{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LV4PS3HQDSEVGMFL6AXH5HF3R6","short_pith_number":"pith:LV4PS3HQ","canonical_record":{"source":{"id":"1505.08145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-29T19:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"43f5331ec5d3d8d87e7ce60e9e1c2b052214290dcdaf92cfa0652a06d92a54c4","abstract_canon_sha256":"a7c0af7d6a585514d66c9b1ae16e0ac657f215b368f2b880866448b234368b52"},"schema_version":"1.0"},"canonical_sha256":"5d78f96cf01c895330abf02e7e9cbb8f9751c9a5a8987a61e983288ebb9f6c99","source":{"kind":"arxiv","id":"1505.08145","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.08145","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.08145v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08145","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"LV4PS3HQDSEV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LV4PS3HQDSEVGMFL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LV4PS3HQ","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LV4PS3HQDSEVGMFL6AXH5HF3R6","target":"record","payload":{"canonical_record":{"source":{"id":"1505.08145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-29T19:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"43f5331ec5d3d8d87e7ce60e9e1c2b052214290dcdaf92cfa0652a06d92a54c4","abstract_canon_sha256":"a7c0af7d6a585514d66c9b1ae16e0ac657f215b368f2b880866448b234368b52"},"schema_version":"1.0"},"canonical_sha256":"5d78f96cf01c895330abf02e7e9cbb8f9751c9a5a8987a61e983288ebb9f6c99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:53.845667Z","signature_b64":"U+MJFoRxWCJs1fVVK+4bd6vyJYG3fg/uJ40Euch8igc2BwFEHh2UAtAF9b0aoCv44L5AygFynvBtlY17aH/fBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d78f96cf01c895330abf02e7e9cbb8f9751c9a5a8987a61e983288ebb9f6c99","last_reissued_at":"2026-05-18T01:19:53.845247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:53.845247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.08145","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MAZmS9U8DK3xYfcZfrfEKcihdaL/qMwgPqwGxu0BUoZrc4Kvh5ZtY56m1nhz9g2C4yfv94kVx36b1CtPzl6fAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:37:50.114506Z"},"content_sha256":"324f11eb2a6431c14603a8dd8cd5f8545f3bc567e36211281104a690f3dc236f","schema_version":"1.0","event_id":"sha256:324f11eb2a6431c14603a8dd8cd5f8545f3bc567e36211281104a690f3dc236f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LV4PS3HQDSEVGMFL6AXH5HF3R6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bruce Reznick, Charu Goel, Salma Kuhlmann","submitted_at":"2015-05-29T19:00:39Z","abstract_excerpt":"A famous theorem of Hilbert from 1888 states that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if $n=2$ or $d=1$ or $(n,2d)=(3,4)$, where $n$ is the number of variables and $2d$ the degree of the form. In 1976, Choi and Lam proved the analogue of Hilbert's Theorem for symmetric forms by assuming the existence of psd not sos symmetric $n$-ary quartics for $n \\geq 5$. In this paper we complete their proof by constructing explicit psd not sos symmetric $n$-ary quartics for $n \\geq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08145","kind":"arxiv","version":2},"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":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uh+gFTUDl8acCgyK9dwVy5I6TzhMftul2zr+WUMqNkCHDJrNWK7ipTZtobCGUmzdAgadboX4/yRyq+vNnD9BAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:37:50.115184Z"},"content_sha256":"40f8c679e4f0c9bcc482d571b584e6316d57d0ea606e070ae5aa2cfcf09118ed","schema_version":"1.0","event_id":"sha256:40f8c679e4f0c9bcc482d571b584e6316d57d0ea606e070ae5aa2cfcf09118ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6/bundle.json","state_url":"https://pith.science/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6/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":"2026-05-30T12:37:50Z","links":{"resolver":"https://pith.science/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6","bundle":"https://pith.science/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6/bundle.json","state":"https://pith.science/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LV4PS3HQDSEVGMFL6AXH5HF3R6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LV4PS3HQDSEVGMFL6AXH5HF3R6","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":"a7c0af7d6a585514d66c9b1ae16e0ac657f215b368f2b880866448b234368b52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-29T19:00:39Z","title_canon_sha256":"43f5331ec5d3d8d87e7ce60e9e1c2b052214290dcdaf92cfa0652a06d92a54c4"},"schema_version":"1.0","source":{"id":"1505.08145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.08145","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.08145v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08145","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"LV4PS3HQDSEV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LV4PS3HQDSEVGMFL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LV4PS3HQ","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:40f8c679e4f0c9bcc482d571b584e6316d57d0ea606e070ae5aa2cfcf09118ed","target":"graph","created_at":"2026-05-18T01:19:53Z","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 famous theorem of Hilbert from 1888 states that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if $n=2$ or $d=1$ or $(n,2d)=(3,4)$, where $n$ is the number of variables and $2d$ the degree of the form. In 1976, Choi and Lam proved the analogue of Hilbert's Theorem for symmetric forms by assuming the existence of psd not sos symmetric $n$-ary quartics for $n \\geq 5$. In this paper we complete their proof by constructing explicit psd not sos symmetric $n$-ary quartics for $n \\geq 5$.","authors_text":"Bruce Reznick, Charu Goel, Salma Kuhlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-29T19:00:39Z","title":"On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08145","kind":"arxiv","version":2},"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":"sha256:324f11eb2a6431c14603a8dd8cd5f8545f3bc567e36211281104a690f3dc236f","target":"record","created_at":"2026-05-18T01:19:53Z","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":"a7c0af7d6a585514d66c9b1ae16e0ac657f215b368f2b880866448b234368b52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-29T19:00:39Z","title_canon_sha256":"43f5331ec5d3d8d87e7ce60e9e1c2b052214290dcdaf92cfa0652a06d92a54c4"},"schema_version":"1.0","source":{"id":"1505.08145","kind":"arxiv","version":2}},"canonical_sha256":"5d78f96cf01c895330abf02e7e9cbb8f9751c9a5a8987a61e983288ebb9f6c99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d78f96cf01c895330abf02e7e9cbb8f9751c9a5a8987a61e983288ebb9f6c99","first_computed_at":"2026-05-18T01:19:53.845247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:53.845247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U+MJFoRxWCJs1fVVK+4bd6vyJYG3fg/uJ40Euch8igc2BwFEHh2UAtAF9b0aoCv44L5AygFynvBtlY17aH/fBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:53.845667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.08145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:324f11eb2a6431c14603a8dd8cd5f8545f3bc567e36211281104a690f3dc236f","sha256:40f8c679e4f0c9bcc482d571b584e6316d57d0ea606e070ae5aa2cfcf09118ed"],"state_sha256":"771332525f918145ee81b73956dbdb96d82138b67f98224dbefdb5a75090aa18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9PUQfv0bhnNq3MXJAB/XC3ztDLXTQ3tatx3Q1NNq/xm1hiYdhjchwpOlJCKeJ8muiC6y6IzxXVp9zOJO6OyPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:37:50.119121Z","bundle_sha256":"78d1c23b734d17bf73cf95a7aca4aba0d2a5fd90c512d089ce611f765dee6ed2"}}