{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SQDMDSY75WBOVE3FXVM6QFNYYJ","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":"2cc022950a4057692c835c6429e82cdbf8327c51143fc8a48282b7c4291f247e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-10T16:22:50Z","title_canon_sha256":"5a6f6dc052c3caf74bc203e6fa217237eb5e3d796fbe10a45af857804b80e53b"},"schema_version":"1.0","source":{"id":"1411.2488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2488","created_at":"2026-05-18T02:38:01Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2488v1","created_at":"2026-05-18T02:38:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2488","created_at":"2026-05-18T02:38:01Z"},{"alias_kind":"pith_short_12","alias_value":"SQDMDSY75WBO","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SQDMDSY75WBOVE3F","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SQDMDSY7","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:2c655f0d2f3af89f2325b68c11d060f8f1db4abcb40e15d765067c69b9240909","target":"graph","created_at":"2026-05-18T02:38:01Z","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":"Following an idea of Ozawa, we give a new proof of Kazhdan's property (T) for ${\\rm SL}(3,\\mathbb Z)$, by showing that $\\Delta^2- \\frac{1}{6} \\Delta$ is a hermitian sum of squares in the group algebra, where $\\Delta$ is the unnormalized Laplace operator with respect to the natural generating set. This corresponds to a spectral gap of $\\frac{1}{72}\\sim 0.014$ for the associated random walk operator.\n  The sum of squares representation was found numerically by a semidefinite programming algorithm, and then turned into an exact symbolic representation, provided in an attached Mathematica file.","authors_text":"Andreas Thom, Tim Netzer","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-10T16:22:50Z","title":"Kazhdan's Property (T) via Semidefinite Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2488","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":"sha256:9ff42eea6bc3bc0c771c9d1fe4bb94b5e3c2585f93767cebef7e16d1bf1f2941","target":"record","created_at":"2026-05-18T02:38:01Z","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":"2cc022950a4057692c835c6429e82cdbf8327c51143fc8a48282b7c4291f247e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-10T16:22:50Z","title_canon_sha256":"5a6f6dc052c3caf74bc203e6fa217237eb5e3d796fbe10a45af857804b80e53b"},"schema_version":"1.0","source":{"id":"1411.2488","kind":"arxiv","version":1}},"canonical_sha256":"9406c1cb1fed82ea9365bd59e815b8c2432527a3dffacf23f1b41e2de57d073f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9406c1cb1fed82ea9365bd59e815b8c2432527a3dffacf23f1b41e2de57d073f","first_computed_at":"2026-05-18T02:38:01.296049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:01.296049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b+c92CXfGLpnndeGBdBLGS0Z/E+M9URoTuZPSr2Mwj40LQof7PpOHeBr2jV07eTBM8Qkpcx6nE04kC3b6fXiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:01.296461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ff42eea6bc3bc0c771c9d1fe4bb94b5e3c2585f93767cebef7e16d1bf1f2941","sha256:2c655f0d2f3af89f2325b68c11d060f8f1db4abcb40e15d765067c69b9240909"],"state_sha256":"886f093ca0a5247341323c46ea4f427e8ba98dd54d35da4483f4c4a651c315b2"}