{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V7LVS6YWGMKNQPSSET3KKA3CMS","short_pith_number":"pith:V7LVS6YW","canonical_record":{"source":{"id":"1106.4789","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-23T18:42:47Z","cross_cats_sorted":["math-ph","math.DG","math.GT","math.MP"],"title_canon_sha256":"28039d0f4e357e0299c790675dddd584823f0ebf1d7c5850b3bc709a3822cbfe","abstract_canon_sha256":"9d8584a3dbf0ab1c42ef065eb6e8bbe92922e412ebf7c9aecd37ab4f5702c18a"},"schema_version":"1.0"},"canonical_sha256":"afd7597b163314d83e5224f6a50362648076ac7f02b0dcdece57eff3de5b0f81","source":{"kind":"arxiv","id":"1106.4789","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4789","created_at":"2026-05-18T02:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4789v1","created_at":"2026-05-18T02:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4789","created_at":"2026-05-18T02:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"V7LVS6YWGMKN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V7LVS6YWGMKNQPSS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V7LVS6YW","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V7LVS6YWGMKNQPSSET3KKA3CMS","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4789","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-23T18:42:47Z","cross_cats_sorted":["math-ph","math.DG","math.GT","math.MP"],"title_canon_sha256":"28039d0f4e357e0299c790675dddd584823f0ebf1d7c5850b3bc709a3822cbfe","abstract_canon_sha256":"9d8584a3dbf0ab1c42ef065eb6e8bbe92922e412ebf7c9aecd37ab4f5702c18a"},"schema_version":"1.0"},"canonical_sha256":"afd7597b163314d83e5224f6a50362648076ac7f02b0dcdece57eff3de5b0f81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:31.479063Z","signature_b64":"s4UNodQi7g1CrapG1SO2hJfhgnGu5xEflDAD4S2QvpUlWwT3KDLaeCUhrb4Js0VC01UfwXsax1k2J3gRQ0A6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afd7597b163314d83e5224f6a50362648076ac7f02b0dcdece57eff3de5b0f81","last_reissued_at":"2026-05-18T02:01:31.478478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:31.478478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4789","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFCt+d/JiqWr+hPu36K5YDMveM9lGCOKjlHtMuZGUStQAOj6UEni6dfbpDfByTqiIqfYfywlmrQ3QFh83rSBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:26:32.966862Z"},"content_sha256":"c6b79e5c4515d43c544a841431eb869272fb665cf10cf1c15d834c59d90506f0","schema_version":"1.0","event_id":"sha256:c6b79e5c4515d43c544a841431eb869272fb665cf10cf1c15d834c59d90506f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V7LVS6YWGMKNQPSSET3KKA3CMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knot Invariants from Four-Dimensional Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.GT","math.MP"],"primary_cat":"hep-th","authors_text":"Davide Gaiotto, Edward Witten","submitted_at":"2011-06-23T18:42:47Z","abstract_excerpt":"It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solutions, without reference to any quantum dualities. After suitably perturbing the equations to make their behavior more generic, we are able to get a fairly clear understanding of how the Jones polynomial emerges. The main ingredient in the argument is a link between the four-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4789","kind":"arxiv","version":1},"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":"2026-05-18T02:01:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Odr3HxUxP1+1BdlBcJFrQ2ydy9GMPsEtX2/0+ZDE6TDYsZoYn7BJyJESsGqNmKbJJvE5adRkGqemvKR+qZ4IBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:26:32.967583Z"},"content_sha256":"af5828e7e9522dbf3c22fe9b9e1ea254870091f3c327cf38d13060973e10db2f","schema_version":"1.0","event_id":"sha256:af5828e7e9522dbf3c22fe9b9e1ea254870091f3c327cf38d13060973e10db2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7LVS6YWGMKNQPSSET3KKA3CMS/bundle.json","state_url":"https://pith.science/pith/V7LVS6YWGMKNQPSSET3KKA3CMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7LVS6YWGMKNQPSSET3KKA3CMS/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":"2026-05-26T15:26:32Z","links":{"resolver":"https://pith.science/pith/V7LVS6YWGMKNQPSSET3KKA3CMS","bundle":"https://pith.science/pith/V7LVS6YWGMKNQPSSET3KKA3CMS/bundle.json","state":"https://pith.science/pith/V7LVS6YWGMKNQPSSET3KKA3CMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7LVS6YWGMKNQPSSET3KKA3CMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V7LVS6YWGMKNQPSSET3KKA3CMS","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":"9d8584a3dbf0ab1c42ef065eb6e8bbe92922e412ebf7c9aecd37ab4f5702c18a","cross_cats_sorted":["math-ph","math.DG","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-23T18:42:47Z","title_canon_sha256":"28039d0f4e357e0299c790675dddd584823f0ebf1d7c5850b3bc709a3822cbfe"},"schema_version":"1.0","source":{"id":"1106.4789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4789","created_at":"2026-05-18T02:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4789v1","created_at":"2026-05-18T02:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4789","created_at":"2026-05-18T02:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"V7LVS6YWGMKN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V7LVS6YWGMKNQPSS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V7LVS6YW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:af5828e7e9522dbf3c22fe9b9e1ea254870091f3c327cf38d13060973e10db2f","target":"graph","created_at":"2026-05-18T02:01:31Z","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":"It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solutions, without reference to any quantum dualities. After suitably perturbing the equations to make their behavior more generic, we are able to get a fairly clear understanding of how the Jones polynomial emerges. The main ingredient in the argument is a link between the four-dimen","authors_text":"Davide Gaiotto, Edward Witten","cross_cats":["math-ph","math.DG","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-23T18:42:47Z","title":"Knot Invariants from Four-Dimensional Gauge Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4789","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:c6b79e5c4515d43c544a841431eb869272fb665cf10cf1c15d834c59d90506f0","target":"record","created_at":"2026-05-18T02:01:31Z","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":"9d8584a3dbf0ab1c42ef065eb6e8bbe92922e412ebf7c9aecd37ab4f5702c18a","cross_cats_sorted":["math-ph","math.DG","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-06-23T18:42:47Z","title_canon_sha256":"28039d0f4e357e0299c790675dddd584823f0ebf1d7c5850b3bc709a3822cbfe"},"schema_version":"1.0","source":{"id":"1106.4789","kind":"arxiv","version":1}},"canonical_sha256":"afd7597b163314d83e5224f6a50362648076ac7f02b0dcdece57eff3de5b0f81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd7597b163314d83e5224f6a50362648076ac7f02b0dcdece57eff3de5b0f81","first_computed_at":"2026-05-18T02:01:31.478478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:31.478478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s4UNodQi7g1CrapG1SO2hJfhgnGu5xEflDAD4S2QvpUlWwT3KDLaeCUhrb4Js0VC01UfwXsax1k2J3gRQ0A6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:31.479063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6b79e5c4515d43c544a841431eb869272fb665cf10cf1c15d834c59d90506f0","sha256:af5828e7e9522dbf3c22fe9b9e1ea254870091f3c327cf38d13060973e10db2f"],"state_sha256":"3d2667e9e46e80a86d9187bacdf8e06ce33de558a9a1ae811ebfb18100eb3926"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SUwShBU/uqG28991tmLkeJHS/QyYHatgq0ADXeTnzZLg+jcJUg1EKzanMo9hJLuzQvpeiS54laDSZGX+AoAtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:26:32.971454Z","bundle_sha256":"7d45acd3c0e663e4f3dc791ae7bc7d3f0caa04bc67afaaed11c586166a703ad3"}}