{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7G63D5XCCYZQTUQNLLSK347HBO","short_pith_number":"pith:7G63D5XC","canonical_record":{"source":{"id":"1508.05674","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-23T23:46:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d491cf980d105f5030dd5e09103c8177fad419fb010bb9bef58d4d918e60325c","abstract_canon_sha256":"97b67f8f30fcee82cd6ee0fc868b702c65e291fd3c29fe82125e2bea2b401e71"},"schema_version":"1.0"},"canonical_sha256":"f9bdb1f6e2163309d20d5ae4adf3e70bba6f962d80fa910665b69c7dabb375e9","source":{"kind":"arxiv","id":"1508.05674","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05674","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05674v2","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05674","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"7G63D5XCCYZQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7G63D5XCCYZQTUQN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7G63D5XC","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7G63D5XCCYZQTUQNLLSK347HBO","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05674","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-23T23:46:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d491cf980d105f5030dd5e09103c8177fad419fb010bb9bef58d4d918e60325c","abstract_canon_sha256":"97b67f8f30fcee82cd6ee0fc868b702c65e291fd3c29fe82125e2bea2b401e71"},"schema_version":"1.0"},"canonical_sha256":"f9bdb1f6e2163309d20d5ae4adf3e70bba6f962d80fa910665b69c7dabb375e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:15.026350Z","signature_b64":"Qn7ohPrjzu10uqb4Jd+UVffLaasSCNJHy3vnr4uOA+Jf1og4tM9ZvXowMLZxtoyol056IhS+4PmqY8MyNMQrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9bdb1f6e2163309d20d5ae4adf3e70bba6f962d80fa910665b69c7dabb375e9","last_reissued_at":"2026-05-18T01:34:15.025647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:15.025647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05674","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":"2026-05-18T01:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oeQ8Xto5tSZ27K0PNXsPU2sPciOVZ3N6V5/jQ/pK58EB6PKbw7u5lkVldZhdQls4mIV3ETaaYXRRxyaUzdL1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:36:25.213971Z"},"content_sha256":"76d774d780753494663db34d239d081e1d9b85485574c1fe064353ce241e45a0","schema_version":"1.0","event_id":"sha256:76d774d780753494663db34d239d081e1d9b85485574c1fe064353ce241e45a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7G63D5XCCYZQTUQNLLSK347HBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two infinite classes of rotation symmetric bent functions with simple representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chunming Tang, Cuiling Fan, Yanfeng Qi, Zhengchun Zhou","submitted_at":"2015-08-23T23:46:31Z","abstract_excerpt":"In the literature, few $n$-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on $\\mathbb{F}_2^{n}$ of the two forms:\n  {\\rm (i)} $f(x)=\\sum_{i=0}^{m-1}x_ix_{i+m} + \\gamma(x_0+x_m,\\cdots, x_{m-1}+x_{2m-1})$,\n  {\\rm (ii)} $f_t(x)= \\sum_{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \\sum_{i=0}^{m-1}x_ix_{i+m}+ \\gamma(x_0+x_m,\\cdots, x_{m-1}+x_{2m-1})$,\n  \\noindent where $n=2m$, $\\gamma(X_0,X_1,\\cdots, X_{m-1})$ is any rotation symmetric polynomial, and $m/gcd(m,t)$ is odd. The class (i) of rotation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05674","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":"2026-05-18T01:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64OeC58EZVZZ2AKpPjKgWr3AOJPhaict7R7AFJbyLEED0jvwI5hjcN/QqluGo9Ni/xLtZtIhSXACDyBF0BjhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:36:25.214720Z"},"content_sha256":"e153a797ce83e843d5f40e2374166491987648edfce4df2ee25c504ce9dbf96b","schema_version":"1.0","event_id":"sha256:e153a797ce83e843d5f40e2374166491987648edfce4df2ee25c504ce9dbf96b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7G63D5XCCYZQTUQNLLSK347HBO/bundle.json","state_url":"https://pith.science/pith/7G63D5XCCYZQTUQNLLSK347HBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7G63D5XCCYZQTUQNLLSK347HBO/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":"2026-06-04T00:36:25Z","links":{"resolver":"https://pith.science/pith/7G63D5XCCYZQTUQNLLSK347HBO","bundle":"https://pith.science/pith/7G63D5XCCYZQTUQNLLSK347HBO/bundle.json","state":"https://pith.science/pith/7G63D5XCCYZQTUQNLLSK347HBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7G63D5XCCYZQTUQNLLSK347HBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7G63D5XCCYZQTUQNLLSK347HBO","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":"97b67f8f30fcee82cd6ee0fc868b702c65e291fd3c29fe82125e2bea2b401e71","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-23T23:46:31Z","title_canon_sha256":"d491cf980d105f5030dd5e09103c8177fad419fb010bb9bef58d4d918e60325c"},"schema_version":"1.0","source":{"id":"1508.05674","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05674","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05674v2","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05674","created_at":"2026-05-18T01:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"7G63D5XCCYZQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7G63D5XCCYZQTUQN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7G63D5XC","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e153a797ce83e843d5f40e2374166491987648edfce4df2ee25c504ce9dbf96b","target":"graph","created_at":"2026-05-18T01:34:15Z","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":"In the literature, few $n$-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on $\\mathbb{F}_2^{n}$ of the two forms:\n  {\\rm (i)} $f(x)=\\sum_{i=0}^{m-1}x_ix_{i+m} + \\gamma(x_0+x_m,\\cdots, x_{m-1}+x_{2m-1})$,\n  {\\rm (ii)} $f_t(x)= \\sum_{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \\sum_{i=0}^{m-1}x_ix_{i+m}+ \\gamma(x_0+x_m,\\cdots, x_{m-1}+x_{2m-1})$,\n  \\noindent where $n=2m$, $\\gamma(X_0,X_1,\\cdots, X_{m-1})$ is any rotation symmetric polynomial, and $m/gcd(m,t)$ is odd. The class (i) of rotation ","authors_text":"Chunming Tang, Cuiling Fan, Yanfeng Qi, Zhengchun Zhou","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-23T23:46:31Z","title":"Two infinite classes of rotation symmetric bent functions with simple representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05674","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":"sha256:76d774d780753494663db34d239d081e1d9b85485574c1fe064353ce241e45a0","target":"record","created_at":"2026-05-18T01:34:15Z","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":"97b67f8f30fcee82cd6ee0fc868b702c65e291fd3c29fe82125e2bea2b401e71","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-23T23:46:31Z","title_canon_sha256":"d491cf980d105f5030dd5e09103c8177fad419fb010bb9bef58d4d918e60325c"},"schema_version":"1.0","source":{"id":"1508.05674","kind":"arxiv","version":2}},"canonical_sha256":"f9bdb1f6e2163309d20d5ae4adf3e70bba6f962d80fa910665b69c7dabb375e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9bdb1f6e2163309d20d5ae4adf3e70bba6f962d80fa910665b69c7dabb375e9","first_computed_at":"2026-05-18T01:34:15.025647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:15.025647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qn7ohPrjzu10uqb4Jd+UVffLaasSCNJHy3vnr4uOA+Jf1og4tM9ZvXowMLZxtoyol056IhS+4PmqY8MyNMQrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:15.026350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05674","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76d774d780753494663db34d239d081e1d9b85485574c1fe064353ce241e45a0","sha256:e153a797ce83e843d5f40e2374166491987648edfce4df2ee25c504ce9dbf96b"],"state_sha256":"ea1c2ece0c22895e85b8ccd7e8f16da54b1a7ad1af356a732ce55cec5fcda4bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pc2XY0/GBP9B/+y3Q9RhdqN+ZYXm3kGCUd+vbJsdw8n5Nwks4mVV3gP4E+lx3ehKsbBxn/62RQWFJr5GGvzzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T00:36:25.217723Z","bundle_sha256":"9aab70ad113433ce642dede3c2ca329d933d6c862865aa99795bc2451ec1e1a9"}}