{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E4NQA2LEWOIPHHRXEU6LP6SDQ4","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":"2ec44a4c9171e44561c5c929c573aaa6b501683451597f3f5ecb1694afa0be09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T06:53:47Z","title_canon_sha256":"328fc7706760fe9be11d3cb8f7fc320db3422e1edb0a6a59f0d13da08e0cf8cc"},"schema_version":"1.0","source":{"id":"1601.07986","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07986","created_at":"2026-05-18T00:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07986v6","created_at":"2026-05-18T00:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07986","created_at":"2026-05-18T00:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"E4NQA2LEWOIP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E4NQA2LEWOIPHHRX","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E4NQA2LE","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:1e90098ae37c989b73cd11a7cdd60477b4095c7a03e854083728991f0c3db872","target":"graph","created_at":"2026-05-18T00:54:40Z","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":"In this article, we consider the Kapustin-Witten equations on a closed $4$-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an $L^{2}$-lower bound on the extra fields over a closed four-manifold satisfying certain conditions if the connections are not ASD connections. Furthermore, we also obtain a similar result about the Vafa-Witten equations.","authors_text":"Teng Huang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T06:53:47Z","title":"A lower bound on the solutions of Kapustin-Witten equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07986","kind":"arxiv","version":6},"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:bb79139ef7de7603446056d770c662f0700e44e4d6c6b39a383fc69a222a5c1f","target":"record","created_at":"2026-05-18T00:54:40Z","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":"2ec44a4c9171e44561c5c929c573aaa6b501683451597f3f5ecb1694afa0be09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T06:53:47Z","title_canon_sha256":"328fc7706760fe9be11d3cb8f7fc320db3422e1edb0a6a59f0d13da08e0cf8cc"},"schema_version":"1.0","source":{"id":"1601.07986","kind":"arxiv","version":6}},"canonical_sha256":"271b006964b390f39e37253cb7fa43871c926612fd12e2376258d1a601885abb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"271b006964b390f39e37253cb7fa43871c926612fd12e2376258d1a601885abb","first_computed_at":"2026-05-18T00:54:40.919337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:40.919337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHzKrobqYekI7gYF3qWhDROWiCGuCDcEa+OgmqP2kN5y61shHjyJGIVg5JuFXzQV2yBrZY751k+n/1+5XKNWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:40.919785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07986","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb79139ef7de7603446056d770c662f0700e44e4d6c6b39a383fc69a222a5c1f","sha256:1e90098ae37c989b73cd11a7cdd60477b4095c7a03e854083728991f0c3db872"],"state_sha256":"032d63147ce43bc62109fe98bd4c874b8d01d0c028c4b6e58f917ecdf1db39d5"}