{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SJFGYT4WRZJ22YFYIF4ZTAEYKB","short_pith_number":"pith:SJFGYT4W","canonical_record":{"source":{"id":"1708.03824","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-12T21:33:27Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b7384029f9dcc4f9af4982efe864f52f089c4456b3a102baaa1680ef63405de9","abstract_canon_sha256":"82a502dd44254a1f8ea2012deaaaf9fa7667d615ca5d7489d66c3e986580e1b0"},"schema_version":"1.0"},"canonical_sha256":"924a6c4f968e53ad60b84179998098506b08efba23e40e039adc054ab6150940","source":{"kind":"arxiv","id":"1708.03824","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03824","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03824v2","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03824","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"SJFGYT4WRZJ2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SJFGYT4WRZJ22YFY","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SJFGYT4W","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SJFGYT4WRZJ22YFYIF4ZTAEYKB","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03824","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-12T21:33:27Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b7384029f9dcc4f9af4982efe864f52f089c4456b3a102baaa1680ef63405de9","abstract_canon_sha256":"82a502dd44254a1f8ea2012deaaaf9fa7667d615ca5d7489d66c3e986580e1b0"},"schema_version":"1.0"},"canonical_sha256":"924a6c4f968e53ad60b84179998098506b08efba23e40e039adc054ab6150940","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:34.083247Z","signature_b64":"ukGli2xWmqC9/IbkgTgJ3fYmlyTEDtu3zcHcVVPMzXIC2s4V6vxjGDX/9XDm3BDpF3ZlgmE3snIhPl2AY49CBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"924a6c4f968e53ad60b84179998098506b08efba23e40e039adc054ab6150940","last_reissued_at":"2026-05-18T00:25:34.082604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:34.082604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03824","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":"2026-05-18T00:25:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqUYA/GOib4HWEu6a1aJXNbDK102PVktCs8sk0v5hibRYexIvJlaeEpbbxkrUb6lCz78qIuWpLIjPpSlxblTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:52:34.042672Z"},"content_sha256":"fd1ae5d045376c4845cf3d2aae6aad6a4b3e8a71f761efa5c5770f2ef6515449","schema_version":"1.0","event_id":"sha256:fd1ae5d045376c4845cf3d2aae6aad6a4b3e8a71f761efa5c5770f2ef6515449"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SJFGYT4WRZJ22YFYIF4ZTAEYKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anti-Self-Dual 4-Manifolds, Quasi-Fuchsian Groups, and Almost-Kaehler Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Christopher J. Bishop, Claude LeBrun","submitted_at":"2017-08-12T21:33:27Z","abstract_excerpt":"It is known that the almost-Kaehler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show here by example that this subset is not generally closed, and so need not sweep out entire connected components in the moduli space. Our construction hinges on an unexpected link between harmonic functions on certain hyperbolic 3-manifolds and self-dual harmonic 2-forms on associated 4-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03824","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":"2026-05-18T00:25:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w0M0C8xgj7LHwu3pDjmQzZG521/GDhtYiDXlPMAuJcyAVwOfpHTkZvc7sA6ya3CZn/QCbMnrgbWsy06M6TEiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:52:34.043183Z"},"content_sha256":"e1f3097f80fab34f7e0e17e2e1f5cafb7268c919c12f2ee515efa4ac62656b4b","schema_version":"1.0","event_id":"sha256:e1f3097f80fab34f7e0e17e2e1f5cafb7268c919c12f2ee515efa4ac62656b4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB/bundle.json","state_url":"https://pith.science/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB/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":"2026-05-31T12:52:34Z","links":{"resolver":"https://pith.science/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB","bundle":"https://pith.science/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB/bundle.json","state":"https://pith.science/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJFGYT4WRZJ22YFYIF4ZTAEYKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SJFGYT4WRZJ22YFYIF4ZTAEYKB","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":"82a502dd44254a1f8ea2012deaaaf9fa7667d615ca5d7489d66c3e986580e1b0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-12T21:33:27Z","title_canon_sha256":"b7384029f9dcc4f9af4982efe864f52f089c4456b3a102baaa1680ef63405de9"},"schema_version":"1.0","source":{"id":"1708.03824","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03824","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03824v2","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03824","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"SJFGYT4WRZJ2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SJFGYT4WRZJ22YFY","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SJFGYT4W","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:e1f3097f80fab34f7e0e17e2e1f5cafb7268c919c12f2ee515efa4ac62656b4b","target":"graph","created_at":"2026-05-18T00:25:34Z","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":"It is known that the almost-Kaehler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show here by example that this subset is not generally closed, and so need not sweep out entire connected components in the moduli space. Our construction hinges on an unexpected link between harmonic functions on certain hyperbolic 3-manifolds and self-dual harmonic 2-forms on associated 4-manifolds.","authors_text":"Christopher J. Bishop, Claude LeBrun","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-12T21:33:27Z","title":"Anti-Self-Dual 4-Manifolds, Quasi-Fuchsian Groups, and Almost-Kaehler Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03824","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:fd1ae5d045376c4845cf3d2aae6aad6a4b3e8a71f761efa5c5770f2ef6515449","target":"record","created_at":"2026-05-18T00:25:34Z","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":"82a502dd44254a1f8ea2012deaaaf9fa7667d615ca5d7489d66c3e986580e1b0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-12T21:33:27Z","title_canon_sha256":"b7384029f9dcc4f9af4982efe864f52f089c4456b3a102baaa1680ef63405de9"},"schema_version":"1.0","source":{"id":"1708.03824","kind":"arxiv","version":2}},"canonical_sha256":"924a6c4f968e53ad60b84179998098506b08efba23e40e039adc054ab6150940","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"924a6c4f968e53ad60b84179998098506b08efba23e40e039adc054ab6150940","first_computed_at":"2026-05-18T00:25:34.082604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:34.082604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ukGli2xWmqC9/IbkgTgJ3fYmlyTEDtu3zcHcVVPMzXIC2s4V6vxjGDX/9XDm3BDpF3ZlgmE3snIhPl2AY49CBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:34.083247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03824","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd1ae5d045376c4845cf3d2aae6aad6a4b3e8a71f761efa5c5770f2ef6515449","sha256:e1f3097f80fab34f7e0e17e2e1f5cafb7268c919c12f2ee515efa4ac62656b4b"],"state_sha256":"a3bb9dc3fa1a3e6ba98708e55b876a7276e2390301deba3c8fc6060a92fab878"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5RgHCRpMAFvqtNzfTB5jMa8V5gfSXEra+uyvgwHM4ZFaqo/Nqyu61fHLzXH0QU9uYYE0U34Id5SPr4264TvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:52:34.051802Z","bundle_sha256":"ff34651d557287b95c1eef95fe3239833435c313084e5102138679efd5036ce4"}}