{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CAHYHOQBYTTLI2W2Y2HHIK2RWW","short_pith_number":"pith:CAHYHOQB","canonical_record":{"source":{"id":"1907.09025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-21T20:15:27Z","cross_cats_sorted":[],"title_canon_sha256":"834f2f94ec60044ce3c3853567e2459a5b58237d9bff8dc0fb490cc6a82aefa4","abstract_canon_sha256":"98ee86a3aad7aea874da1368d3ff358ce510b297c186efe1f8a6e9014b6c14b0"},"schema_version":"1.0"},"canonical_sha256":"100f83ba01c4e6b46adac68e742b51b5bf51a86d191ec6745d16e741d91f92c4","source":{"kind":"arxiv","id":"1907.09025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09025","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09025v1","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09025","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"CAHYHOQBYTTL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CAHYHOQBYTTLI2W2","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CAHYHOQB","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CAHYHOQBYTTLI2W2Y2HHIK2RWW","target":"record","payload":{"canonical_record":{"source":{"id":"1907.09025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-21T20:15:27Z","cross_cats_sorted":[],"title_canon_sha256":"834f2f94ec60044ce3c3853567e2459a5b58237d9bff8dc0fb490cc6a82aefa4","abstract_canon_sha256":"98ee86a3aad7aea874da1368d3ff358ce510b297c186efe1f8a6e9014b6c14b0"},"schema_version":"1.0"},"canonical_sha256":"100f83ba01c4e6b46adac68e742b51b5bf51a86d191ec6745d16e741d91f92c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:02.377158Z","signature_b64":"ye9bCAyXnBBRw1bCDBNvkfntulp4vFVGZbMYonSYWiNzX8tuYfDNP6YwOl6iV0kgkt5mfK5bxVTpbe5YISjXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"100f83ba01c4e6b46adac68e742b51b5bf51a86d191ec6745d16e741d91f92c4","last_reissued_at":"2026-05-17T23:40:02.376664Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:02.376664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.09025","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":"2026-05-17T23:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaHTDjmpsmyoE4r6399SMi/ZngUkPN/SyYScQSPZ4u2X1Vkt/9CDrGkGS0py8oVUfuQRNMNjFZdWfyY7ODOXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:15:46.096963Z"},"content_sha256":"9e91dafd30a42d8eccd14bc37b743f5175c4fccd83cb0ac2af5e5d9ef71dad4c","schema_version":"1.0","event_id":"sha256:9e91dafd30a42d8eccd14bc37b743f5175c4fccd83cb0ac2af5e5d9ef71dad4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CAHYHOQBYTTLI2W2Y2HHIK2RWW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Gap Theorem for Half-Conformally Flat Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Brian Weber, Martin Citoler-Saumell","submitted_at":"2019-07-21T20:15:27Z","abstract_excerpt":"We show that any compact half-conformally flat manifold of negative type, with bounded $L^2$ energy, sufficiently small scalar curvature, and a non-collapsing assumption, has all betti numbers bounded. We show that this result is optimal from an analytic perspective by demonstrating singularity models that are 2-ended, and are asymptotically K\\\"ahler on both ends. We show that bounded self-dual solutions of $d\\omega=0$ on ALE manifold ends are either asymptotically K\\\"ahler, or they have a decay rate of $O(r^{-4})$ or better."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09025","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":"2026-05-17T23:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sNh8LHSzZ1QRvzVt5ct/BtZlwe3YqRthgE0jrngdkglHN+NuV3Ihwm8YaEbvVVW+aappmSrQy7gTnxLGsqBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:15:46.097308Z"},"content_sha256":"2244589f2e3647060df91d7741be5a78d4daae791f1397b390d17937027fa7b5","schema_version":"1.0","event_id":"sha256:2244589f2e3647060df91d7741be5a78d4daae791f1397b390d17937027fa7b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW/bundle.json","state_url":"https://pith.science/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW/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":"2026-06-20T23:15:46Z","links":{"resolver":"https://pith.science/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW","bundle":"https://pith.science/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW/bundle.json","state":"https://pith.science/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CAHYHOQBYTTLI2W2Y2HHIK2RWW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CAHYHOQBYTTLI2W2Y2HHIK2RWW","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":"98ee86a3aad7aea874da1368d3ff358ce510b297c186efe1f8a6e9014b6c14b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-21T20:15:27Z","title_canon_sha256":"834f2f94ec60044ce3c3853567e2459a5b58237d9bff8dc0fb490cc6a82aefa4"},"schema_version":"1.0","source":{"id":"1907.09025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09025","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09025v1","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09025","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"CAHYHOQBYTTL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CAHYHOQBYTTLI2W2","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CAHYHOQB","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:2244589f2e3647060df91d7741be5a78d4daae791f1397b390d17937027fa7b5","target":"graph","created_at":"2026-05-17T23:40:02Z","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 any compact half-conformally flat manifold of negative type, with bounded $L^2$ energy, sufficiently small scalar curvature, and a non-collapsing assumption, has all betti numbers bounded. We show that this result is optimal from an analytic perspective by demonstrating singularity models that are 2-ended, and are asymptotically K\\\"ahler on both ends. We show that bounded self-dual solutions of $d\\omega=0$ on ALE manifold ends are either asymptotically K\\\"ahler, or they have a decay rate of $O(r^{-4})$ or better.","authors_text":"Brian Weber, Martin Citoler-Saumell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-21T20:15:27Z","title":"A Gap Theorem for Half-Conformally Flat Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09025","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":"sha256:9e91dafd30a42d8eccd14bc37b743f5175c4fccd83cb0ac2af5e5d9ef71dad4c","target":"record","created_at":"2026-05-17T23:40:02Z","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":"98ee86a3aad7aea874da1368d3ff358ce510b297c186efe1f8a6e9014b6c14b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-21T20:15:27Z","title_canon_sha256":"834f2f94ec60044ce3c3853567e2459a5b58237d9bff8dc0fb490cc6a82aefa4"},"schema_version":"1.0","source":{"id":"1907.09025","kind":"arxiv","version":1}},"canonical_sha256":"100f83ba01c4e6b46adac68e742b51b5bf51a86d191ec6745d16e741d91f92c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"100f83ba01c4e6b46adac68e742b51b5bf51a86d191ec6745d16e741d91f92c4","first_computed_at":"2026-05-17T23:40:02.376664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:02.376664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ye9bCAyXnBBRw1bCDBNvkfntulp4vFVGZbMYonSYWiNzX8tuYfDNP6YwOl6iV0kgkt5mfK5bxVTpbe5YISjXDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:02.377158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e91dafd30a42d8eccd14bc37b743f5175c4fccd83cb0ac2af5e5d9ef71dad4c","sha256:2244589f2e3647060df91d7741be5a78d4daae791f1397b390d17937027fa7b5"],"state_sha256":"9334a3aabb1835ee87f1e612ba02eea8f748567ba002737f4964c64e5974a191"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLNacGkceQmRtj+mY+IFL4Xfp6TO6yjUUz6D3ZgBD/YxiwykfRstNKDQpsIMd5mqMvpGUGQupDm+oVoIU/pvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:15:46.099212Z","bundle_sha256":"c3a4a1dfb6bf848f19c23b2369a50ddeb65d07c5010fdd8a01cff3cf97e20720"}}