{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:55C53MLJX6BCZ2ZBWOECLGYB3O","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":"2875ecc7db50ff21a3a6cc274994b2e205b66a3c1cfbccd33039a7ae3fb91781","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-06T10:31:14Z","title_canon_sha256":"58e35dfebaeb76fed22f464aa28858c02ed41044114a3f3932335cf008800066"},"schema_version":"1.0","source":{"id":"2606.08089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08089","created_at":"2026-06-09T01:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08089v1","created_at":"2026-06-09T01:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08089","created_at":"2026-06-09T01:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"55C53MLJX6BC","created_at":"2026-06-09T01:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"55C53MLJX6BCZ2ZB","created_at":"2026-06-09T01:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"55C53MLJ","created_at":"2026-06-09T01:05:25Z"}],"graph_snapshots":[{"event_id":"sha256:b55375984e9db31d8ad9b21ffe0442af9233a4ab6b1ef564f3964d4c4a4369a4","target":"graph","created_at":"2026-06-09T01:05:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.08089/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For every positive integer $a$ which is coprime with $p$, $p$ is an odd prime, we denote by $\\overline{a}$ the unique integer satisfying $1\\leq \\overline{a}\\leq p$ and $a\\overline{a}\\equiv 1(\\mathrm{mod}~p)$. Put $$L(p)=\\{a\\in Z^+:(a,p)=1,2\\nmid a+\\overline{a}\\}.$$ The elements of $L(p)$ are called D.H. Lehmer numbers. The main purpose of this paper is to prove that every sufficiently large number unless it is congruent to 15 or 16$(\\mathrm{mod}~{16})$ is representable as the sum of 14 fourth powers of D.H. Lehmer numbers. Furthermore, every sufficiently large number is representable as the su","authors_text":"Rong Ma, Yang Qu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-06T10:31:14Z","title":"Waring's problem involving D.H. Lehmer numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08089","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:bd823d25c6ad0b12e42c3586c36267e46595860797c4aeb3bbbf16cad30e51c4","target":"record","created_at":"2026-06-09T01:05:25Z","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":"2875ecc7db50ff21a3a6cc274994b2e205b66a3c1cfbccd33039a7ae3fb91781","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-06T10:31:14Z","title_canon_sha256":"58e35dfebaeb76fed22f464aa28858c02ed41044114a3f3932335cf008800066"},"schema_version":"1.0","source":{"id":"2606.08089","kind":"arxiv","version":1}},"canonical_sha256":"ef45ddb169bf822ceb21b388259b01dba866d89c3ed307725cc9a3bc44e3d5fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef45ddb169bf822ceb21b388259b01dba866d89c3ed307725cc9a3bc44e3d5fd","first_computed_at":"2026-06-09T01:05:25.954525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:25.954525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fLx03in9WslHonfJAyHrotnCGRAVGCeRmQ1sOJaFV5IbGJ7ZNoVtgnME8XjEo7SNpKzdr3XkDnVnbFih+SGxCg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:25.954980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd823d25c6ad0b12e42c3586c36267e46595860797c4aeb3bbbf16cad30e51c4","sha256:b55375984e9db31d8ad9b21ffe0442af9233a4ab6b1ef564f3964d4c4a4369a4"],"state_sha256":"b45fcb1f13298d191a8dc2d230604dfb34875d3b8e6ecdafcad5a5a241a5fda2"}