{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W3IES4QHPBWD24DWM7UQDQ7T4R","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":"908e456fd95c8f5d389c9f6f8b1e035e29877c06e483ef171790cc3cfb92d265","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-28T16:38:57Z","title_canon_sha256":"fa2ca317acd9ff9f6bb53f9cddc6005c7470e656f764f9845c7c3d31e2fcea9b"},"schema_version":"1.0","source":{"id":"1702.08854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08854","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08854v1","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08854","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"W3IES4QHPBWD","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"W3IES4QHPBWD24DW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"W3IES4QH","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:34737f37a00ad37442f81061a02f653d14a9f8322a939a2448b7741045dc574c","target":"graph","created_at":"2026-05-18T00:49:47Z","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":"For each positive integer $n$, let $g_{\\mathbb Z}(n)$ be the smallest integer such that if an integral quadratic form in $n$ variables can be written as a sum of squares of integral linear forms, then it can be written as a sum of $g_{\\mathbb Z}(n)$ squares of integral linear forms. We show that as $n$ goes to infinity, the growth of $g_{\\mathbb Z}(n)$ is at most an exponential of $\\sqrt{n}$. Our result improves the best known upper bound on $g_{\\mathbb Z}(n)$ which is in the order of an exponential of $n$. We also define an analogous number $g_{\\mathcal O}^*(n)$ for writing hermitian forms ov","authors_text":"Constantin N. Beli, Jingbo Liu, Maria Ines Icaza, Wai Kiu Chan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-28T16:38:57Z","title":"On a Waring's problem for integral quadratic and hermitian forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08854","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:ca0fb8bc6b84a8299051286361a005d53501448c4df1bd5f305bd11a17a06abc","target":"record","created_at":"2026-05-18T00:49:47Z","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":"908e456fd95c8f5d389c9f6f8b1e035e29877c06e483ef171790cc3cfb92d265","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-28T16:38:57Z","title_canon_sha256":"fa2ca317acd9ff9f6bb53f9cddc6005c7470e656f764f9845c7c3d31e2fcea9b"},"schema_version":"1.0","source":{"id":"1702.08854","kind":"arxiv","version":1}},"canonical_sha256":"b6d0497207786c3d707667e901c3f3e458a55431f05cd89cc3566e12970ca359","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6d0497207786c3d707667e901c3f3e458a55431f05cd89cc3566e12970ca359","first_computed_at":"2026-05-18T00:49:47.731845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:47.731845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mkWZFdoaEmLnHAMzm0xyXyKA+3v7zg2uAcK4WhLuUuQ8BytBMFzyLvurZpLiv9HVmInauJJ4x+VNpWNYiezLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:47.732477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0fb8bc6b84a8299051286361a005d53501448c4df1bd5f305bd11a17a06abc","sha256:34737f37a00ad37442f81061a02f653d14a9f8322a939a2448b7741045dc574c"],"state_sha256":"659840fe2b31e3ac32439615c7b6bfa29d17c29f832d87e629274f12d7ab87ea"}