{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:U5YS2DTNU7PNWHHBA7ZDA52GIB","short_pith_number":"pith:U5YS2DTN","canonical_record":{"source":{"id":"2606.30172","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T11:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"5d5a41b319da11ad7c49be84e5b9d493c2bf186ef2a3d61f03890d2caa20f048","abstract_canon_sha256":"07130af8fffcd16fc4e5ab1fd20e06defd461962813e2a91dad25a39bb7c30a7"},"schema_version":"1.0"},"canonical_sha256":"a7712d0e6da7dedb1ce107f2307746406a7bde834ae382caa857b3e0e4dd4470","source":{"kind":"arxiv","id":"2606.30172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30172","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30172v1","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30172","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"U5YS2DTNU7PN","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"pith_short_16","alias_value":"U5YS2DTNU7PNWHHB","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"pith_short_8","alias_value":"U5YS2DTN","created_at":"2026-06-30T02:17:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:U5YS2DTNU7PNWHHBA7ZDA52GIB","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30172","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T11:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"5d5a41b319da11ad7c49be84e5b9d493c2bf186ef2a3d61f03890d2caa20f048","abstract_canon_sha256":"07130af8fffcd16fc4e5ab1fd20e06defd461962813e2a91dad25a39bb7c30a7"},"schema_version":"1.0"},"canonical_sha256":"a7712d0e6da7dedb1ce107f2307746406a7bde834ae382caa857b3e0e4dd4470","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:52.508538Z","signature_b64":"F4nmdhs+BLk3JtUO12ipHxNnCaTiyQLvHU2Cg9X+u5gfGgfZdEqzG00UAD8yLAwvju+U2tblwuIxXuiT6Ev+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7712d0e6da7dedb1ce107f2307746406a7bde834ae382caa857b3e0e4dd4470","last_reissued_at":"2026-06-30T02:17:52.508015Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:52.508015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30172","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":"2026-06-30T02:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3d1WRkS6rlU2eMtcBjGsN/jUJBevxS4EODGuYM/SHs2JTXjiKfoNBo/sN6bc3FXRLcGO7DJOlRXT/c45FEPYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:14:52.794206Z"},"content_sha256":"f40dc9688565758979e7eff417913f0fc3a912e84b8b3db93e07de12defedc4d","schema_version":"1.0","event_id":"sha256:f40dc9688565758979e7eff417913f0fc3a912e84b8b3db93e07de12defedc4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:U5YS2DTNU7PNWHHBA7ZDA52GIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virtual K-theoretic invariants of the nested Hilbert scheme on $\\mathbb{C}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Felix Minddal","submitted_at":"2026-06-29T11:48:37Z","abstract_excerpt":"We construct a nested version of the non-commutative Hilbert scheme and embed the nested Hilbert scheme of points on $\\mathbb{C}^n$ as the commutativity locus. In the $\\mathbb{C}^2$-case, we exhibit this locus as the zero locus of two different sections of bundles and use this description to equip the nested Hilbert scheme of points with a perfect obstruction theory equivalent to that of Gholampour, Sheshmani and Yau. We study the torus equivariant pushforward of the virtual structure sheaf under the map of nested Hilbert schemes forgetting the largest subscheme of the nesting. Using a map of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30172","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30172/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":"2026-06-30T02:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GT15tqEYS/OSQ7rwi6AW/rVQP6OQasu8btjOIOSy8TvDZFGa7oo+EW0nKEtJUQ7XqAWRftXOvG/K0GsSxk3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:14:52.794602Z"},"content_sha256":"126ead5613e56ed40891b8253c98453e46642c2d58b5625d9c640ff23697bca5","schema_version":"1.0","event_id":"sha256:126ead5613e56ed40891b8253c98453e46642c2d58b5625d9c640ff23697bca5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB/bundle.json","state_url":"https://pith.science/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB/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":"2026-06-30T20:14:52Z","links":{"resolver":"https://pith.science/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB","bundle":"https://pith.science/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB/bundle.json","state":"https://pith.science/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5YS2DTNU7PNWHHBA7ZDA52GIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:U5YS2DTNU7PNWHHBA7ZDA52GIB","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":"07130af8fffcd16fc4e5ab1fd20e06defd461962813e2a91dad25a39bb7c30a7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T11:48:37Z","title_canon_sha256":"5d5a41b319da11ad7c49be84e5b9d493c2bf186ef2a3d61f03890d2caa20f048"},"schema_version":"1.0","source":{"id":"2606.30172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30172","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30172v1","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30172","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"U5YS2DTNU7PN","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"pith_short_16","alias_value":"U5YS2DTNU7PNWHHB","created_at":"2026-06-30T02:17:52Z"},{"alias_kind":"pith_short_8","alias_value":"U5YS2DTN","created_at":"2026-06-30T02:17:52Z"}],"graph_snapshots":[{"event_id":"sha256:126ead5613e56ed40891b8253c98453e46642c2d58b5625d9c640ff23697bca5","target":"graph","created_at":"2026-06-30T02:17:52Z","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/2606.30172/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a nested version of the non-commutative Hilbert scheme and embed the nested Hilbert scheme of points on $\\mathbb{C}^n$ as the commutativity locus. In the $\\mathbb{C}^2$-case, we exhibit this locus as the zero locus of two different sections of bundles and use this description to equip the nested Hilbert scheme of points with a perfect obstruction theory equivalent to that of Gholampour, Sheshmani and Yau. We study the torus equivariant pushforward of the virtual structure sheaf under the map of nested Hilbert schemes forgetting the largest subscheme of the nesting. Using a map of ","authors_text":"Felix Minddal","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T11:48:37Z","title":"Virtual K-theoretic invariants of the nested Hilbert scheme on $\\mathbb{C}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30172","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:f40dc9688565758979e7eff417913f0fc3a912e84b8b3db93e07de12defedc4d","target":"record","created_at":"2026-06-30T02:17:52Z","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":"07130af8fffcd16fc4e5ab1fd20e06defd461962813e2a91dad25a39bb7c30a7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T11:48:37Z","title_canon_sha256":"5d5a41b319da11ad7c49be84e5b9d493c2bf186ef2a3d61f03890d2caa20f048"},"schema_version":"1.0","source":{"id":"2606.30172","kind":"arxiv","version":1}},"canonical_sha256":"a7712d0e6da7dedb1ce107f2307746406a7bde834ae382caa857b3e0e4dd4470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7712d0e6da7dedb1ce107f2307746406a7bde834ae382caa857b3e0e4dd4470","first_computed_at":"2026-06-30T02:17:52.508015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:52.508015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4nmdhs+BLk3JtUO12ipHxNnCaTiyQLvHU2Cg9X+u5gfGgfZdEqzG00UAD8yLAwvju+U2tblwuIxXuiT6Ev+AA==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:52.508538Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f40dc9688565758979e7eff417913f0fc3a912e84b8b3db93e07de12defedc4d","sha256:126ead5613e56ed40891b8253c98453e46642c2d58b5625d9c640ff23697bca5"],"state_sha256":"8d67d0c0848f02d3a1013b6faeb4a3d565ef67bd406354034b72c1b0a9579d6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XxEvhSClB7Vzz4iOvsk4oX7+viD7hfs8jnrv2j1cgy+OzfUMWBNzmcLaH+CNYs8BXFAIzUqTSm9705emP7+fDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:14:52.796691Z","bundle_sha256":"0f553d0eb7e08fedf9166bde533f578ae95e98c27f28b148ef01ce548f6af7f4"}}