{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5T3UF323JLTKRA5W4GCVPDCPAP","short_pith_number":"pith:5T3UF323","canonical_record":{"source":{"id":"1506.06191","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-20T01:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"aa5a7d33c169e001d61a099427670c58539ab048112078f5dccdb2fa8f3f4b46","abstract_canon_sha256":"f8d435e05ae027b8bd0de9212f7d0f42369f21a85b3297c928e357910346b102"},"schema_version":"1.0"},"canonical_sha256":"ecf742ef5b4ae6a883b6e185578c4f03cbfefe4ffde2880c77e7c97eb0cc230a","source":{"kind":"arxiv","id":"1506.06191","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06191","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06191v3","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06191","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"5T3UF323JLTK","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5T3UF323JLTKRA5W","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5T3UF323","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5T3UF323JLTKRA5W4GCVPDCPAP","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06191","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-20T01:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"aa5a7d33c169e001d61a099427670c58539ab048112078f5dccdb2fa8f3f4b46","abstract_canon_sha256":"f8d435e05ae027b8bd0de9212f7d0f42369f21a85b3297c928e357910346b102"},"schema_version":"1.0"},"canonical_sha256":"ecf742ef5b4ae6a883b6e185578c4f03cbfefe4ffde2880c77e7c97eb0cc230a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:58.367015Z","signature_b64":"v6h0X0w2Ke5+vcydC4KYUBX2SrnzFOiICmO9kov2rDN8JWK1rjApvqBbvIvczXtMt3jFNmbVxAm4JpL4PLmxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecf742ef5b4ae6a883b6e185578c4f03cbfefe4ffde2880c77e7c97eb0cc230a","last_reissued_at":"2026-05-18T00:44:58.366611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:58.366611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06191","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cruxUiToui94/9hUdHy15zO1V0tEyvsKWa95DBrChFKNiGe9zlG7nhLavV1xlOQacXV7GHPsTedlS19G7leOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:30:54.456180Z"},"content_sha256":"e9b4fe5aa64c242b43c3b3b0789323503bb26b23f344b210c99e4359870bd35e","schema_version":"1.0","event_id":"sha256:e9b4fe5aa64c242b43c3b3b0789323503bb26b23f344b210c99e4359870bd35e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5T3UF323JLTKRA5W4GCVPDCPAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of a natural sheaf over the cartesian square of the Hilbert scheme of points on a K3 surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eyal Markman","submitted_at":"2015-06-20T01:48:55Z","abstract_excerpt":"Let S be a K3 surface and S^[n] the Hilbert scheme of length n subschemes of S. Over the cartesian square of S^[n] there exists a natural reflexive rank 2n-2 coherent sheaf E, which is locally free away from the diagonal. The fiber of E, over a pair of ideal sheaves of distinct subschemes, is the vector space of extensions of the first ideal sheaf by the second. We prove that E is slope stable if the rank of the Picard group of S is less than or equal to 19. The Chern classes of End(E) are known to be monodromy invariant. Consequently, the sheaf End(E) is polystable-hyperholomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06191","kind":"arxiv","version":3},"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":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QkRcKAINQXj99X4152tY17EaoqG/3/krXMrmphBTGtEjr2br0+UXVIC4PVctwRH7NLnzIpx3UOKqf05knsO9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:30:54.456840Z"},"content_sha256":"2d6e2eb74fc0de5e1811eb7924b584e9918e5ebb2cf307889560442adf3d817d","schema_version":"1.0","event_id":"sha256:2d6e2eb74fc0de5e1811eb7924b584e9918e5ebb2cf307889560442adf3d817d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5T3UF323JLTKRA5W4GCVPDCPAP/bundle.json","state_url":"https://pith.science/pith/5T3UF323JLTKRA5W4GCVPDCPAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5T3UF323JLTKRA5W4GCVPDCPAP/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":"2026-05-26T13:30:54Z","links":{"resolver":"https://pith.science/pith/5T3UF323JLTKRA5W4GCVPDCPAP","bundle":"https://pith.science/pith/5T3UF323JLTKRA5W4GCVPDCPAP/bundle.json","state":"https://pith.science/pith/5T3UF323JLTKRA5W4GCVPDCPAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5T3UF323JLTKRA5W4GCVPDCPAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5T3UF323JLTKRA5W4GCVPDCPAP","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":"f8d435e05ae027b8bd0de9212f7d0f42369f21a85b3297c928e357910346b102","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-20T01:48:55Z","title_canon_sha256":"aa5a7d33c169e001d61a099427670c58539ab048112078f5dccdb2fa8f3f4b46"},"schema_version":"1.0","source":{"id":"1506.06191","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06191","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06191v3","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06191","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"5T3UF323JLTK","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5T3UF323JLTKRA5W","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5T3UF323","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:2d6e2eb74fc0de5e1811eb7924b584e9918e5ebb2cf307889560442adf3d817d","target":"graph","created_at":"2026-05-18T00:44:58Z","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":"Let S be a K3 surface and S^[n] the Hilbert scheme of length n subschemes of S. Over the cartesian square of S^[n] there exists a natural reflexive rank 2n-2 coherent sheaf E, which is locally free away from the diagonal. The fiber of E, over a pair of ideal sheaves of distinct subschemes, is the vector space of extensions of the first ideal sheaf by the second. We prove that E is slope stable if the rank of the Picard group of S is less than or equal to 19. The Chern classes of End(E) are known to be monodromy invariant. Consequently, the sheaf End(E) is polystable-hyperholomorphic.","authors_text":"Eyal Markman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-20T01:48:55Z","title":"Stability of a natural sheaf over the cartesian square of the Hilbert scheme of points on a K3 surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06191","kind":"arxiv","version":3},"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:e9b4fe5aa64c242b43c3b3b0789323503bb26b23f344b210c99e4359870bd35e","target":"record","created_at":"2026-05-18T00:44:58Z","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":"f8d435e05ae027b8bd0de9212f7d0f42369f21a85b3297c928e357910346b102","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-20T01:48:55Z","title_canon_sha256":"aa5a7d33c169e001d61a099427670c58539ab048112078f5dccdb2fa8f3f4b46"},"schema_version":"1.0","source":{"id":"1506.06191","kind":"arxiv","version":3}},"canonical_sha256":"ecf742ef5b4ae6a883b6e185578c4f03cbfefe4ffde2880c77e7c97eb0cc230a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecf742ef5b4ae6a883b6e185578c4f03cbfefe4ffde2880c77e7c97eb0cc230a","first_computed_at":"2026-05-18T00:44:58.366611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:58.366611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6h0X0w2Ke5+vcydC4KYUBX2SrnzFOiICmO9kov2rDN8JWK1rjApvqBbvIvczXtMt3jFNmbVxAm4JpL4PLmxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:58.367015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06191","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9b4fe5aa64c242b43c3b3b0789323503bb26b23f344b210c99e4359870bd35e","sha256:2d6e2eb74fc0de5e1811eb7924b584e9918e5ebb2cf307889560442adf3d817d"],"state_sha256":"a8331ba9a777084c4af06a7cf4f8685b00e0564bbea776ab6c719fe107e0f9e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+w/K14FCWW75jhKsktLtvShI7rkezxGdxK9T9QTUwCxcFgvCm3vHhLDbl5m813Ak5+tDrN3dzuZHwKFElUUyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:30:54.460292Z","bundle_sha256":"3c2a3bb642090bbcf94b75fc33e26dd78b47a79a0fc69ae174e5c4b3ef082938"}}