{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SBSY62SL332ZIBU547WYU4ZJ3W","short_pith_number":"pith:SBSY62SL","canonical_record":{"source":{"id":"1601.08146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T15:01:34Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"e85876703a7c192833a538c10c9d0c9dde930a753907db8c291b3b852b3ce54d","abstract_canon_sha256":"2ee7f24617f1c6c490c6a0246d7b7a1f11e694fae3b5ef5d108c663b3f26b4bc"},"schema_version":"1.0"},"canonical_sha256":"90658f6a4bdef594069de7ed8a7329ddad5616b38cf684c763924e6cc689bdf3","source":{"kind":"arxiv","id":"1601.08146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08146","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08146v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08146","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"SBSY62SL332Z","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SBSY62SL332ZIBU5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SBSY62SL","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SBSY62SL332ZIBU547WYU4ZJ3W","target":"record","payload":{"canonical_record":{"source":{"id":"1601.08146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T15:01:34Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"e85876703a7c192833a538c10c9d0c9dde930a753907db8c291b3b852b3ce54d","abstract_canon_sha256":"2ee7f24617f1c6c490c6a0246d7b7a1f11e694fae3b5ef5d108c663b3f26b4bc"},"schema_version":"1.0"},"canonical_sha256":"90658f6a4bdef594069de7ed8a7329ddad5616b38cf684c763924e6cc689bdf3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:39.122498Z","signature_b64":"SRkiiL/lzl+u4+8fu0v6XHA9AKntsdKRJCYPPdw68+raRWjdY5Rrd5wxhvBZ47wdPIDbE/PEgYVlrNs4n8RHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90658f6a4bdef594069de7ed8a7329ddad5616b38cf684c763924e6cc689bdf3","last_reissued_at":"2026-05-17T23:55:39.122011Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:39.122011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.08146","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":"2026-05-17T23:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UkEcPQwHQIZ2H+fz4HCcNGjno1ERAgcB+muc/jung8+twEGkDUvlzwbLVJjGIIHSKjEc2lFHHO2MmWoDRPTYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:12:22.217600Z"},"content_sha256":"4d8c79d852ba5f11b0f17c1eb81bfe774f60a20146a95e56f7016ca8d8b80d76","schema_version":"1.0","event_id":"sha256:4d8c79d852ba5f11b0f17c1eb81bfe774f60a20146a95e56f7016ca8d8b80d76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SBSY62SL332ZIBU547WYU4ZJ3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the cohomology of almost complex and symplectic manifolds and proper surjective maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Adriano Tomassini, Nicoletta Tardini","submitted_at":"2016-01-29T15:01:34Z","abstract_excerpt":"Let $(X,J)$ be an almost-complex manifold. In \\cite{li-zhang} Li and Zhang introduce $H^{(p,q),(q,p)}_J(X)_{\\rr}$ as the cohomology subgroups of the $(p+q)$-th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology groups introduced in \\cite{tsengyauI} by Tseng and Yau and a new characterization of the Hard Lefschetz condition in dimension $4$ is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08146","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":"2026-05-17T23:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzdOoUJZRPcd91JVyTU1aBfr574Whdm5VQYjHO7AyPJqUtfKHKh+gPtivSwhI7+GhNX0qgN13HrNUFFylk1IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:12:22.217956Z"},"content_sha256":"3791b7fd964c44b48899703171c630444b89f96ed183c49a8e21ebc9e0372c8a","schema_version":"1.0","event_id":"sha256:3791b7fd964c44b48899703171c630444b89f96ed183c49a8e21ebc9e0372c8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBSY62SL332ZIBU547WYU4ZJ3W/bundle.json","state_url":"https://pith.science/pith/SBSY62SL332ZIBU547WYU4ZJ3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBSY62SL332ZIBU547WYU4ZJ3W/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":"2026-06-03T16:12:22Z","links":{"resolver":"https://pith.science/pith/SBSY62SL332ZIBU547WYU4ZJ3W","bundle":"https://pith.science/pith/SBSY62SL332ZIBU547WYU4ZJ3W/bundle.json","state":"https://pith.science/pith/SBSY62SL332ZIBU547WYU4ZJ3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBSY62SL332ZIBU547WYU4ZJ3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SBSY62SL332ZIBU547WYU4ZJ3W","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":"2ee7f24617f1c6c490c6a0246d7b7a1f11e694fae3b5ef5d108c663b3f26b4bc","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T15:01:34Z","title_canon_sha256":"e85876703a7c192833a538c10c9d0c9dde930a753907db8c291b3b852b3ce54d"},"schema_version":"1.0","source":{"id":"1601.08146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08146","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08146v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08146","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"SBSY62SL332Z","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SBSY62SL332ZIBU5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SBSY62SL","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:3791b7fd964c44b48899703171c630444b89f96ed183c49a8e21ebc9e0372c8a","target":"graph","created_at":"2026-05-17T23:55:39Z","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 $(X,J)$ be an almost-complex manifold. In \\cite{li-zhang} Li and Zhang introduce $H^{(p,q),(q,p)}_J(X)_{\\rr}$ as the cohomology subgroups of the $(p+q)$-th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology groups introduced in \\cite{tsengyauI} by Tseng and Yau and a new characterization of the Hard Lefschetz condition in dimension $4$ is provided.","authors_text":"Adriano Tomassini, Nicoletta Tardini","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T15:01:34Z","title":"On the cohomology of almost complex and symplectic manifolds and proper surjective maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08146","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":"sha256:4d8c79d852ba5f11b0f17c1eb81bfe774f60a20146a95e56f7016ca8d8b80d76","target":"record","created_at":"2026-05-17T23:55:39Z","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":"2ee7f24617f1c6c490c6a0246d7b7a1f11e694fae3b5ef5d108c663b3f26b4bc","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T15:01:34Z","title_canon_sha256":"e85876703a7c192833a538c10c9d0c9dde930a753907db8c291b3b852b3ce54d"},"schema_version":"1.0","source":{"id":"1601.08146","kind":"arxiv","version":1}},"canonical_sha256":"90658f6a4bdef594069de7ed8a7329ddad5616b38cf684c763924e6cc689bdf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90658f6a4bdef594069de7ed8a7329ddad5616b38cf684c763924e6cc689bdf3","first_computed_at":"2026-05-17T23:55:39.122011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:39.122011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SRkiiL/lzl+u4+8fu0v6XHA9AKntsdKRJCYPPdw68+raRWjdY5Rrd5wxhvBZ47wdPIDbE/PEgYVlrNs4n8RHBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:39.122498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d8c79d852ba5f11b0f17c1eb81bfe774f60a20146a95e56f7016ca8d8b80d76","sha256:3791b7fd964c44b48899703171c630444b89f96ed183c49a8e21ebc9e0372c8a"],"state_sha256":"d442ea9070b783e6b2294f0001bd453cc9769939a4adbc9bcde34e881c68df67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NaLggqmcuxFdUNC8S1wLriUV6v3lV7MR6IOBrWkFUrhwfMbcbsOdbaYv23FWO0rKG4UT44rx7MlyS4/ye1unCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:12:22.219973Z","bundle_sha256":"b80b5119761d198862a0ee7e1a4c5bccc2f335e5cdf223e88703c849e2976deb"}}