{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7RG7SKOTFUZHRVLERUCRWA2A4E","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":"b5af8360d897a094bf54a8471f58de832d91fb2d517821e304d25c3f44b2c413","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-28T18:53:55Z","title_canon_sha256":"215fe0e29a21a607c921c0bce955346056419b6dc40c8296cbaee7b09320c6f5"},"schema_version":"1.0","source":{"id":"1212.6553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6553","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6553v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6553","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"7RG7SKOTFUZH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7RG7SKOTFUZHRVLE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7RG7SKOT","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:8f18bafe56939d6a4b42e35bc38033c2f206f71c2ef09d102e08d08a452b5ac4","target":"graph","created_at":"2026-05-18T03:37:31Z","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 are concern about a conjecture proposed in the middle of the seventies by Hellesseth in the framework of maximal sequences and theirs cross-correlations. The conjecture claims the existence of a zero outphase Fourier coefficient. We give some divisibility properties in this direction.","authors_text":"IMATH), Philippe Langevin (IMATH), Yves Aubry (IML","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-28T18:53:55Z","title":"On a conjecture of Helleseth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6553","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":"sha256:9fd579300c8e658ac284d123842d7e6b0ac5ec7bc53b45725edb8e4ac1405abf","target":"record","created_at":"2026-05-18T03:37:31Z","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":"b5af8360d897a094bf54a8471f58de832d91fb2d517821e304d25c3f44b2c413","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-28T18:53:55Z","title_canon_sha256":"215fe0e29a21a607c921c0bce955346056419b6dc40c8296cbaee7b09320c6f5"},"schema_version":"1.0","source":{"id":"1212.6553","kind":"arxiv","version":1}},"canonical_sha256":"fc4df929d32d3278d5648d051b0340e13e347c6e4dfa3384769d91d003b0a5ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4df929d32d3278d5648d051b0340e13e347c6e4dfa3384769d91d003b0a5ac","first_computed_at":"2026-05-18T03:37:31.591163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:31.591163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K7Xc4+8URQGePGxX4/G3vp+IsoW3XyUjR1trCNA0f76Jt290MaZsslWkbabU0ZqVT1roKgy2R7JJ/tmIaQAGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:31.591915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fd579300c8e658ac284d123842d7e6b0ac5ec7bc53b45725edb8e4ac1405abf","sha256:8f18bafe56939d6a4b42e35bc38033c2f206f71c2ef09d102e08d08a452b5ac4"],"state_sha256":"03386eee0d597ba5d65c7dfa675ff837f48ae0114d6ff8993dc5504cebcb4be3"}