{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z5XA32QKET7RYEBHLHZXQY6JC2","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":"4fa2508db536512144cc2c7879618b10f0a39ab3402adee61e6d2d584bcf01f6","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-04T15:51:15Z","title_canon_sha256":"a10bf2ae686619d08d91229b6a3cab66bf04ed5e7e03a27ad72ecfab2030da06"},"schema_version":"1.0","source":{"id":"2506.04094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04094","created_at":"2026-07-05T11:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04094v1","created_at":"2026-07-05T11:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04094","created_at":"2026-07-05T11:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z5XA32QKET7R","created_at":"2026-07-05T11:15:56Z"},{"alias_kind":"pith_short_16","alias_value":"Z5XA32QKET7RYEBH","created_at":"2026-07-05T11:15:56Z"},{"alias_kind":"pith_short_8","alias_value":"Z5XA32QK","created_at":"2026-07-05T11:15:56Z"}],"graph_snapshots":[{"event_id":"sha256:68c831a2790e4f896bf9554b5d44db03490d15c0aa6352f7220fee9af6c7c1ed","target":"graph","created_at":"2026-07-05T11:15:56Z","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/2506.04094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a hypersurface $i \\colon X \\hookrightarrow \\widetilde{P}^n$ in a weighted projective space, we compute the intersection form on the second cohomology $H^2(X, \\mathbb{Z})^{\\otimes n-1} \\to \\mathbb{Z}$ for the purpose of identifying Fano manifolds obtained from smoothing singular Fanos. In the process, we describe the integer cohomology groups $H^k(X, \\mathbb{Z})$ for $k<n$ and give an explicit formula for the pullback map $i^*$.","authors_text":"Anna-Maria Raukh","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-04T15:51:15Z","title":"Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04094","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":"sha256:7f7383e267919e6fa1e568e295dccf8241a132d82b129673cc087b928c0a6a82","target":"record","created_at":"2026-07-05T11:15:56Z","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":"4fa2508db536512144cc2c7879618b10f0a39ab3402adee61e6d2d584bcf01f6","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-04T15:51:15Z","title_canon_sha256":"a10bf2ae686619d08d91229b6a3cab66bf04ed5e7e03a27ad72ecfab2030da06"},"schema_version":"1.0","source":{"id":"2506.04094","kind":"arxiv","version":1}},"canonical_sha256":"cf6e0dea0a24ff1c102759f37863c916adaebab7d5bceb9ef0fa043c171d807b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf6e0dea0a24ff1c102759f37863c916adaebab7d5bceb9ef0fa043c171d807b","first_computed_at":"2026-07-05T11:15:56.843922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:56.843922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L3Khmr3eR8kRiuzEVndnnZ7q2PYPIGNl+w0l3VtkO6oUbzTLArB2KBwqzLACDOEg1i3hloZzVYjUwbZZHN/HDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:56.844469Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f7383e267919e6fa1e568e295dccf8241a132d82b129673cc087b928c0a6a82","sha256:68c831a2790e4f896bf9554b5d44db03490d15c0aa6352f7220fee9af6c7c1ed"],"state_sha256":"acb48fb93516ea043907aa5e7112ab1fcc45bc76c0c3597823eacc01e8b08717"}