{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6R5J2KG54GZ2HNCF76HOV7SRKJ","short_pith_number":"pith:6R5J2KG5","canonical_record":{"source":{"id":"1401.7408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T03:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"c663b79d5bf5290b8b2ee135a9e3f3ab2081230e91134e8d9b0573f468cfd371","abstract_canon_sha256":"b5d32bc9adf8c406ae4d639fa562db3b976895e32c6d060a17aae38bae668af0"},"schema_version":"1.0"},"canonical_sha256":"f47a9d28dde1b3a3b445ff8eeafe51525a422dd680fbe01c3ad16371898f6dad","source":{"kind":"arxiv","id":"1401.7408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7408","created_at":"2026-05-18T03:00:48Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7408v1","created_at":"2026-05-18T03:00:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7408","created_at":"2026-05-18T03:00:48Z"},{"alias_kind":"pith_short_12","alias_value":"6R5J2KG54GZ2","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6R5J2KG54GZ2HNCF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6R5J2KG5","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6R5J2KG54GZ2HNCF76HOV7SRKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T03:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"c663b79d5bf5290b8b2ee135a9e3f3ab2081230e91134e8d9b0573f468cfd371","abstract_canon_sha256":"b5d32bc9adf8c406ae4d639fa562db3b976895e32c6d060a17aae38bae668af0"},"schema_version":"1.0"},"canonical_sha256":"f47a9d28dde1b3a3b445ff8eeafe51525a422dd680fbe01c3ad16371898f6dad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:48.572196Z","signature_b64":"ibSjACrwJkOkQSnYwQ6Gq7WB8EwLfqAo0FjTunBMSxW5I23+OSxdrz70SYY5goBrKh1qH5MgiFYnqHfe+S+uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f47a9d28dde1b3a3b445ff8eeafe51525a422dd680fbe01c3ad16371898f6dad","last_reissued_at":"2026-05-18T03:00:48.571520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:48.571520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7408","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":"2026-05-18T03:00:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FThpfr11dwNvRJuUl4NqerPJLiYCHK3j/A7dQpduNrb2qBrNbjOHPnTtRgwZ1JJy7MxvVosdktw5IP/oChsCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:41:59.109567Z"},"content_sha256":"bef456e2cb9a86a71715615c6e212271120dcf18b608a036474260a1b6ec55f9","schema_version":"1.0","event_id":"sha256:bef456e2cb9a86a71715615c6e212271120dcf18b608a036474260a1b6ec55f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6R5J2KG54GZ2HNCF76HOV7SRKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the K\\\"ahler structures over Quot schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Indranil Biswas","submitted_at":"2014-01-29T03:46:19Z","abstract_excerpt":"Let $S^n(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^n(X)$ admits a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonpositive if and only if $n < d$. Let ${\\mathcal Q}_X(r,n)$ be the Quot scheme parametrizing the torsion quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $n$. If $g \\geq 2$ and $n \\leq 2g-2$, we prove that ${\\mathcal Q}_X(r,n)$ does not admit a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonnegative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7408","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":"2026-05-18T03:00:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gAzR5mvn/8i487vkDl1mIhk/9UDUbd7dF8CVLUMlOhdQpm16WU92SNqW415d8uel0Cctjy+dXVLpmBvzdek/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:41:59.109915Z"},"content_sha256":"bca6647dd7ff84a89eced19752db1d7606572aa4b33c19390a3d494bdc986303","schema_version":"1.0","event_id":"sha256:bca6647dd7ff84a89eced19752db1d7606572aa4b33c19390a3d494bdc986303"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/bundle.json","state_url":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/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":"2026-06-02T00:41:59Z","links":{"resolver":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ","bundle":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/bundle.json","state":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6R5J2KG54GZ2HNCF76HOV7SRKJ","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":"b5d32bc9adf8c406ae4d639fa562db3b976895e32c6d060a17aae38bae668af0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T03:46:19Z","title_canon_sha256":"c663b79d5bf5290b8b2ee135a9e3f3ab2081230e91134e8d9b0573f468cfd371"},"schema_version":"1.0","source":{"id":"1401.7408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7408","created_at":"2026-05-18T03:00:48Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7408v1","created_at":"2026-05-18T03:00:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7408","created_at":"2026-05-18T03:00:48Z"},{"alias_kind":"pith_short_12","alias_value":"6R5J2KG54GZ2","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6R5J2KG54GZ2HNCF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6R5J2KG5","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:bca6647dd7ff84a89eced19752db1d7606572aa4b33c19390a3d494bdc986303","target":"graph","created_at":"2026-05-18T03:00:48Z","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 $S^n(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^n(X)$ admits a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonpositive if and only if $n < d$. Let ${\\mathcal Q}_X(r,n)$ be the Quot scheme parametrizing the torsion quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $n$. If $g \\geq 2$ and $n \\leq 2g-2$, we prove that ${\\mathcal Q}_X(r,n)$ does not admit a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonnegative.","authors_text":"Harish Seshadri, Indranil Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T03:46:19Z","title":"On the K\\\"ahler structures over Quot schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7408","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:bef456e2cb9a86a71715615c6e212271120dcf18b608a036474260a1b6ec55f9","target":"record","created_at":"2026-05-18T03:00:48Z","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":"b5d32bc9adf8c406ae4d639fa562db3b976895e32c6d060a17aae38bae668af0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T03:46:19Z","title_canon_sha256":"c663b79d5bf5290b8b2ee135a9e3f3ab2081230e91134e8d9b0573f468cfd371"},"schema_version":"1.0","source":{"id":"1401.7408","kind":"arxiv","version":1}},"canonical_sha256":"f47a9d28dde1b3a3b445ff8eeafe51525a422dd680fbe01c3ad16371898f6dad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47a9d28dde1b3a3b445ff8eeafe51525a422dd680fbe01c3ad16371898f6dad","first_computed_at":"2026-05-18T03:00:48.571520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:48.571520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ibSjACrwJkOkQSnYwQ6Gq7WB8EwLfqAo0FjTunBMSxW5I23+OSxdrz70SYY5goBrKh1qH5MgiFYnqHfe+S+uBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:48.572196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bef456e2cb9a86a71715615c6e212271120dcf18b608a036474260a1b6ec55f9","sha256:bca6647dd7ff84a89eced19752db1d7606572aa4b33c19390a3d494bdc986303"],"state_sha256":"9e4a0bcda05bec859646566acc02de411bdfca1aa38eb135b095b64bbe7bae60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDTEVC9k7iX5pP7xHMZHaMGpyA5Aa3n+X3CdqYRJTOZDdBDy6rkYdfoKoEzoiQkwpeKjiNL4kz7oCM63ryOMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:41:59.112082Z","bundle_sha256":"524bef53779418cb67bbf48999a0e56c001dd96f4af3b032a908b8d376b436de"}}