{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YJ6OSWYXDJX2NFI7YTP6J7DFDA","short_pith_number":"pith:YJ6OSWYX","canonical_record":{"source":{"id":"1508.01900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-08T13:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"ec8a7dbd35685bc3d3d924e90af29e87d849a0f1a4a08e2bde501179d43a5ee0","abstract_canon_sha256":"3709f4bdd2d94610c3fb9ead65a0f5f5eebbc193fa3df0676100ce8a0fb1b465"},"schema_version":"1.0"},"canonical_sha256":"c27ce95b171a6fa6951fc4dfe4fc65183d132f3254a4195e6d4dae32a6c22133","source":{"kind":"arxiv","id":"1508.01900","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01900","created_at":"2026-05-18T01:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01900v2","created_at":"2026-05-18T01:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01900","created_at":"2026-05-18T01:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"YJ6OSWYXDJX2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YJ6OSWYXDJX2NFI7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YJ6OSWYX","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YJ6OSWYXDJX2NFI7YTP6J7DFDA","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-08T13:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"ec8a7dbd35685bc3d3d924e90af29e87d849a0f1a4a08e2bde501179d43a5ee0","abstract_canon_sha256":"3709f4bdd2d94610c3fb9ead65a0f5f5eebbc193fa3df0676100ce8a0fb1b465"},"schema_version":"1.0"},"canonical_sha256":"c27ce95b171a6fa6951fc4dfe4fc65183d132f3254a4195e6d4dae32a6c22133","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:03.481504Z","signature_b64":"L9tP+JmbNDq1pS2OfL74tli8qnbewvFdhgq77pNGPqcle2KfXSHdoP3XDAAOtQUV7OuOKnEl+7wlVnXQfFyxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c27ce95b171a6fa6951fc4dfe4fc65183d132f3254a4195e6d4dae32a6c22133","last_reissued_at":"2026-05-18T01:23:03.480987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:03.480987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01900","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jxD+Tx1vUqijKG396GW8DNKKE/A2w/8E5kDv3uK4NlFLJQoQwABVSOOlQXuH/EDyIB+u9tn0GP6r+kgGwRxYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:16:48.361713Z"},"content_sha256":"167ba9710e1489061c2d5d41b588a45926299a22e8a6a83447080494ed209fc0","schema_version":"1.0","event_id":"sha256:167ba9710e1489061c2d5d41b588a45926299a22e8a6a83447080494ed209fc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YJ6OSWYXDJX2NFI7YTP6J7DFDA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Special birational structures on non-K\\\"ahler complex surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Georges Dloussky","submitted_at":"2015-08-08T13:23:08Z","abstract_excerpt":"We investigate the following conjecture: all compact non-K\\\"ahler complex surfaces admit birational structures. After Inoue-Kobayashi-Ochiai, the remaining cases to study are essentially surfaces in class VII_0^+. In case of Kato surfaces with a cycle and one branch of rational curves we show that they have a special birational structure given by new normal forms of contracting germs in Cremona group Bir(P^2(C)). In particular all surfaces S with GSS and 0<b_2(S)<4 admit a birational structure. From the existence of a special birational structure we deduce meromorphic mappings from the univers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01900","kind":"arxiv","version":2},"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":"2026-05-18T01:23:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/G3ybPQaMWbKr9vbmTbfaq9IRyG43yShDSzbhpZl5EupYNoJ1Pb7TY1TmKm6GgVcsSgfkjluxOoHXAzKqb2SAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:16:48.362293Z"},"content_sha256":"d3a352ae2a46687cd4e95e7c7e510bc9012962c4ae51ed0475105e2380d0a580","schema_version":"1.0","event_id":"sha256:d3a352ae2a46687cd4e95e7c7e510bc9012962c4ae51ed0475105e2380d0a580"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA/bundle.json","state_url":"https://pith.science/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA/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":"2026-06-01T00:16:48Z","links":{"resolver":"https://pith.science/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA","bundle":"https://pith.science/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA/bundle.json","state":"https://pith.science/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJ6OSWYXDJX2NFI7YTP6J7DFDA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YJ6OSWYXDJX2NFI7YTP6J7DFDA","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":"3709f4bdd2d94610c3fb9ead65a0f5f5eebbc193fa3df0676100ce8a0fb1b465","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-08T13:23:08Z","title_canon_sha256":"ec8a7dbd35685bc3d3d924e90af29e87d849a0f1a4a08e2bde501179d43a5ee0"},"schema_version":"1.0","source":{"id":"1508.01900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01900","created_at":"2026-05-18T01:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01900v2","created_at":"2026-05-18T01:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01900","created_at":"2026-05-18T01:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"YJ6OSWYXDJX2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YJ6OSWYXDJX2NFI7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YJ6OSWYX","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:d3a352ae2a46687cd4e95e7c7e510bc9012962c4ae51ed0475105e2380d0a580","target":"graph","created_at":"2026-05-18T01:23:03Z","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 investigate the following conjecture: all compact non-K\\\"ahler complex surfaces admit birational structures. After Inoue-Kobayashi-Ochiai, the remaining cases to study are essentially surfaces in class VII_0^+. In case of Kato surfaces with a cycle and one branch of rational curves we show that they have a special birational structure given by new normal forms of contracting germs in Cremona group Bir(P^2(C)). In particular all surfaces S with GSS and 0<b_2(S)<4 admit a birational structure. From the existence of a special birational structure we deduce meromorphic mappings from the univers","authors_text":"Georges Dloussky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-08T13:23:08Z","title":"Special birational structures on non-K\\\"ahler complex surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01900","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":"sha256:167ba9710e1489061c2d5d41b588a45926299a22e8a6a83447080494ed209fc0","target":"record","created_at":"2026-05-18T01:23:03Z","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":"3709f4bdd2d94610c3fb9ead65a0f5f5eebbc193fa3df0676100ce8a0fb1b465","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-08T13:23:08Z","title_canon_sha256":"ec8a7dbd35685bc3d3d924e90af29e87d849a0f1a4a08e2bde501179d43a5ee0"},"schema_version":"1.0","source":{"id":"1508.01900","kind":"arxiv","version":2}},"canonical_sha256":"c27ce95b171a6fa6951fc4dfe4fc65183d132f3254a4195e6d4dae32a6c22133","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c27ce95b171a6fa6951fc4dfe4fc65183d132f3254a4195e6d4dae32a6c22133","first_computed_at":"2026-05-18T01:23:03.480987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:03.480987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L9tP+JmbNDq1pS2OfL74tli8qnbewvFdhgq77pNGPqcle2KfXSHdoP3XDAAOtQUV7OuOKnEl+7wlVnXQfFyxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:03.481504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:167ba9710e1489061c2d5d41b588a45926299a22e8a6a83447080494ed209fc0","sha256:d3a352ae2a46687cd4e95e7c7e510bc9012962c4ae51ed0475105e2380d0a580"],"state_sha256":"147ba0163504a5d19a9ba6dbe5642fdf0c9012636fe8f0bc3d914417fefd5867"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5T4HjsQeY0dF6J0lC10i3cy39wFqTsACi7FiFFPJL/8qqUvrFmhMd6FmHaVJ9Qqd/U9BZV8oVMhI8+FAxeMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:16:48.364594Z","bundle_sha256":"ad057eb5570fb610cc83638ce9ca89300c98c0e36c428cd13d6095772c56b2e5"}}