{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MFRIXBJNQMZZCKO6RP2ZMQOZ4I","short_pith_number":"pith:MFRIXBJN","canonical_record":{"source":{"id":"1710.05316","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-15T11:26:06Z","cross_cats_sorted":["math.DG","math.KT"],"title_canon_sha256":"8e7528b9f75e702dd711459a0d70b2f928f2b7ccf8433d334764660a2fb81e49","abstract_canon_sha256":"bdedcc03e3baf83fdd751702940080002915f1193343a2663120834c06c2ae30"},"schema_version":"1.0"},"canonical_sha256":"61628b852d83339129de8bf59641d9e20c2ea04d9e73b77b85079fc7fa79eb5f","source":{"kind":"arxiv","id":"1710.05316","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05316","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05316v4","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05316","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"MFRIXBJNQMZZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MFRIXBJNQMZZCKO6","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MFRIXBJN","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MFRIXBJNQMZZCKO6RP2ZMQOZ4I","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05316","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-15T11:26:06Z","cross_cats_sorted":["math.DG","math.KT"],"title_canon_sha256":"8e7528b9f75e702dd711459a0d70b2f928f2b7ccf8433d334764660a2fb81e49","abstract_canon_sha256":"bdedcc03e3baf83fdd751702940080002915f1193343a2663120834c06c2ae30"},"schema_version":"1.0"},"canonical_sha256":"61628b852d83339129de8bf59641d9e20c2ea04d9e73b77b85079fc7fa79eb5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:06.145402Z","signature_b64":"jk5iB+XzX2+br3U3I/UpgOgmqobWfi9VdbLICV/f5tznzeg9GkjnVHuGk4zRJ9zmI3ZryGah+yWQHis8K5NVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61628b852d83339129de8bf59641d9e20c2ea04d9e73b77b85079fc7fa79eb5f","last_reissued_at":"2026-05-17T23:49:06.144733Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:06.144733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05316","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+u3QPlF0N2dmeUFmxHU4jP2SCGOXVd3rAtSCw5Wkuwnc3hO4MSHMIh1rAAWMHJOmpBrRp+q2oRDSG+2CTOTsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:02:32.041525Z"},"content_sha256":"012f31ea0c78721c0b2c89dbc6d73892dde4a283a64085a5b7cd15508b9b3ecd","schema_version":"1.0","event_id":"sha256:012f31ea0c78721c0b2c89dbc6d73892dde4a283a64085a5b7cd15508b9b3ecd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MFRIXBJNQMZZCKO6RP2ZMQOZ4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost complex structures on connected sums of complex projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.KT"],"primary_cat":"math.AT","authors_text":"Oliver Goertsches, Panagiotis Konstantis","submitted_at":"2017-10-15T11:26:06Z","abstract_excerpt":"We show that the m-fold connected sum $m\\#\\mathbb{C}\\mathbb{P}^{2n}$ admits an almost complex structure if and only if m is odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05316","kind":"arxiv","version":4},"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":"2026-05-17T23:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0bmPX1r6VpUP04+t3VOUMHPhw+x0WN4PLMbSi+tQo0RKzNJ4gGGgTWb4pPVCfE/yizVM4OmGzN9mZ1Ge4fc5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:02:32.042096Z"},"content_sha256":"bde20e202b032a7270442990ca3b6ff2b42449be91b9df8194d285ac78563fdf","schema_version":"1.0","event_id":"sha256:bde20e202b032a7270442990ca3b6ff2b42449be91b9df8194d285ac78563fdf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I/bundle.json","state_url":"https://pith.science/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I/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":"2026-06-05T02:02:32Z","links":{"resolver":"https://pith.science/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I","bundle":"https://pith.science/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I/bundle.json","state":"https://pith.science/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFRIXBJNQMZZCKO6RP2ZMQOZ4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MFRIXBJNQMZZCKO6RP2ZMQOZ4I","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":"bdedcc03e3baf83fdd751702940080002915f1193343a2663120834c06c2ae30","cross_cats_sorted":["math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-15T11:26:06Z","title_canon_sha256":"8e7528b9f75e702dd711459a0d70b2f928f2b7ccf8433d334764660a2fb81e49"},"schema_version":"1.0","source":{"id":"1710.05316","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05316","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05316v4","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05316","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"MFRIXBJNQMZZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MFRIXBJNQMZZCKO6","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MFRIXBJN","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:bde20e202b032a7270442990ca3b6ff2b42449be91b9df8194d285ac78563fdf","target":"graph","created_at":"2026-05-17T23:49:06Z","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 the m-fold connected sum $m\\#\\mathbb{C}\\mathbb{P}^{2n}$ admits an almost complex structure if and only if m is odd.","authors_text":"Oliver Goertsches, Panagiotis Konstantis","cross_cats":["math.DG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-15T11:26:06Z","title":"Almost complex structures on connected sums of complex projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05316","kind":"arxiv","version":4},"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":"sha256:012f31ea0c78721c0b2c89dbc6d73892dde4a283a64085a5b7cd15508b9b3ecd","target":"record","created_at":"2026-05-17T23:49:06Z","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":"bdedcc03e3baf83fdd751702940080002915f1193343a2663120834c06c2ae30","cross_cats_sorted":["math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-15T11:26:06Z","title_canon_sha256":"8e7528b9f75e702dd711459a0d70b2f928f2b7ccf8433d334764660a2fb81e49"},"schema_version":"1.0","source":{"id":"1710.05316","kind":"arxiv","version":4}},"canonical_sha256":"61628b852d83339129de8bf59641d9e20c2ea04d9e73b77b85079fc7fa79eb5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61628b852d83339129de8bf59641d9e20c2ea04d9e73b77b85079fc7fa79eb5f","first_computed_at":"2026-05-17T23:49:06.144733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.144733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jk5iB+XzX2+br3U3I/UpgOgmqobWfi9VdbLICV/f5tznzeg9GkjnVHuGk4zRJ9zmI3ZryGah+yWQHis8K5NVCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.145402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05316","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:012f31ea0c78721c0b2c89dbc6d73892dde4a283a64085a5b7cd15508b9b3ecd","sha256:bde20e202b032a7270442990ca3b6ff2b42449be91b9df8194d285ac78563fdf"],"state_sha256":"a60ee282e8091a6f8746120924f9111f900e611d15d34deb918ae537466fdcee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbC8jywjWSLtw1OpGJkyVoAp2Y25qbxblzI/ZfZ5z/afbfL8uw/p6JxK7e0VcRbwfk5WKF2RhMFIjkG3IDBzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:02:32.045675Z","bundle_sha256":"4efcae1cce6fa43900eabea0a01643d62128f71ccfaecf83955be26adaa3c574"}}