{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5JNTG5N7PAN2WVILPTOPRA773G","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":"5152391d2e75544b3fba59557380a7bf2e76f20ca362a1692e2a0999c86597a4","cross_cats_sorted":["math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-29T19:52:13Z","title_canon_sha256":"c51822bb584df2aab2e04663c239a32ef57c7157010224903d3385df431f0725"},"schema_version":"1.0","source":{"id":"1606.09237","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09237","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09237v3","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09237","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"5JNTG5N7PAN2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5JNTG5N7PAN2WVIL","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5JNTG5N7","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:ae79c5b06b6043f53c399ec215af434e6b9974e5945a6931d63bfbe3f5f2dd02","target":"graph","created_at":"2026-05-17T23:47:49Z","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":"We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kaehler manifold. Moreover, for given Betti numbers, there are only finitely many deformation types and hence topological types of smooth complex projectve spin threefolds of general type. Finally, on a fixed spin 6-manifold, the Chern numbers take on only finitely many values on all possible Kaehler structures.","authors_text":"Luca Tasin, Stefan Schreieder","cross_cats":["math.CV","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-29T19:52:13Z","title":"Kaehler structures on spin 6-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09237","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":"sha256:19965cd6c93d3699585116f36db740f7883f6defdf78949fb91d9170be5dead7","target":"record","created_at":"2026-05-17T23:47:49Z","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":"5152391d2e75544b3fba59557380a7bf2e76f20ca362a1692e2a0999c86597a4","cross_cats_sorted":["math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-29T19:52:13Z","title_canon_sha256":"c51822bb584df2aab2e04663c239a32ef57c7157010224903d3385df431f0725"},"schema_version":"1.0","source":{"id":"1606.09237","kind":"arxiv","version":3}},"canonical_sha256":"ea5b3375bf781bab550b7cdcf883ffd99ce2008196d0f339cb3109bad1b55787","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea5b3375bf781bab550b7cdcf883ffd99ce2008196d0f339cb3109bad1b55787","first_computed_at":"2026-05-17T23:47:49.431759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:49.431759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ln4IfUNJxzuMYVhwV3ROxcZrKOXBgwd6uXNVHmgKO/+5uQ/OBYho6mUYBh6oxFlIDwFCyX3yyRXJ4phAibdBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:49.432307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09237","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19965cd6c93d3699585116f36db740f7883f6defdf78949fb91d9170be5dead7","sha256:ae79c5b06b6043f53c399ec215af434e6b9974e5945a6931d63bfbe3f5f2dd02"],"state_sha256":"afa6b158991962a113837904984fff9957e6ff1f01da0f9c6ee0364925f9f168"}