{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7L7K7FI7QH6SKX2DYCM4SSDWIQ","short_pith_number":"pith:7L7K7FI7","canonical_record":{"source":{"id":"1510.03029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-11T09:47:10Z","cross_cats_sorted":[],"title_canon_sha256":"dc3fc34b31ce48f88477b3d5fb3e0fa5619004a3139ff1494afa0f3510c86ee9","abstract_canon_sha256":"58be3bd8dba5311a33cfea508e59cdb4e8518919efdb3d5099e6da558c710cb0"},"schema_version":"1.0"},"canonical_sha256":"fafeaf951f81fd255f43c099c9487644179264807f46815baadb7930d52c27b4","source":{"kind":"arxiv","id":"1510.03029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03029","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03029v1","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03029","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"7L7K7FI7QH6S","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7L7K7FI7QH6SKX2D","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7L7K7FI7","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7L7K7FI7QH6SKX2DYCM4SSDWIQ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-11T09:47:10Z","cross_cats_sorted":[],"title_canon_sha256":"dc3fc34b31ce48f88477b3d5fb3e0fa5619004a3139ff1494afa0f3510c86ee9","abstract_canon_sha256":"58be3bd8dba5311a33cfea508e59cdb4e8518919efdb3d5099e6da558c710cb0"},"schema_version":"1.0"},"canonical_sha256":"fafeaf951f81fd255f43c099c9487644179264807f46815baadb7930d52c27b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:48.822840Z","signature_b64":"wEIp/fE/OX12z05CPXZJmizSIAwS288wSkctM5v1geaEhmUNosGW3kVbk7TGNbVAvY7hrO7A4Ts63JkkBJ4pAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fafeaf951f81fd255f43c099c9487644179264807f46815baadb7930d52c27b4","last_reissued_at":"2026-05-18T00:37:48.822357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:48.822357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03029","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":"2026-05-18T00:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ukya9rJFIbPvAnlkGn/TI10XBS4t8XLK4re2IVGVKrrFL8x2d8F8wekoNChf08tdVNrm5TaA0HF7F0Ar8nDIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:35:23.858370Z"},"content_sha256":"0ddd34ee6b2a07046f23ba4b87789f2a738f5e2e664da95c980736e698cb3994","schema_version":"1.0","event_id":"sha256:0ddd34ee6b2a07046f23ba4b87789f2a738f5e2e664da95c980736e698cb3994"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7L7K7FI7QH6SKX2DYCM4SSDWIQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Farrell-Jones spheres and inertia groups of complex projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ramesh Kasilingam","submitted_at":"2015-10-11T09:47:10Z","abstract_excerpt":"We introduce and study a new class of homotopy spheres called Farrell-Jones spheres. Using Farrell-Jones sphere we construct examples of closed negatively curved manifolds $M^{2n}$, where $n=7$ or $8$, which are homeomorphic but not diffeomorphic to complex hyperbolic manifolds, thereby giving a partial answer to a question raised by C.S. Aravinda and F.T. Farrell. We show that every exotic sphere not bounding a spin manifold (Hitchin sphere) is a Farrell-Jones sphere. We also discuss the relationship between inertia groups of $\\mathbb{C}\\mathbb{P}^n$ and Farrell-Jones spheres."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03029","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":"2026-05-18T00:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkqu8xZJaq6rPIlHc9Qu5XHKXuV2MTtoWU2GK5lwVpunDutdJdXI2VWzcEyMsAzhgH+PCVUptx07Kh8Nz+7DCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:35:23.858725Z"},"content_sha256":"e1f489a4bea786792e9a77a6cfea470a0784e679e56a019ee1abc4a23b11a636","schema_version":"1.0","event_id":"sha256:e1f489a4bea786792e9a77a6cfea470a0784e679e56a019ee1abc4a23b11a636"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ/bundle.json","state_url":"https://pith.science/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ/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":"2026-06-03T06:35:23Z","links":{"resolver":"https://pith.science/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ","bundle":"https://pith.science/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ/bundle.json","state":"https://pith.science/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7L7K7FI7QH6SKX2DYCM4SSDWIQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7L7K7FI7QH6SKX2DYCM4SSDWIQ","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":"58be3bd8dba5311a33cfea508e59cdb4e8518919efdb3d5099e6da558c710cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-11T09:47:10Z","title_canon_sha256":"dc3fc34b31ce48f88477b3d5fb3e0fa5619004a3139ff1494afa0f3510c86ee9"},"schema_version":"1.0","source":{"id":"1510.03029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03029","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03029v1","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03029","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"7L7K7FI7QH6S","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7L7K7FI7QH6SKX2D","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7L7K7FI7","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e1f489a4bea786792e9a77a6cfea470a0784e679e56a019ee1abc4a23b11a636","target":"graph","created_at":"2026-05-18T00:37:48Z","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 introduce and study a new class of homotopy spheres called Farrell-Jones spheres. Using Farrell-Jones sphere we construct examples of closed negatively curved manifolds $M^{2n}$, where $n=7$ or $8$, which are homeomorphic but not diffeomorphic to complex hyperbolic manifolds, thereby giving a partial answer to a question raised by C.S. Aravinda and F.T. Farrell. We show that every exotic sphere not bounding a spin manifold (Hitchin sphere) is a Farrell-Jones sphere. We also discuss the relationship between inertia groups of $\\mathbb{C}\\mathbb{P}^n$ and Farrell-Jones spheres.","authors_text":"Ramesh Kasilingam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-11T09:47:10Z","title":"Farrell-Jones spheres and inertia groups of complex projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03029","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":"sha256:0ddd34ee6b2a07046f23ba4b87789f2a738f5e2e664da95c980736e698cb3994","target":"record","created_at":"2026-05-18T00:37:48Z","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":"58be3bd8dba5311a33cfea508e59cdb4e8518919efdb3d5099e6da558c710cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-11T09:47:10Z","title_canon_sha256":"dc3fc34b31ce48f88477b3d5fb3e0fa5619004a3139ff1494afa0f3510c86ee9"},"schema_version":"1.0","source":{"id":"1510.03029","kind":"arxiv","version":1}},"canonical_sha256":"fafeaf951f81fd255f43c099c9487644179264807f46815baadb7930d52c27b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fafeaf951f81fd255f43c099c9487644179264807f46815baadb7930d52c27b4","first_computed_at":"2026-05-18T00:37:48.822357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:48.822357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wEIp/fE/OX12z05CPXZJmizSIAwS288wSkctM5v1geaEhmUNosGW3kVbk7TGNbVAvY7hrO7A4Ts63JkkBJ4pAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:48.822840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ddd34ee6b2a07046f23ba4b87789f2a738f5e2e664da95c980736e698cb3994","sha256:e1f489a4bea786792e9a77a6cfea470a0784e679e56a019ee1abc4a23b11a636"],"state_sha256":"5f922aeca0558f027a5543a42f383e6953d0737b7220e5a4b93266e6762359b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"loX599/Du4N7U8IxdX60JdFfjfKZvt+49y6TdGmr3ZLGB2LhFQCTGTbby9Q43DoJ6Cv4xEx7S6L+kB7O5DagCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:35:23.860946Z","bundle_sha256":"9d5a1ef535c28d5ecba731ac97c47d917199b7c3839dba71514e8f02f08f6d37"}}