{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QBX7SJNE2HZQT2FMEYYTU6FOP3","short_pith_number":"pith:QBX7SJNE","canonical_record":{"source":{"id":"1705.04560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-12T13:19:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6cc204a64f3b278b3c39ee215c017a29de7f6ebce8418550a44507a6f94fb4bb","abstract_canon_sha256":"36146b322dda5ae10efccd9416d2b3afa62738933fbc91060ebcd68d6ac412cb"},"schema_version":"1.0"},"canonical_sha256":"806ff925a4d1f309e8ac26313a78ae7ed28b8a095c3e59c7be0998362b1586d2","source":{"kind":"arxiv","id":"1705.04560","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04560","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04560v2","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04560","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"QBX7SJNE2HZQ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QBX7SJNE2HZQT2FM","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QBX7SJNE","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QBX7SJNE2HZQT2FMEYYTU6FOP3","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-12T13:19:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6cc204a64f3b278b3c39ee215c017a29de7f6ebce8418550a44507a6f94fb4bb","abstract_canon_sha256":"36146b322dda5ae10efccd9416d2b3afa62738933fbc91060ebcd68d6ac412cb"},"schema_version":"1.0"},"canonical_sha256":"806ff925a4d1f309e8ac26313a78ae7ed28b8a095c3e59c7be0998362b1586d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:15.227522Z","signature_b64":"QeKb6qX7i1HxEVHRYtnqBluo+2RGfiKWH/PePAs8Kx5QLAiz/IuYO/tNswYlEtrzU3OwHqBgGOk/YeOblr5PCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"806ff925a4d1f309e8ac26313a78ae7ed28b8a095c3e59c7be0998362b1586d2","last_reissued_at":"2026-05-18T00:44:15.226863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:15.226863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04560","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":"2026-05-18T00:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7WMTsig+W31BSmqKUjihT4k3INfJI7i1An+TeAvaTBTDAL4Fn4i5/Wqz1E+cz9mHhiBNBRddlcPKO/NqWJfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:50:30.105222Z"},"content_sha256":"705d98da74442dba8a8f685094bf61f396ca51792944032aacd5ee0ccf8d0b86","schema_version":"1.0","event_id":"sha256:705d98da74442dba8a8f685094bf61f396ca51792944032aacd5ee0ccf8d0b86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QBX7SJNE2HZQT2FMEYYTU6FOP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of Sidon spaces with applications to coding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Itzhak Tamo, Netanel Raviv, Ron M. Roth","submitted_at":"2017-05-12T13:19:43Z","abstract_excerpt":"A subspace of a finite extension field is called a Sidon space if the product of any two of its elements is unique up to a scalar multiplier from the base field. Sidon spaces were recently introduced by Bachoc et al. as a means to characterize multiplicative properties of subspaces, and yet no explicit constructions were given. In this paper, several constructions of Sidon spaces are provided. In particular, in some of the constructions the relation between $k$, the dimension of the Sidon space, and $n$, the dimension of the ambient extension field, is optimal.\n  These constructions are shown "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04560","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":"2026-05-18T00:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXmJK/i0bx62exCjVN4ADPtzP/0s34i6xqRhpxBSrq+MhyAmTk8F+Bf8Oq0jA1m4geo44Il3GGxRZe9iSfmuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:50:30.105953Z"},"content_sha256":"bdb43759a38f60dae19e9c4925860e6ed663279cc717458022d6e073231fb7e3","schema_version":"1.0","event_id":"sha256:bdb43759a38f60dae19e9c4925860e6ed663279cc717458022d6e073231fb7e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3/bundle.json","state_url":"https://pith.science/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3/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":"2026-06-05T04:50:30Z","links":{"resolver":"https://pith.science/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3","bundle":"https://pith.science/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3/bundle.json","state":"https://pith.science/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBX7SJNE2HZQT2FMEYYTU6FOP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QBX7SJNE2HZQT2FMEYYTU6FOP3","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":"36146b322dda5ae10efccd9416d2b3afa62738933fbc91060ebcd68d6ac412cb","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-12T13:19:43Z","title_canon_sha256":"6cc204a64f3b278b3c39ee215c017a29de7f6ebce8418550a44507a6f94fb4bb"},"schema_version":"1.0","source":{"id":"1705.04560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04560","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04560v2","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04560","created_at":"2026-05-18T00:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"QBX7SJNE2HZQ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QBX7SJNE2HZQT2FM","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QBX7SJNE","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:bdb43759a38f60dae19e9c4925860e6ed663279cc717458022d6e073231fb7e3","target":"graph","created_at":"2026-05-18T00:44:15Z","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":"A subspace of a finite extension field is called a Sidon space if the product of any two of its elements is unique up to a scalar multiplier from the base field. Sidon spaces were recently introduced by Bachoc et al. as a means to characterize multiplicative properties of subspaces, and yet no explicit constructions were given. In this paper, several constructions of Sidon spaces are provided. In particular, in some of the constructions the relation between $k$, the dimension of the Sidon space, and $n$, the dimension of the ambient extension field, is optimal.\n  These constructions are shown ","authors_text":"Itzhak Tamo, Netanel Raviv, Ron M. Roth","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-12T13:19:43Z","title":"Construction of Sidon spaces with applications to coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04560","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":"sha256:705d98da74442dba8a8f685094bf61f396ca51792944032aacd5ee0ccf8d0b86","target":"record","created_at":"2026-05-18T00:44:15Z","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":"36146b322dda5ae10efccd9416d2b3afa62738933fbc91060ebcd68d6ac412cb","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-12T13:19:43Z","title_canon_sha256":"6cc204a64f3b278b3c39ee215c017a29de7f6ebce8418550a44507a6f94fb4bb"},"schema_version":"1.0","source":{"id":"1705.04560","kind":"arxiv","version":2}},"canonical_sha256":"806ff925a4d1f309e8ac26313a78ae7ed28b8a095c3e59c7be0998362b1586d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"806ff925a4d1f309e8ac26313a78ae7ed28b8a095c3e59c7be0998362b1586d2","first_computed_at":"2026-05-18T00:44:15.226863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:15.226863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QeKb6qX7i1HxEVHRYtnqBluo+2RGfiKWH/PePAs8Kx5QLAiz/IuYO/tNswYlEtrzU3OwHqBgGOk/YeOblr5PCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:15.227522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:705d98da74442dba8a8f685094bf61f396ca51792944032aacd5ee0ccf8d0b86","sha256:bdb43759a38f60dae19e9c4925860e6ed663279cc717458022d6e073231fb7e3"],"state_sha256":"93bc00b6d7273158e857aaef191356b16ec30a9c740157bce605f503c05dbb29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wC8EcXi6RpB+ZuSOggfkFMGD72gBKcbtv7HI3ceaO4nhdR6S0WKyi4wruRmGog9dNwzzKzfBlAfBzudsC29RCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:50:30.109563Z","bundle_sha256":"c1e8278ef92d8c6fba240d12f0973a9674957373b88bd7409af3e971c34e48e7"}}