{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FUGFF6CK42Y5PA34VJ6NJ4DVOK","short_pith_number":"pith:FUGFF6CK","canonical_record":{"source":{"id":"1708.00665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-02T09:33:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f3c0dc221f2b3fca20628a889b87285702f2a73bec9d5216eb29bc1fe2d8f20","abstract_canon_sha256":"95e5955eb48ff61d42c031904901aac97aaf2ae2c094f6c97784d94898f5f37d"},"schema_version":"1.0"},"canonical_sha256":"2d0c52f84ae6b1d7837caa7cd4f075728e99369949efd766049445133923b370","source":{"kind":"arxiv","id":"1708.00665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00665","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00665v1","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00665","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"FUGFF6CK42Y5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FUGFF6CK42Y5PA34","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FUGFF6CK","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FUGFF6CK42Y5PA34VJ6NJ4DVOK","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-02T09:33:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f3c0dc221f2b3fca20628a889b87285702f2a73bec9d5216eb29bc1fe2d8f20","abstract_canon_sha256":"95e5955eb48ff61d42c031904901aac97aaf2ae2c094f6c97784d94898f5f37d"},"schema_version":"1.0"},"canonical_sha256":"2d0c52f84ae6b1d7837caa7cd4f075728e99369949efd766049445133923b370","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:45.077617Z","signature_b64":"UkmpBpikVWYP+uckrsVdz2n1ZDvTWht0A9HZOBFse3XMiCtPZvttoPZVvAjzmRFTOMj9DoFQXpaB/3Xk7QV3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d0c52f84ae6b1d7837caa7cd4f075728e99369949efd766049445133923b370","last_reissued_at":"2026-05-18T00:38:45.077009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:45.077009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00665","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":"2026-05-18T00:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TLLXw+Buh1UzD1cXenw9yMNCVRHUkftSYjI/FDzxsdYr58LoE026WrtNX4qgPJzufVHlyrK8ZxIv7IRWLslTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:09:59.908037Z"},"content_sha256":"f1ff1775333d2f3fff17d97133f1c03f1769a43fdde32e31f7c7372af91012c5","schema_version":"1.0","event_id":"sha256:f1ff1775333d2f3fff17d97133f1c03f1769a43fdde32e31f7c7372af91012c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FUGFF6CK42Y5PA34VJ6NJ4DVOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to Compute Modulo Prime-Power Sums ?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Farhad Shirani, Mohsen Heidari, Sandeep Pradhan","submitted_at":"2017-08-02T09:33:07Z","abstract_excerpt":"A new class of structured codes called Quasi Group Codes (QGC) is introduced. A QGC is a subset of a group code. In contrast with group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen such that the size of $\\mathcal{C}+\\mathcal{C}$ is equal to any number between $|\\mathcal{C}|$ and $|\\mathcal{C}|^2$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00665","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":"2026-05-18T00:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LEixLDn+iIVazVeg5oc71/hyByL7fpy4outLySZrU2kBHS4O4AKfy8cqAc5krPtElzkwT0zwSg+fEp3z6jw8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:09:59.908401Z"},"content_sha256":"ee5da1c044b66b59f71f9a07bbb6d9cb82a307150a0206390d4b9741e0801770","schema_version":"1.0","event_id":"sha256:ee5da1c044b66b59f71f9a07bbb6d9cb82a307150a0206390d4b9741e0801770"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK/bundle.json","state_url":"https://pith.science/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK/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":"2026-06-20T07:09:59Z","links":{"resolver":"https://pith.science/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK","bundle":"https://pith.science/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK/bundle.json","state":"https://pith.science/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUGFF6CK42Y5PA34VJ6NJ4DVOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FUGFF6CK42Y5PA34VJ6NJ4DVOK","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":"95e5955eb48ff61d42c031904901aac97aaf2ae2c094f6c97784d94898f5f37d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-02T09:33:07Z","title_canon_sha256":"3f3c0dc221f2b3fca20628a889b87285702f2a73bec9d5216eb29bc1fe2d8f20"},"schema_version":"1.0","source":{"id":"1708.00665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00665","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00665v1","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00665","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"FUGFF6CK42Y5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FUGFF6CK42Y5PA34","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FUGFF6CK","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ee5da1c044b66b59f71f9a07bbb6d9cb82a307150a0206390d4b9741e0801770","target":"graph","created_at":"2026-05-18T00:38:45Z","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 new class of structured codes called Quasi Group Codes (QGC) is introduced. A QGC is a subset of a group code. In contrast with group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen such that the size of $\\mathcal{C}+\\mathcal{C}$ is equal to any number between $|\\mathcal{C}|$ and $|\\mathcal{C}|^2$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typic","authors_text":"Farhad Shirani, Mohsen Heidari, Sandeep Pradhan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-02T09:33:07Z","title":"How to Compute Modulo Prime-Power Sums ?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00665","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:f1ff1775333d2f3fff17d97133f1c03f1769a43fdde32e31f7c7372af91012c5","target":"record","created_at":"2026-05-18T00:38:45Z","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":"95e5955eb48ff61d42c031904901aac97aaf2ae2c094f6c97784d94898f5f37d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-02T09:33:07Z","title_canon_sha256":"3f3c0dc221f2b3fca20628a889b87285702f2a73bec9d5216eb29bc1fe2d8f20"},"schema_version":"1.0","source":{"id":"1708.00665","kind":"arxiv","version":1}},"canonical_sha256":"2d0c52f84ae6b1d7837caa7cd4f075728e99369949efd766049445133923b370","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d0c52f84ae6b1d7837caa7cd4f075728e99369949efd766049445133923b370","first_computed_at":"2026-05-18T00:38:45.077009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:45.077009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UkmpBpikVWYP+uckrsVdz2n1ZDvTWht0A9HZOBFse3XMiCtPZvttoPZVvAjzmRFTOMj9DoFQXpaB/3Xk7QV3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:45.077617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1ff1775333d2f3fff17d97133f1c03f1769a43fdde32e31f7c7372af91012c5","sha256:ee5da1c044b66b59f71f9a07bbb6d9cb82a307150a0206390d4b9741e0801770"],"state_sha256":"66a55fd4132a42aa031d32115c2eac94210e9ff4cd4b9e890f6a8b60ff1b2377"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Bb3YGTnc5tDAbQx/h1zRaAoDiEfbdsYHphc0x7RSNOioMVfS+rSZOaQAJdtYTJt5YxbfA7duQP6fcpKlwkLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:09:59.910336Z","bundle_sha256":"dace7a0890da474590c4512a58f082b24b46fddae355aed6a74aa9dd61dc86e4"}}