{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AUPNAX6H5QYRABUYDWVVKNN57J","short_pith_number":"pith:AUPNAX6H","canonical_record":{"source":{"id":"1206.5516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-24T16:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"822e02430e6e6dd80608325669ebafe365d15f760c285c43bc7f62b8ffce8301","abstract_canon_sha256":"6b4803734a4d742283cd213acb397dbb19b4c06cfa394884d1e4e55839cd7b0f"},"schema_version":"1.0"},"canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","source":{"kind":"arxiv","id":"1206.5516","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5516","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5516v1","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5516","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"AUPNAX6H5QYR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AUPNAX6H5QYRABUY","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AUPNAX6H","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AUPNAX6H5QYRABUYDWVVKNN57J","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-24T16:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"822e02430e6e6dd80608325669ebafe365d15f760c285c43bc7f62b8ffce8301","abstract_canon_sha256":"6b4803734a4d742283cd213acb397dbb19b4c06cfa394884d1e4e55839cd7b0f"},"schema_version":"1.0"},"canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:39.857513Z","signature_b64":"Pig2JQ8zHNpoWEHhfAHaj3pN6qT1cO5+l0MTqFew1T0ujNwuEJ3tT0MJ6S5dBfX5Kw+DIPxQIAnMQnDlVVKcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","last_reissued_at":"2026-05-18T03:52:39.856884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:39.856884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5516","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":"2026-05-18T03:52:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AgZFni3/b+1eby3L3LLncOBAra83zwE3DBiDq3MUwCtyWufEXDl6WnUZgPIh8xxg5oszmLN3PWZ/v30QvkqmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:33:47.322932Z"},"content_sha256":"c766e3f93da21cf1ae7db38e3800f3903009203bc302cbe563fc56f66d5da762","schema_version":"1.0","event_id":"sha256:c766e3f93da21cf1ae7db38e3800f3903009203bc302cbe563fc56f66d5da762"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AUPNAX6H5QYRABUYDWVVKNN57J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert schemes as moduli of Higgs bundles and local systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michael Groechenig","submitted_at":"2012-06-24T16:16:26Z","abstract_excerpt":"We construct five families of two-dimensional moduli spaces of parabolic Higgs bundles (respectively local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve. We show that the Hilbert scheme of m points of these surfaces is again a moduli space of parabolic Higgs bundles (respectively local systems), confirming a conjecture of Boalch in these cases and extending a result of Gorsky--Nekrasov--Rubtsov. Using the McKay correspondence we establish the autoduality conjecture for the derived categories of the moduli spaces "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5516","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":"2026-05-18T03:52:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmC+Di2STC9mgQcMIqdPYmP+NryJ5Yoq67IeotPXoGWjOW5QdimFQr+eGhAit5qZU0Z5Axknt42wa8/zG3hVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:33:47.323280Z"},"content_sha256":"01896681f9b7a2ab06a54464731714ef8b0cccc2cdee67d104d222a5850f89f7","schema_version":"1.0","event_id":"sha256:01896681f9b7a2ab06a54464731714ef8b0cccc2cdee67d104d222a5850f89f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/bundle.json","state_url":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUPNAX6H5QYRABUYDWVVKNN57J/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":"2026-06-12T06:33:47Z","links":{"resolver":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J","bundle":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/bundle.json","state":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUPNAX6H5QYRABUYDWVVKNN57J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AUPNAX6H5QYRABUYDWVVKNN57J","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":"6b4803734a4d742283cd213acb397dbb19b4c06cfa394884d1e4e55839cd7b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-24T16:16:26Z","title_canon_sha256":"822e02430e6e6dd80608325669ebafe365d15f760c285c43bc7f62b8ffce8301"},"schema_version":"1.0","source":{"id":"1206.5516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5516","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5516v1","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5516","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"AUPNAX6H5QYR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AUPNAX6H5QYRABUY","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AUPNAX6H","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:01896681f9b7a2ab06a54464731714ef8b0cccc2cdee67d104d222a5850f89f7","target":"graph","created_at":"2026-05-18T03:52:39Z","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":"We construct five families of two-dimensional moduli spaces of parabolic Higgs bundles (respectively local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve. We show that the Hilbert scheme of m points of these surfaces is again a moduli space of parabolic Higgs bundles (respectively local systems), confirming a conjecture of Boalch in these cases and extending a result of Gorsky--Nekrasov--Rubtsov. Using the McKay correspondence we establish the autoduality conjecture for the derived categories of the moduli spaces ","authors_text":"Michael Groechenig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-24T16:16:26Z","title":"Hilbert schemes as moduli of Higgs bundles and local systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5516","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:c766e3f93da21cf1ae7db38e3800f3903009203bc302cbe563fc56f66d5da762","target":"record","created_at":"2026-05-18T03:52:39Z","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":"6b4803734a4d742283cd213acb397dbb19b4c06cfa394884d1e4e55839cd7b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-24T16:16:26Z","title_canon_sha256":"822e02430e6e6dd80608325669ebafe365d15f760c285c43bc7f62b8ffce8301"},"schema_version":"1.0","source":{"id":"1206.5516","kind":"arxiv","version":1}},"canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","first_computed_at":"2026-05-18T03:52:39.856884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:39.856884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pig2JQ8zHNpoWEHhfAHaj3pN6qT1cO5+l0MTqFew1T0ujNwuEJ3tT0MJ6S5dBfX5Kw+DIPxQIAnMQnDlVVKcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:39.857513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c766e3f93da21cf1ae7db38e3800f3903009203bc302cbe563fc56f66d5da762","sha256:01896681f9b7a2ab06a54464731714ef8b0cccc2cdee67d104d222a5850f89f7"],"state_sha256":"a581fd2cd89dee792d1401d7f597f03d010617d47a42e502d182dbc41c34841d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npGB7IidoB9+eM1BwJdrxeECsBGppfsiUjOZVhmqpcYrrQAlXI5nuuvqHM9bF6Ox2xY2VLYLF2zyXwNg839iCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:33:47.325287Z","bundle_sha256":"8f78d8cff11d04c572ad45fe353b9861a5b47650ab7104b387d7f3d6f18d01ab"}}