{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:J6MWXNDTYV7OFFBASUA5ENWOIK","short_pith_number":"pith:J6MWXNDT","canonical_record":{"source":{"id":"0807.0837","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-05T02:56:44Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"90cdf1ebda8f988809b729409056d9adf30b4fcbfc780baa8df44ef8be7aeb8c","abstract_canon_sha256":"8cbfd8fd76993f8e3b17d180670053d3a4c520a75d63caabafc7f3c14ba227ec"},"schema_version":"1.0"},"canonical_sha256":"4f996bb473c57ee294209501d236ce428c6178c669c8e6e459d4418ce3c6878a","source":{"kind":"arxiv","id":"0807.0837","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0837","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0837v5","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0837","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"J6MWXNDTYV7O","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"J6MWXNDTYV7OFFBA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"J6MWXNDT","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:J6MWXNDTYV7OFFBASUA5ENWOIK","target":"record","payload":{"canonical_record":{"source":{"id":"0807.0837","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-05T02:56:44Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"90cdf1ebda8f988809b729409056d9adf30b4fcbfc780baa8df44ef8be7aeb8c","abstract_canon_sha256":"8cbfd8fd76993f8e3b17d180670053d3a4c520a75d63caabafc7f3c14ba227ec"},"schema_version":"1.0"},"canonical_sha256":"4f996bb473c57ee294209501d236ce428c6178c669c8e6e459d4418ce3c6878a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:26.814989Z","signature_b64":"49GITHw56qvJkw3nUK654ws/MnvsfNQVrGQYA7BWjf8LelDvEf5cCy4+b0bUVh7O1obaHp4sB889XZ4iGPVNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f996bb473c57ee294209501d236ce428c6178c669c8e6e459d4418ce3c6878a","last_reissued_at":"2026-05-18T03:35:26.814345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:26.814345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.0837","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhncitSoBeJIW4IYFy7T0p6gGQPxWjXx461Ivyx9zu5Lk9PC12ZpvWiOn3tujm3kvhn1fxvilZK9S2dXmTsDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:29:00.104143Z"},"content_sha256":"cd160e6f7437b568d6031943e4edc5e984d6ab3bed6b02151ee8b67422143700","schema_version":"1.0","event_id":"sha256:cd160e6f7437b568d6031943e4edc5e984d6ab3bed6b02151ee8b67422143700"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:J6MWXNDTYV7OFFBASUA5ENWOIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A class of locally conformally flat 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Mustafa Kalafat, Selman Akbulut","submitted_at":"2008-07-05T02:56:44Z","abstract_excerpt":"We construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not admit any Einstein metrics. Such 4-manifolds are of particular interest as examples of Bach-flat but non-Einstein spaces in the non-simply connected case. Besides that the underlying smooth manifolds are examples of spaces that admit open book decomposition in dimension 4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0837","kind":"arxiv","version":5},"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":"2026-05-18T03:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q9xaHa7RKB9rjcNfQbgCyCDyBcH5fIZmAy7YoNP+7phHUwriLlUNPotDJlcTcuAoH1i72tdA+Cii2x27tFBbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:29:00.104525Z"},"content_sha256":"c5afb3803025f19969f13046502ac1a37ac7342caac9578e8aad2fe742ef26ff","schema_version":"1.0","event_id":"sha256:c5afb3803025f19969f13046502ac1a37ac7342caac9578e8aad2fe742ef26ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6MWXNDTYV7OFFBASUA5ENWOIK/bundle.json","state_url":"https://pith.science/pith/J6MWXNDTYV7OFFBASUA5ENWOIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6MWXNDTYV7OFFBASUA5ENWOIK/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":"2026-06-22T14:29:00Z","links":{"resolver":"https://pith.science/pith/J6MWXNDTYV7OFFBASUA5ENWOIK","bundle":"https://pith.science/pith/J6MWXNDTYV7OFFBASUA5ENWOIK/bundle.json","state":"https://pith.science/pith/J6MWXNDTYV7OFFBASUA5ENWOIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6MWXNDTYV7OFFBASUA5ENWOIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:J6MWXNDTYV7OFFBASUA5ENWOIK","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":"8cbfd8fd76993f8e3b17d180670053d3a4c520a75d63caabafc7f3c14ba227ec","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-05T02:56:44Z","title_canon_sha256":"90cdf1ebda8f988809b729409056d9adf30b4fcbfc780baa8df44ef8be7aeb8c"},"schema_version":"1.0","source":{"id":"0807.0837","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0837","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0837v5","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0837","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"J6MWXNDTYV7O","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"J6MWXNDTYV7OFFBA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"J6MWXNDT","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:c5afb3803025f19969f13046502ac1a37ac7342caac9578e8aad2fe742ef26ff","target":"graph","created_at":"2026-05-18T03:35:26Z","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 construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not admit any Einstein metrics. Such 4-manifolds are of particular interest as examples of Bach-flat but non-Einstein spaces in the non-simply connected case. Besides that the underlying smooth manifolds are examples of spaces that admit open book decomposition in dimension 4.","authors_text":"Mustafa Kalafat, Selman Akbulut","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-05T02:56:44Z","title":"A class of locally conformally flat 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0837","kind":"arxiv","version":5},"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:cd160e6f7437b568d6031943e4edc5e984d6ab3bed6b02151ee8b67422143700","target":"record","created_at":"2026-05-18T03:35:26Z","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":"8cbfd8fd76993f8e3b17d180670053d3a4c520a75d63caabafc7f3c14ba227ec","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-05T02:56:44Z","title_canon_sha256":"90cdf1ebda8f988809b729409056d9adf30b4fcbfc780baa8df44ef8be7aeb8c"},"schema_version":"1.0","source":{"id":"0807.0837","kind":"arxiv","version":5}},"canonical_sha256":"4f996bb473c57ee294209501d236ce428c6178c669c8e6e459d4418ce3c6878a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f996bb473c57ee294209501d236ce428c6178c669c8e6e459d4418ce3c6878a","first_computed_at":"2026-05-18T03:35:26.814345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:26.814345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49GITHw56qvJkw3nUK654ws/MnvsfNQVrGQYA7BWjf8LelDvEf5cCy4+b0bUVh7O1obaHp4sB889XZ4iGPVNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:26.814989Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.0837","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd160e6f7437b568d6031943e4edc5e984d6ab3bed6b02151ee8b67422143700","sha256:c5afb3803025f19969f13046502ac1a37ac7342caac9578e8aad2fe742ef26ff"],"state_sha256":"449b37905673bde898b06c1ebb724214706797ff6048d055d9c1b6ae9d45c002"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGVaWa5/pIK4JZq7C9mNlsqG3q0YJIxn7iFv/Zg0M24P2Q2rLVByXrXKF+flj+ddgdMXs40woPLAA5Z4CacnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:29:00.106614Z","bundle_sha256":"8b0743198297ff7e59b92aa60dac7355e437d453aaa1a277e60255248d141f69"}}