{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4XUQDIU47NQYIAAALHC4YZBGJE","short_pith_number":"pith:4XUQDIU4","canonical_record":{"source":{"id":"1304.7044","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-26T00:24:12Z","cross_cats_sorted":[],"title_canon_sha256":"9134480ab88fa5e800e2aa3e84b632dbdd20d827f9211532e352529605f7b909","abstract_canon_sha256":"c349f1342498eaa440ba8230da15b000fb9770b6d6664cdfab2bf8ef1a5a37aa"},"schema_version":"1.0"},"canonical_sha256":"e5e901a29cfb6184000059c5cc642649268859796151176d7d16d07080c8defb","source":{"kind":"arxiv","id":"1304.7044","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7044","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7044v3","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7044","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"4XUQDIU47NQY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XUQDIU47NQYIAAA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XUQDIU4","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4XUQDIU47NQYIAAALHC4YZBGJE","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7044","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-26T00:24:12Z","cross_cats_sorted":[],"title_canon_sha256":"9134480ab88fa5e800e2aa3e84b632dbdd20d827f9211532e352529605f7b909","abstract_canon_sha256":"c349f1342498eaa440ba8230da15b000fb9770b6d6664cdfab2bf8ef1a5a37aa"},"schema_version":"1.0"},"canonical_sha256":"e5e901a29cfb6184000059c5cc642649268859796151176d7d16d07080c8defb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:47.664990Z","signature_b64":"wMeRcw9eMG3C/8GW2yPvtzEko5r1+PZuMXFPb+XZ8smHsO7qE/xTGtxiFMiihb9t8L5ihZFa6z+sRD2C8xarDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5e901a29cfb6184000059c5cc642649268859796151176d7d16d07080c8defb","last_reissued_at":"2026-05-18T01:37:47.664329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:47.664329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7044","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSdo7PxEop/9N0dMUhUAajEYiyLew1fUJoXABJsdJoBQ9qb51x3hKHLDZeklgJvTJlHSGoK52vabnpVo47uPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:32:59.053281Z"},"content_sha256":"5b0ec575e7bd2fa0f2d29584227a8f0817bb605e592e4e48f26aacc0fa62db6d","schema_version":"1.0","event_id":"sha256:5b0ec575e7bd2fa0f2d29584227a8f0817bb605e592e4e48f26aacc0fa62db6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4XUQDIU47NQYIAAALHC4YZBGJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New pseudo-planar binomials in characteristic two and related schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gennian Ge, Shuxing Li, Sihuang Hu, Tao Feng, Tao Zhang","submitted_at":"2013-04-26T00:24:12Z","abstract_excerpt":"Planar functions in odd characteristic were introduced by Dembowski and Ostrom in order to construct finite projective planes in 1968. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and signal sets. Recently, a new notion of pseudo-planar functions in even characteristic was proposed by Zhou. These new pseudo-planar functions, as an analogue of planar functions in odd characteristic, also bring about finite projective planes. There are three known infinite families of pseudo-planar monomial functions constructed by Schmidt and Zhou, and Scherr an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7044","kind":"arxiv","version":3},"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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2br7/ip+9X/yCF/FrLzji/DpM6+b/+GpiaIUd+wPJziKeo911iC0tiFZBghLgeyPEvLo5dzPfMXn5T2RDV74CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:32:59.054001Z"},"content_sha256":"cf4b33758b251d148f3af89ebff540479d4049fd36c283325ad701445aa6edb5","schema_version":"1.0","event_id":"sha256:cf4b33758b251d148f3af89ebff540479d4049fd36c283325ad701445aa6edb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XUQDIU47NQYIAAALHC4YZBGJE/bundle.json","state_url":"https://pith.science/pith/4XUQDIU47NQYIAAALHC4YZBGJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XUQDIU47NQYIAAALHC4YZBGJE/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":"2026-05-27T23:32:59Z","links":{"resolver":"https://pith.science/pith/4XUQDIU47NQYIAAALHC4YZBGJE","bundle":"https://pith.science/pith/4XUQDIU47NQYIAAALHC4YZBGJE/bundle.json","state":"https://pith.science/pith/4XUQDIU47NQYIAAALHC4YZBGJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XUQDIU47NQYIAAALHC4YZBGJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4XUQDIU47NQYIAAALHC4YZBGJE","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":"c349f1342498eaa440ba8230da15b000fb9770b6d6664cdfab2bf8ef1a5a37aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-26T00:24:12Z","title_canon_sha256":"9134480ab88fa5e800e2aa3e84b632dbdd20d827f9211532e352529605f7b909"},"schema_version":"1.0","source":{"id":"1304.7044","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7044","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7044v3","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7044","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"4XUQDIU47NQY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XUQDIU47NQYIAAA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XUQDIU4","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:cf4b33758b251d148f3af89ebff540479d4049fd36c283325ad701445aa6edb5","target":"graph","created_at":"2026-05-18T01:37:47Z","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":"Planar functions in odd characteristic were introduced by Dembowski and Ostrom in order to construct finite projective planes in 1968. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and signal sets. Recently, a new notion of pseudo-planar functions in even characteristic was proposed by Zhou. These new pseudo-planar functions, as an analogue of planar functions in odd characteristic, also bring about finite projective planes. There are three known infinite families of pseudo-planar monomial functions constructed by Schmidt and Zhou, and Scherr an","authors_text":"Gennian Ge, Shuxing Li, Sihuang Hu, Tao Feng, Tao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-26T00:24:12Z","title":"New pseudo-planar binomials in characteristic two and related schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7044","kind":"arxiv","version":3},"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":"sha256:5b0ec575e7bd2fa0f2d29584227a8f0817bb605e592e4e48f26aacc0fa62db6d","target":"record","created_at":"2026-05-18T01:37:47Z","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":"c349f1342498eaa440ba8230da15b000fb9770b6d6664cdfab2bf8ef1a5a37aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-26T00:24:12Z","title_canon_sha256":"9134480ab88fa5e800e2aa3e84b632dbdd20d827f9211532e352529605f7b909"},"schema_version":"1.0","source":{"id":"1304.7044","kind":"arxiv","version":3}},"canonical_sha256":"e5e901a29cfb6184000059c5cc642649268859796151176d7d16d07080c8defb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5e901a29cfb6184000059c5cc642649268859796151176d7d16d07080c8defb","first_computed_at":"2026-05-18T01:37:47.664329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:47.664329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wMeRcw9eMG3C/8GW2yPvtzEko5r1+PZuMXFPb+XZ8smHsO7qE/xTGtxiFMiihb9t8L5ihZFa6z+sRD2C8xarDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:47.664990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7044","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b0ec575e7bd2fa0f2d29584227a8f0817bb605e592e4e48f26aacc0fa62db6d","sha256:cf4b33758b251d148f3af89ebff540479d4049fd36c283325ad701445aa6edb5"],"state_sha256":"8636619ff908eed320b69467e46ac2a358a4defc41761011122d4cbceb3d6215"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bP4NhEUx5ZCN3SzkR8sF32zNd3S6pSdvgToGVcIWDwvHsOdM2KDvPmnNcCiObXCq1hU0v6DXboe9XIVdH0EKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:32:59.057848Z","bundle_sha256":"7427c212a35f2822bd0bd9b37103bfdecab58994e107db98548e741c2c113f36"}}