303236f3ee12eccaca199c7b251a7dd69e0b18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CUGNCX76ZYCBNO6JXI7YCU4DW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Bounds For Frameproof Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Chong Shangguan, Gennian Ge, Xin Wang, Ying Miao","submitted_at":"2014-11-21T07:47:09Z","abstract_excerpt":"Frameproof codes are used to fingerprint digital data. It can prevent copyrighted materials from unauthorized use. In this paper, we study upper and lower bounds for $w$-frameproof codes of length $N$ over an alphabet of size $q$. The upper bound is based on a combinatorial approach and the lower bound is based on a probabilistic construction. Both bounds can improve previous results when $q$ is small compared to $w$, say $cq\\leq w$ for some constant $c\\leq q$. Furthermore, we pay special attention to binary frameproof codes. We show a binary $w$-frameproof code of length $N$ can not have more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5782","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":"2026-05-18T02:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOhIZISydL4vUTmH99JbnONnKx9qN97EBCSuviDcc3Rk1wZLl6nzkzMHqAA/UTyMK2/rP1ITqVu7hQPe6s9iAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:28:22.869369Z"},"content_sha256":"5acc80b39343cbfa147bff565f4821060ca5169215c36368e90cf0c286efbbc7","schema_version":"1.0","event_id":"sha256:5acc80b39343cbfa147bff565f4821060ca5169215c36368e90cf0c286efbbc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3/bundle.json","state_url":"https://pith.science/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3/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":"2026-06-02T10:28:22Z","links":{"resolver":"https://pith.science/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3","bundle":"https://pith.science/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3/bundle.json","state":"https://pith.science/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUGNCX76ZYCBNO6JXI7YCU4DW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CUGNCX76ZYCBNO6JXI7YCU4DW3","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":"f5b72f9dad497e8988990e837c701410d23919e7676ff66fe7c073c3a5db8a46","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-21T07:47:09Z","title_canon_sha256":"f2417a2c2853cf021c6547ce8ff0d4ab11aded4382d5d6f373934a1d4ba3c603"},"schema_version":"1.0","source":{"id":"1411.5782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5782","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5782v1","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5782","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"CUGNCX76ZYCB","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CUGNCX76ZYCBNO6J","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CUGNCX76","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5acc80b39343cbfa147bff565f4821060ca5169215c36368e90cf0c286efbbc7","target":"graph","created_at":"2026-05-18T02:33:07Z","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":"Frameproof codes are used to fingerprint digital data. It can prevent copyrighted materials from unauthorized use. In this paper, we study upper and lower bounds for $w$-frameproof codes of length $N$ over an alphabet of size $q$. The upper bound is based on a combinatorial approach and the lower bound is based on a probabilistic construction. Both bounds can improve previous results when $q$ is small compared to $w$, say $cq\\leq w$ for some constant $c\\leq q$. Furthermore, we pay special attention to binary frameproof codes. We show a binary $w$-frameproof code of length $N$ can not have more","authors_text":"Chong Shangguan, Gennian Ge, Xin Wang, Ying Miao","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-21T07:47:09Z","title":"New Bounds For Frameproof Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5782","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":"sha256:26e44c2d41a10b4eda92e275db303236f3ee12eccaca199c7b251a7dd69e0b18","target":"record","created_at":"2026-05-18T02:33:07Z","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":"f5b72f9dad497e8988990e837c701410d23919e7676ff66fe7c073c3a5db8a46","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-21T07:47:09Z","title_canon_sha256":"f2417a2c2853cf021c6547ce8ff0d4ab11aded4382d5d6f373934a1d4ba3c603"},"schema_version":"1.0","source":{"id":"1411.5782","kind":"arxiv","version":1}},"canonical_sha256":"150cd15ffece0416bbc9ba3f815383b6efeaa5f865e53f6e7c20e8f49b9de147","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"150cd15ffece0416bbc9ba3f815383b6efeaa5f865e53f6e7c20e8f49b9de147","first_computed_at":"2026-05-18T02:33:07.109424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:07.109424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D380QYFbMx2tNvQQnttPjVm48L7kfbwULGPHj9ces6JE4mmna23/zcp6xqPY6s9YZrUfNaIkIz0MqTghBJxUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:07.109782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26e44c2d41a10b4eda92e275db303236f3ee12eccaca199c7b251a7dd69e0b18","sha256:5acc80b39343cbfa147bff565f4821060ca5169215c36368e90cf0c286efbbc7"],"state_sha256":"1b948337a1410a811bc5173ac679d2a3db52d9025987592e53e3e1ae4c713e1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/Gv23x/5HbdoSIcUaRAM1L0vkd7fML9nkDuxMV4i/lZsi6S2sEgj3mV6bhthCJzK0XHR4HeTMCeZDh3nQ7KBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:28:22.871270Z","bundle_sha256":"488adbd96f595fe9664013f279c05013f379ef836ce810f0d21e8562d3ea9759"}}