{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2LDZJ4HTR2AHUDRWZIIIM3B2UF","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":"630bf7682ee468a6446c58bc27396dc37647c6abc265ab1f29a778d7f6bd56ba","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-10-04T04:46:05Z","title_canon_sha256":"e6feef120777064c044ccfa78f40c42060c9f7b2bda7a2aedf561390ffe27f7b"},"schema_version":"1.0","source":{"id":"1710.01458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01458","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01458v2","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01458","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"2LDZJ4HTR2AH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2LDZJ4HTR2AHUDRW","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2LDZJ4HT","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:deefc981566e010a4a53d6a6fe8741c23aa4bfd96cd899ee1d4e27afe5b7928a","target":"graph","created_at":"2026-05-18T00:33:34Z","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":"Brascamp-Lieb inequality is an important mathematical tool in analysis, geometry and information theory. There are various ways to prove Brascamp-Lieb inequality such as heat flow method, Brownian motion and subadditivity of the entropy. While Brascamp-Lieb inequality is originally stated in Euclidean Space, discussed Brascamp-Lieb inequality for discrete Abelian group and discussed Brascamp-Lieb inequality for Markov semigroups.\n  Many mathematical inequalities can be formulated as algebraic inequalities which asserts some given polynomial is nonnegative. In 1927, Artin proved that any non- n","authors_text":"Yueqi Sheng, Zhixian Lei","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-10-04T04:46:05Z","title":"Sum of Square Proof for Brascamp-Lieb Type Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01458","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":"sha256:2e5d0524642599f82da8effee6b42a836a7b4c12e1dd97b2e4256c2d56e37135","target":"record","created_at":"2026-05-18T00:33:34Z","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":"630bf7682ee468a6446c58bc27396dc37647c6abc265ab1f29a778d7f6bd56ba","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-10-04T04:46:05Z","title_canon_sha256":"e6feef120777064c044ccfa78f40c42060c9f7b2bda7a2aedf561390ffe27f7b"},"schema_version":"1.0","source":{"id":"1710.01458","kind":"arxiv","version":2}},"canonical_sha256":"d2c794f0f38e807a0e36ca10866c3aa16fef1a6fbfd0e31487cd0953ad7276cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2c794f0f38e807a0e36ca10866c3aa16fef1a6fbfd0e31487cd0953ad7276cb","first_computed_at":"2026-05-18T00:33:34.402262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:34.402262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ucpeztkTLAN9GoH8zDVk2F+V0KW5ltvQ/icfHQ56Xeu1NKgLk66CRfjPN5s+eQEauGP6LhW3iF6sTBAh8Y5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:34.402982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e5d0524642599f82da8effee6b42a836a7b4c12e1dd97b2e4256c2d56e37135","sha256:deefc981566e010a4a53d6a6fe8741c23aa4bfd96cd899ee1d4e27afe5b7928a"],"state_sha256":"469be45ee64b462449acf89c35a227bb82e0b3f5633036b7377fab2333804626"}