{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UEP667CYNUQ6T4GXZJVQNMSSE4","short_pith_number":"pith:UEP667CY","canonical_record":{"source":{"id":"1711.09373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-26T12:12:37Z","cross_cats_sorted":[],"title_canon_sha256":"cc14aa2e34aba05920105f997d72b16c63ac3eb0ab2e2a57544c975ed83aa311","abstract_canon_sha256":"b1abaed2f7860e267584d3afbff2894abdaee90e25160a1510e72ee9a9f5153c"},"schema_version":"1.0"},"canonical_sha256":"a11fef7c586d21e9f0d7ca6b06b252271837724aeefd3fb487e1a2d21fa4d7c0","source":{"kind":"arxiv","id":"1711.09373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09373","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09373v1","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09373","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"pith_short_12","alias_value":"UEP667CYNUQ6","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEP667CYNUQ6T4GX","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEP667CY","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UEP667CYNUQ6T4GXZJVQNMSSE4","target":"record","payload":{"canonical_record":{"source":{"id":"1711.09373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-26T12:12:37Z","cross_cats_sorted":[],"title_canon_sha256":"cc14aa2e34aba05920105f997d72b16c63ac3eb0ab2e2a57544c975ed83aa311","abstract_canon_sha256":"b1abaed2f7860e267584d3afbff2894abdaee90e25160a1510e72ee9a9f5153c"},"schema_version":"1.0"},"canonical_sha256":"a11fef7c586d21e9f0d7ca6b06b252271837724aeefd3fb487e1a2d21fa4d7c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:35.823728Z","signature_b64":"j/dCd/n5TCmSw5+jQWlIbNdRAeTFexJQW0RHPhwBtSEFnPUM475/8ynbnandTiSUcCcQF6fEwaox6OzPgelUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a11fef7c586d21e9f0d7ca6b06b252271837724aeefd3fb487e1a2d21fa4d7c0","last_reissued_at":"2026-05-18T00:29:35.822866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:35.822866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.09373","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":"2026-05-18T00:29:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVAnyneoErZGcLvSb82ErNK/5g6bT5uR0TPGRa3DGr9uCjaI7s+fRP4/a6Vz5W2GUoGca5LOOxVRLOU42rEPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:15:24.011384Z"},"content_sha256":"de08f3ae797cae4d8b447b37397a3540f756f0efb92bc5f37c9899271168506d","schema_version":"1.0","event_id":"sha256:de08f3ae797cae4d8b447b37397a3540f756f0efb92bc5f37c9899271168506d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UEP667CYNUQ6T4GXZJVQNMSSE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circulant Hadamard matrices as HFP-codes of type $C_{4n}\\times C_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Josep Rif\\`a","submitted_at":"2017-11-26T12:12:37Z","abstract_excerpt":"We prove that a circulant Hadamard code of length $4n$ can always be seen as an HFP-code (Hadamard full propelinear code) of type $C_{4n}\\times C_2$, where $C_2=\\langle u\\rangle$ or the same, as a cocyclic Hadamard code. We compute the rank and dimension of the kernel of these kind of codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09373","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":"2026-05-18T00:29:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1gPxSg2hUXT6y+dR8rb2mPWb1ukL/TQA8TJhsg+1vBCMq/pLbx9mxpczF6TruZ4SYQSZJG8lzdai8WwhRfA5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:15:24.011737Z"},"content_sha256":"0876713acc4d614ecf3fe3b00f86cf5a9eff1756398f8d0de558264d0c4d1c20","schema_version":"1.0","event_id":"sha256:0876713acc4d614ecf3fe3b00f86cf5a9eff1756398f8d0de558264d0c4d1c20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEP667CYNUQ6T4GXZJVQNMSSE4/bundle.json","state_url":"https://pith.science/pith/UEP667CYNUQ6T4GXZJVQNMSSE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEP667CYNUQ6T4GXZJVQNMSSE4/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":"2026-06-09T14:15:24Z","links":{"resolver":"https://pith.science/pith/UEP667CYNUQ6T4GXZJVQNMSSE4","bundle":"https://pith.science/pith/UEP667CYNUQ6T4GXZJVQNMSSE4/bundle.json","state":"https://pith.science/pith/UEP667CYNUQ6T4GXZJVQNMSSE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEP667CYNUQ6T4GXZJVQNMSSE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UEP667CYNUQ6T4GXZJVQNMSSE4","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":"b1abaed2f7860e267584d3afbff2894abdaee90e25160a1510e72ee9a9f5153c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-26T12:12:37Z","title_canon_sha256":"cc14aa2e34aba05920105f997d72b16c63ac3eb0ab2e2a57544c975ed83aa311"},"schema_version":"1.0","source":{"id":"1711.09373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09373","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09373v1","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09373","created_at":"2026-05-18T00:29:35Z"},{"alias_kind":"pith_short_12","alias_value":"UEP667CYNUQ6","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEP667CYNUQ6T4GX","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEP667CY","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:0876713acc4d614ecf3fe3b00f86cf5a9eff1756398f8d0de558264d0c4d1c20","target":"graph","created_at":"2026-05-18T00:29:35Z","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":"We prove that a circulant Hadamard code of length $4n$ can always be seen as an HFP-code (Hadamard full propelinear code) of type $C_{4n}\\times C_2$, where $C_2=\\langle u\\rangle$ or the same, as a cocyclic Hadamard code. We compute the rank and dimension of the kernel of these kind of codes.","authors_text":"Josep Rif\\`a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-26T12:12:37Z","title":"Circulant Hadamard matrices as HFP-codes of type $C_{4n}\\times C_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09373","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:de08f3ae797cae4d8b447b37397a3540f756f0efb92bc5f37c9899271168506d","target":"record","created_at":"2026-05-18T00:29:35Z","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":"b1abaed2f7860e267584d3afbff2894abdaee90e25160a1510e72ee9a9f5153c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-26T12:12:37Z","title_canon_sha256":"cc14aa2e34aba05920105f997d72b16c63ac3eb0ab2e2a57544c975ed83aa311"},"schema_version":"1.0","source":{"id":"1711.09373","kind":"arxiv","version":1}},"canonical_sha256":"a11fef7c586d21e9f0d7ca6b06b252271837724aeefd3fb487e1a2d21fa4d7c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a11fef7c586d21e9f0d7ca6b06b252271837724aeefd3fb487e1a2d21fa4d7c0","first_computed_at":"2026-05-18T00:29:35.822866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:35.822866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j/dCd/n5TCmSw5+jQWlIbNdRAeTFexJQW0RHPhwBtSEFnPUM475/8ynbnandTiSUcCcQF6fEwaox6OzPgelUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:35.823728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de08f3ae797cae4d8b447b37397a3540f756f0efb92bc5f37c9899271168506d","sha256:0876713acc4d614ecf3fe3b00f86cf5a9eff1756398f8d0de558264d0c4d1c20"],"state_sha256":"186126ebd66c65c78fa5a4f736b4b5b5a03f853f8a2b2b50579b3bb56a20d801"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PTxpsLKrDG/fjNVYde8T72f8S1oYocywEUGLRS8sPhAtGIZasEeotmpyU9ZxMhycrXQNAmsD9bVtZWHLAAIBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:15:24.013687Z","bundle_sha256":"67ce06f3e30df4967f75d50a7b06d4881a06224d8537675c7d68007d4db95607"}}