{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KEBQMF7A72MVR5RBI6TVAH52WW","short_pith_number":"pith:KEBQMF7A","canonical_record":{"source":{"id":"1008.1012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-05T15:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"cfdaa56e39e0b8674c082b5ff1ebbd1d6a486e4fb610134cfd7802d972a0677a","abstract_canon_sha256":"a7fd763d5a488fe63e90e1e6ee3f8318b407b048c542d8f5bcfddd131daddafc"},"schema_version":"1.0"},"canonical_sha256":"51030617e0fe9958f62147a7501fbab5beaa0d9429b412c689bc52d1dc00c083","source":{"kind":"arxiv","id":"1008.1012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1012","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1012v1","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1012","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"KEBQMF7A72MV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KEBQMF7A72MVR5RB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KEBQMF7A","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KEBQMF7A72MVR5RBI6TVAH52WW","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-05T15:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"cfdaa56e39e0b8674c082b5ff1ebbd1d6a486e4fb610134cfd7802d972a0677a","abstract_canon_sha256":"a7fd763d5a488fe63e90e1e6ee3f8318b407b048c542d8f5bcfddd131daddafc"},"schema_version":"1.0"},"canonical_sha256":"51030617e0fe9958f62147a7501fbab5beaa0d9429b412c689bc52d1dc00c083","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:34.787290Z","signature_b64":"FUJ/WsttAyc7vD3f1gLfMvexyXG92lQ8Gz4uBnsRcDhXCK5ttwFUMYDRE1mIYYibncjRr7dJzYsAe6VM/TXJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51030617e0fe9958f62147a7501fbab5beaa0d9429b412c689bc52d1dc00c083","last_reissued_at":"2026-05-18T04:42:34.786592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:34.786592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1012","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":"2026-05-18T04:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hvwJRUms56ZIhJGbBvs2x2+fOkArPnAqAUXSbKTW0IabvGkD9XgD1jlPsLYwHIlZjxIGv+2R2mtdpM79i1eiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:57:08.200389Z"},"content_sha256":"065d08b9d62a8fd683648f537e9431d732a28f54ca15f3086145473dacca81dd","schema_version":"1.0","event_id":"sha256:065d08b9d62a8fd683648f537e9431d732a28f54ca15f3086145473dacca81dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KEBQMF7A72MVR5RBI6TVAH52WW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial functions on the units of Z_{2^n}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Danilo Gligoroski, Smile Markovski, Zoran Sunic","submitted_at":"2010-08-05T15:53:12Z","abstract_excerpt":"Polynomial functions on the group of units Q_n of the ring Z_{2^n} are considered. A finite set of reduced polynomials RP_n in Z[x] that induces the polynomial functions on Q_n is determined. Each polynomial function on Q_n is induced by a unique reduced polynomial - the reduction being made using a suitable ideal in Z[x]. The set of reduced polynomials forms a multiplicative 2-group. The obtained results are used to efficiently construct families of exponential cardinality of, so called, huge k-ary quasigroups, which are useful in the design of various types of cryptographic primitives. Along"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1012","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":"2026-05-18T04:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2BsUa90CQCttqYZi9xY73TB6NnuQHVY0jg11rP5sNDq2quau42xN6QteCWCqGzxX5Y5Va4uoOpNDT0hX3NKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:57:08.201016Z"},"content_sha256":"d43e9588ecde14f89f570e556ed9002a6af255e931d8dac4d39bf4288977c3d9","schema_version":"1.0","event_id":"sha256:d43e9588ecde14f89f570e556ed9002a6af255e931d8dac4d39bf4288977c3d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEBQMF7A72MVR5RBI6TVAH52WW/bundle.json","state_url":"https://pith.science/pith/KEBQMF7A72MVR5RBI6TVAH52WW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEBQMF7A72MVR5RBI6TVAH52WW/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":"2026-05-29T14:57:08Z","links":{"resolver":"https://pith.science/pith/KEBQMF7A72MVR5RBI6TVAH52WW","bundle":"https://pith.science/pith/KEBQMF7A72MVR5RBI6TVAH52WW/bundle.json","state":"https://pith.science/pith/KEBQMF7A72MVR5RBI6TVAH52WW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEBQMF7A72MVR5RBI6TVAH52WW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KEBQMF7A72MVR5RBI6TVAH52WW","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":"a7fd763d5a488fe63e90e1e6ee3f8318b407b048c542d8f5bcfddd131daddafc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-05T15:53:12Z","title_canon_sha256":"cfdaa56e39e0b8674c082b5ff1ebbd1d6a486e4fb610134cfd7802d972a0677a"},"schema_version":"1.0","source":{"id":"1008.1012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1012","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1012v1","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1012","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"KEBQMF7A72MV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KEBQMF7A72MVR5RB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KEBQMF7A","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:d43e9588ecde14f89f570e556ed9002a6af255e931d8dac4d39bf4288977c3d9","target":"graph","created_at":"2026-05-18T04:42:34Z","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":"Polynomial functions on the group of units Q_n of the ring Z_{2^n} are considered. A finite set of reduced polynomials RP_n in Z[x] that induces the polynomial functions on Q_n is determined. Each polynomial function on Q_n is induced by a unique reduced polynomial - the reduction being made using a suitable ideal in Z[x]. The set of reduced polynomials forms a multiplicative 2-group. The obtained results are used to efficiently construct families of exponential cardinality of, so called, huge k-ary quasigroups, which are useful in the design of various types of cryptographic primitives. Along","authors_text":"Danilo Gligoroski, Smile Markovski, Zoran Sunic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-05T15:53:12Z","title":"Polynomial functions on the units of Z_{2^n}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1012","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":"sha256:065d08b9d62a8fd683648f537e9431d732a28f54ca15f3086145473dacca81dd","target":"record","created_at":"2026-05-18T04:42:34Z","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":"a7fd763d5a488fe63e90e1e6ee3f8318b407b048c542d8f5bcfddd131daddafc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-05T15:53:12Z","title_canon_sha256":"cfdaa56e39e0b8674c082b5ff1ebbd1d6a486e4fb610134cfd7802d972a0677a"},"schema_version":"1.0","source":{"id":"1008.1012","kind":"arxiv","version":1}},"canonical_sha256":"51030617e0fe9958f62147a7501fbab5beaa0d9429b412c689bc52d1dc00c083","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51030617e0fe9958f62147a7501fbab5beaa0d9429b412c689bc52d1dc00c083","first_computed_at":"2026-05-18T04:42:34.786592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:34.786592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FUJ/WsttAyc7vD3f1gLfMvexyXG92lQ8Gz4uBnsRcDhXCK5ttwFUMYDRE1mIYYibncjRr7dJzYsAe6VM/TXJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:34.787290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065d08b9d62a8fd683648f537e9431d732a28f54ca15f3086145473dacca81dd","sha256:d43e9588ecde14f89f570e556ed9002a6af255e931d8dac4d39bf4288977c3d9"],"state_sha256":"6e7700b712d11f74050f9692c4022df813ea807c4ee1b66c6bb21b1dd20cc042"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3azAlPhhW+2aTEytFtLi77Cd5p1zdPg+L2hF/XDiPHDLxxpQXTZHL2uCIS/JwFC9VKhdnYqpZnCcQN8Wxos/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:57:08.203878Z","bundle_sha256":"ab725f81435e65a9fbffe0794f6dfcdfe8a9ad9b11b34b838605eb00e9245829"}}