{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AA7FSJ4LKMGTXPK4LBZM74MMQC","short_pith_number":"pith:AA7FSJ4L","canonical_record":{"source":{"id":"1908.01199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-03T17:02:14Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"title_canon_sha256":"b7da8cdcf2cbe7f5e5708336c3bc2923a9472c7d88668a4f3d251f3fc0d2db7f","abstract_canon_sha256":"1b83d54f4f7ad546aba63efe2b4854a4b2e0e9e9e5bce9cbee69c558926987cc"},"schema_version":"1.0"},"canonical_sha256":"003e59278b530d3bbd5c5872cff18c80b318247612c4ae097a03752bcb719057","source":{"kind":"arxiv","id":"1908.01199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01199","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01199v2","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01199","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"pith_short_12","alias_value":"AA7FSJ4LKMGT","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"pith_short_16","alias_value":"AA7FSJ4LKMGTXPK4","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"pith_short_8","alias_value":"AA7FSJ4L","created_at":"2026-07-05T01:10:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AA7FSJ4LKMGTXPK4LBZM74MMQC","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-03T17:02:14Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"title_canon_sha256":"b7da8cdcf2cbe7f5e5708336c3bc2923a9472c7d88668a4f3d251f3fc0d2db7f","abstract_canon_sha256":"1b83d54f4f7ad546aba63efe2b4854a4b2e0e9e9e5bce9cbee69c558926987cc"},"schema_version":"1.0"},"canonical_sha256":"003e59278b530d3bbd5c5872cff18c80b318247612c4ae097a03752bcb719057","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:55.614069Z","signature_b64":"joYz9OMsbwJVd5fshnxE9uDc5nYIhTBE3r14HVqrKrUzJb88XiAPqTLoKzX9ypLM96+yp3d0znwziJpMQFDRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"003e59278b530d3bbd5c5872cff18c80b318247612c4ae097a03752bcb719057","last_reissued_at":"2026-07-05T01:10:55.613659Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:55.613659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01199","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":"2026-07-05T01:10:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rg5aqYg2pyEBmPuthfoSKRllC5m3m5zB2m9oFCB/VCty61xbmZcutI+hL39hRP28L3ervGOoCWot0iNNikEEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:27:42.914353Z"},"content_sha256":"e124207d42e68be5be29e8601411d1d6bae0d77e3d8c3ce71b4cb480f5fb6c87","schema_version":"1.0","event_id":"sha256:e124207d42e68be5be29e8601411d1d6bae0d77e3d8c3ce71b4cb480f5fb6c87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AA7FSJ4LKMGTXPK4LBZM74MMQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"Andrey Smirnov, Hunter Dinkins","submitted_at":"2019-08-03T17:02:14Z","abstract_excerpt":"Let $X$ be a Nakajima quiver variety and $X'$ its $3d$-mirror. We consider the action of the Picard torus $\\mathsf{K}=\\mathrm{Pic}(X)\\otimes \\mathbb{C}^{\\times}$ on $X'$. Assuming that $(X')^{\\mathsf{K}}$ is finite, we propose a formula for the $\\mathsf{K}$-character of the tangent spaces at the fixed points in terms of certain enumerative invariants of $X$ known as vertex functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01199","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01199/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:10:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UH7d7qBjzFn9ZtueoivaljWJ2SMOVUdwdv4jlKNOxLE1c7xGlUJh3nExQMGfJwHUNOGq6GG8nXx1Dk3adpDaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:27:42.915165Z"},"content_sha256":"776a981005841b2202e0150b80801f0e98b48329105dfb4c0e0279bbb9f03c01","schema_version":"1.0","event_id":"sha256:776a981005841b2202e0150b80801f0e98b48329105dfb4c0e0279bbb9f03c01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC/bundle.json","state_url":"https://pith.science/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC/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":"2026-08-15T19:27:42Z","links":{"resolver":"https://pith.science/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC","bundle":"https://pith.science/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC/bundle.json","state":"https://pith.science/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AA7FSJ4LKMGTXPK4LBZM74MMQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AA7FSJ4LKMGTXPK4LBZM74MMQC","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":"1b83d54f4f7ad546aba63efe2b4854a4b2e0e9e9e5bce9cbee69c558926987cc","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-03T17:02:14Z","title_canon_sha256":"b7da8cdcf2cbe7f5e5708336c3bc2923a9472c7d88668a4f3d251f3fc0d2db7f"},"schema_version":"1.0","source":{"id":"1908.01199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01199","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01199v2","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01199","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"pith_short_12","alias_value":"AA7FSJ4LKMGT","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"pith_short_16","alias_value":"AA7FSJ4LKMGTXPK4","created_at":"2026-07-05T01:10:55Z"},{"alias_kind":"pith_short_8","alias_value":"AA7FSJ4L","created_at":"2026-07-05T01:10:55Z"}],"graph_snapshots":[{"event_id":"sha256:776a981005841b2202e0150b80801f0e98b48329105dfb4c0e0279bbb9f03c01","target":"graph","created_at":"2026-07-05T01:10:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.01199/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a Nakajima quiver variety and $X'$ its $3d$-mirror. We consider the action of the Picard torus $\\mathsf{K}=\\mathrm{Pic}(X)\\otimes \\mathbb{C}^{\\times}$ on $X'$. Assuming that $(X')^{\\mathsf{K}}$ is finite, we propose a formula for the $\\mathsf{K}$-character of the tangent spaces at the fixed points in terms of certain enumerative invariants of $X$ known as vertex functions.","authors_text":"Andrey Smirnov, Hunter Dinkins","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-03T17:02:14Z","title":"Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01199","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:e124207d42e68be5be29e8601411d1d6bae0d77e3d8c3ce71b4cb480f5fb6c87","target":"record","created_at":"2026-07-05T01:10:55Z","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":"1b83d54f4f7ad546aba63efe2b4854a4b2e0e9e9e5bce9cbee69c558926987cc","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-03T17:02:14Z","title_canon_sha256":"b7da8cdcf2cbe7f5e5708336c3bc2923a9472c7d88668a4f3d251f3fc0d2db7f"},"schema_version":"1.0","source":{"id":"1908.01199","kind":"arxiv","version":2}},"canonical_sha256":"003e59278b530d3bbd5c5872cff18c80b318247612c4ae097a03752bcb719057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"003e59278b530d3bbd5c5872cff18c80b318247612c4ae097a03752bcb719057","first_computed_at":"2026-07-05T01:10:55.613659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:10:55.613659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"joYz9OMsbwJVd5fshnxE9uDc5nYIhTBE3r14HVqrKrUzJb88XiAPqTLoKzX9ypLM96+yp3d0znwziJpMQFDRBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:10:55.614069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e124207d42e68be5be29e8601411d1d6bae0d77e3d8c3ce71b4cb480f5fb6c87","sha256:776a981005841b2202e0150b80801f0e98b48329105dfb4c0e0279bbb9f03c01"],"state_sha256":"7807a15908b0f9fce99d85733926eb6fbc6b043a74668d6d74f3bbf6defb9013"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yirzn159EjSe4G84KZBjoJP/5SffKTPeZwbpVx1118IpqcPu336PN6hHjnyfiaFJK5FSRbRhkTM4WtA5d0vOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T19:27:42.919936Z","bundle_sha256":"ca4712ad10a2958b5b5708a0490458f6e9684d29c6c83c10dcc68831443df3cf"}}