{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:AT2MAJDQILTZI6CHM3X7ODDK6A","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":"a029018e6937b408b9095b71e2703b484ced25a890ed493f231ef820b054de0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-12-08T12:41:07Z","title_canon_sha256":"f8ee36dbbfae96f1524bdd610cd7a043e27eb29fe8f0bd0b95d88af24556ef4c"},"schema_version":"1.0","source":{"id":"2212.04238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.04238","created_at":"2026-07-05T06:16:14Z"},{"alias_kind":"arxiv_version","alias_value":"2212.04238v2","created_at":"2026-07-05T06:16:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.04238","created_at":"2026-07-05T06:16:14Z"},{"alias_kind":"pith_short_12","alias_value":"AT2MAJDQILTZ","created_at":"2026-07-05T06:16:14Z"},{"alias_kind":"pith_short_16","alias_value":"AT2MAJDQILTZI6CH","created_at":"2026-07-05T06:16:14Z"},{"alias_kind":"pith_short_8","alias_value":"AT2MAJDQ","created_at":"2026-07-05T06:16:14Z"}],"graph_snapshots":[{"event_id":"sha256:27d9c48deaf1e6d346a1a6e50403155afee401424310fb6f8103d352999fb6fc","target":"graph","created_at":"2026-07-05T06:16:14Z","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/2212.04238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce the notion of the diagonal property and the weak point property for an ind-variety. We prove that the ind-varieties of higher rank divisors of integral slopes on a smooth projective curve have the weak point property. Moreover, we show that the ind-variety of $(1,n)$-divisors has the diagonal property. Furthermore, we obtain that the Hilbert schemes associated to the good partitions of a constant polynomial satisfy the diagonal property. On the process of obtaining this, we provide an upper bound on the number of such Hilbert schemes up to isomorphism. Furthermore, ","authors_text":"Arijit Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-12-08T12:41:07Z","title":"Diagonal property and weak point property of higher rank divisors and certain Hilbert schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.04238","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:ca16a64b9b3f137d8a032fb5354353e0063b9b88856f47d46d14b9d3a2a9aa79","target":"record","created_at":"2026-07-05T06:16:14Z","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":"a029018e6937b408b9095b71e2703b484ced25a890ed493f231ef820b054de0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-12-08T12:41:07Z","title_canon_sha256":"f8ee36dbbfae96f1524bdd610cd7a043e27eb29fe8f0bd0b95d88af24556ef4c"},"schema_version":"1.0","source":{"id":"2212.04238","kind":"arxiv","version":2}},"canonical_sha256":"04f4c0247042e794784766eff70c6af00f98bee963bc746201c66a3e81018caa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04f4c0247042e794784766eff70c6af00f98bee963bc746201c66a3e81018caa","first_computed_at":"2026-07-05T06:16:14.146410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:16:14.146410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwXu8h6CNtlSXievJ3sKD0j8p5wi7tiZWLQOMvwHuxuvMBbHyRgraGpqm7RPE5xDpHa10U1WdkLWp9j/chz+CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:16:14.146886Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.04238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca16a64b9b3f137d8a032fb5354353e0063b9b88856f47d46d14b9d3a2a9aa79","sha256:27d9c48deaf1e6d346a1a6e50403155afee401424310fb6f8103d352999fb6fc"],"state_sha256":"941be43210395ca56f9bbbf0e74e279609c93a6a171dccf0b516db5595d5288f"}