{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O2PITCXFO74AUJCD76IEYOHVT5","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":"972dbb147d0cb9f13284685a5fc109cf9a0fb5546b4477f613f096ddda16ff94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-03-04T22:22:38Z","title_canon_sha256":"eeb1ac1472c56932197e7937cd435ed7b111ac13b09016667adc0ab250630312"},"schema_version":"1.0","source":{"id":"1403.0967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0967","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0967v1","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0967","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"O2PITCXFO74A","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O2PITCXFO74AUJCD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O2PITCXF","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a7df6203c1f6e43445dfc81eed7f99aa1f3f13261b93a8c14d43c1099a23532d","target":"graph","created_at":"2026-05-18T02:57:06Z","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":"The classical result of J.J. Kohn asserts that over a relatively compact subdomain $D$ with $C^\\infty$ boundary of a Hermitian manifold whose Levi form has at least $n-q$ positive eigenvalues or at least $q+1$ negative eigenvalues at each boundary point, there are natural isomorphisms between the $(p,q)$ Dolbeault cohomology groups defined by means of $C^\\infty$ up to the boundary differential forms on $D$ and the (finite-dimensional) spaces of harmonic $(p,q)$-forms on $D$ determined by the corresponding complex Laplace operator. In the present paper, using Kohn's technique, we give a similar","authors_text":"A. Brudnyi, D. Kinzebulatov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-03-04T22:22:38Z","title":"Kohn decomposition for forms on coverings of complex manifolds constrained along fibres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0967","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":"sha256:4d1505a25c66405f8a4b3a6a936e923bdb3bd59900fc43f4259207a48fd524ec","target":"record","created_at":"2026-05-18T02:57:06Z","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":"972dbb147d0cb9f13284685a5fc109cf9a0fb5546b4477f613f096ddda16ff94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-03-04T22:22:38Z","title_canon_sha256":"eeb1ac1472c56932197e7937cd435ed7b111ac13b09016667adc0ab250630312"},"schema_version":"1.0","source":{"id":"1403.0967","kind":"arxiv","version":1}},"canonical_sha256":"769e898ae577f80a2443ff904c38f59f5a0a16df38d7128f83cc237f7fe2e485","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769e898ae577f80a2443ff904c38f59f5a0a16df38d7128f83cc237f7fe2e485","first_computed_at":"2026-05-18T02:57:06.008839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:06.008839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0AV989lLDorXvkIHzByR5tTYwhK2fVCsEzqNvw5nKUvOxdEHmGLuUEDvNwISBv5szOA+2mDxdCvKTwpEk3dQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:06.009383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1505a25c66405f8a4b3a6a936e923bdb3bd59900fc43f4259207a48fd524ec","sha256:a7df6203c1f6e43445dfc81eed7f99aa1f3f13261b93a8c14d43c1099a23532d"],"state_sha256":"af1587506b6c687dd67aa86e23d5d524596b899e4f53c27ab7f16203d58c7c52"}