{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EFVTZTK5VDMVIHNKRKAJBHEWFJ","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":"b6b1f7fc4444bf80060f62e46813c9e305b534c852b65ce4451b30589a5a3952","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T11:19:05Z","title_canon_sha256":"4447918ff2e92a5c0724c10b6f9d97b1a4d5893f0905218d175fb7450564cc6c"},"schema_version":"1.0","source":{"id":"1603.05430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05430","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05430v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05430","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"EFVTZTK5VDMV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EFVTZTK5VDMVIHNK","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EFVTZTK5","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:0f8606cb3cb622d1e660a8f251aef1392f876e6f6aa975f3239822f0da9d8a50","target":"graph","created_at":"2026-05-18T01:18:56Z","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 $n,\\,d\\ge1$ let $p(n,2d)$ denote the smallest number $p$ such that every sum of squares of forms of degree $d$ in $\\mathbb{R}[x_1,\\dots,x_n]$ is a sum of $p$ squares. We establish lower bounds for these numbers that are considerably stronger than the bounds known so far. Combined with known upper bounds they give $p(3,2d)\\in\\{d+1,\\,d+2\\}$ in the ternary case. Assuming a conjecture of Iarrobino-Kanev on dimensions of tangent spaces to catalecticant varieties, we show that $p(n,2d)\\sim const\\cdot d^{(n-1)/2}$ for $d\\to\\infty$ and all $n\\ge3$. For ternary sextics and quaternary quartics we de","authors_text":"Claus Scheiderer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T11:19:05Z","title":"Sum of squares length of real forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05430","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:cfce61a17e7c9bc757ea0ad3f032cd5217f513dc91a481b17b1f34a1a88439d8","target":"record","created_at":"2026-05-18T01:18:56Z","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":"b6b1f7fc4444bf80060f62e46813c9e305b534c852b65ce4451b30589a5a3952","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T11:19:05Z","title_canon_sha256":"4447918ff2e92a5c0724c10b6f9d97b1a4d5893f0905218d175fb7450564cc6c"},"schema_version":"1.0","source":{"id":"1603.05430","kind":"arxiv","version":1}},"canonical_sha256":"216b3ccd5da8d9541daa8a80909c962a5db22dea9d3091e33919c6bdb639780b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216b3ccd5da8d9541daa8a80909c962a5db22dea9d3091e33919c6bdb639780b","first_computed_at":"2026-05-18T01:18:56.362494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.362494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Ne7ZsF1UWCslObf/8bYe/9IB1vTt0hsHdypdV4EW17eTampilnlwbmnf2QTM4J8ybOFDOH1ITvS9EEXxcRYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.362899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfce61a17e7c9bc757ea0ad3f032cd5217f513dc91a481b17b1f34a1a88439d8","sha256:0f8606cb3cb622d1e660a8f251aef1392f876e6f6aa975f3239822f0da9d8a50"],"state_sha256":"6eb6f2629c0f6160726bd4d9f08668d716d7a1da413de5d30ee0f282b808e7f9"}