{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N54GRHHSPKWET37UKFP3YEJFRC","short_pith_number":"pith:N54GRHHS","canonical_record":{"source":{"id":"1407.4680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-17T14:24:58Z","cross_cats_sorted":[],"title_canon_sha256":"eda8fadd087f9d9aada6bc816fc1bd469380ac1f55a51cff4c885204fa8a1489","abstract_canon_sha256":"de6430fc2c8c0f5638a2ae44a2ddf16ab986547ad847c94eca353ea85d58d9cd"},"schema_version":"1.0"},"canonical_sha256":"6f78689cf27aac49eff4515fbc112588a19694600a57bb3859f786bd5145dcee","source":{"kind":"arxiv","id":"1407.4680","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4680","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4680v2","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4680","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"N54GRHHSPKWE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N54GRHHSPKWET37U","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N54GRHHS","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N54GRHHSPKWET37UKFP3YEJFRC","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-17T14:24:58Z","cross_cats_sorted":[],"title_canon_sha256":"eda8fadd087f9d9aada6bc816fc1bd469380ac1f55a51cff4c885204fa8a1489","abstract_canon_sha256":"de6430fc2c8c0f5638a2ae44a2ddf16ab986547ad847c94eca353ea85d58d9cd"},"schema_version":"1.0"},"canonical_sha256":"6f78689cf27aac49eff4515fbc112588a19694600a57bb3859f786bd5145dcee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:41.812917Z","signature_b64":"94Iqkr26hz7PtI/1PMiBryyWr3pA72PWaE1rfSpycUG0ayXhghGjqjYidqLQp5j95i8+4FN5fNF5aAKCv4/aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f78689cf27aac49eff4515fbc112588a19694600a57bb3859f786bd5145dcee","last_reissued_at":"2026-05-18T01:57:41.812364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:41.812364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4680","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":"2026-05-18T01:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s3n/+IYxJTFEyvIwtrE9ZYA5SCBAcYhjhShbqTTaWpPW1lzpViUNUb8SkrBy/fOtrtfZFBw1jf9azbrpzVTbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T10:44:52.352714Z"},"content_sha256":"e429bcdffe186de19ad203f8ea4acceca0d5df17463f1dd622dc12af60aaa88a","schema_version":"1.0","event_id":"sha256:e429bcdffe186de19ad203f8ea4acceca0d5df17463f1dd622dc12af60aaa88a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N54GRHHSPKWET37UKFP3YEJFRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian quotients of mapping class groups of highly connected manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Oscar Randal-Williams, Soren Galatius","submitted_at":"2014-07-17T14:24:58Z","abstract_excerpt":"We compute the abelianisations of the mapping class groups of the manifolds $W_g^{2n} = g(S^n \\times S^n)$ for $n \\geq 3$ and $g \\geq 5$. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group on the middle homology, and takes values in the abelianisation of the automorphism group of the middle homology. The second part arises from bordism classes of mapping cylinders and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable $J$-homomorphism. We relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4680","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":"2026-05-18T01:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORMIztNBPHJHzkJuHI01W4sCYEfy6KCNa+UH7o4NPW+AYnOe1aZM7Z6YC3sTsdnm+YUB3Z25HByBwsrxl1myBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T10:44:52.353060Z"},"content_sha256":"3e171b65cc7cf07c2425f5673042da8546e1cfec2cbaeb882280a963a54d9091","schema_version":"1.0","event_id":"sha256:3e171b65cc7cf07c2425f5673042da8546e1cfec2cbaeb882280a963a54d9091"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N54GRHHSPKWET37UKFP3YEJFRC/bundle.json","state_url":"https://pith.science/pith/N54GRHHSPKWET37UKFP3YEJFRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N54GRHHSPKWET37UKFP3YEJFRC/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":"2026-06-21T10:44:52Z","links":{"resolver":"https://pith.science/pith/N54GRHHSPKWET37UKFP3YEJFRC","bundle":"https://pith.science/pith/N54GRHHSPKWET37UKFP3YEJFRC/bundle.json","state":"https://pith.science/pith/N54GRHHSPKWET37UKFP3YEJFRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N54GRHHSPKWET37UKFP3YEJFRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N54GRHHSPKWET37UKFP3YEJFRC","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":"de6430fc2c8c0f5638a2ae44a2ddf16ab986547ad847c94eca353ea85d58d9cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-17T14:24:58Z","title_canon_sha256":"eda8fadd087f9d9aada6bc816fc1bd469380ac1f55a51cff4c885204fa8a1489"},"schema_version":"1.0","source":{"id":"1407.4680","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4680","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4680v2","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4680","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"N54GRHHSPKWE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N54GRHHSPKWET37U","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N54GRHHS","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:3e171b65cc7cf07c2425f5673042da8546e1cfec2cbaeb882280a963a54d9091","target":"graph","created_at":"2026-05-18T01:57:41Z","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 compute the abelianisations of the mapping class groups of the manifolds $W_g^{2n} = g(S^n \\times S^n)$ for $n \\geq 3$ and $g \\geq 5$. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group on the middle homology, and takes values in the abelianisation of the automorphism group of the middle homology. The second part arises from bordism classes of mapping cylinders and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable $J$-homomorphism. We relat","authors_text":"Oscar Randal-Williams, Soren Galatius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-17T14:24:58Z","title":"Abelian quotients of mapping class groups of highly connected manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4680","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:e429bcdffe186de19ad203f8ea4acceca0d5df17463f1dd622dc12af60aaa88a","target":"record","created_at":"2026-05-18T01:57:41Z","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":"de6430fc2c8c0f5638a2ae44a2ddf16ab986547ad847c94eca353ea85d58d9cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-17T14:24:58Z","title_canon_sha256":"eda8fadd087f9d9aada6bc816fc1bd469380ac1f55a51cff4c885204fa8a1489"},"schema_version":"1.0","source":{"id":"1407.4680","kind":"arxiv","version":2}},"canonical_sha256":"6f78689cf27aac49eff4515fbc112588a19694600a57bb3859f786bd5145dcee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f78689cf27aac49eff4515fbc112588a19694600a57bb3859f786bd5145dcee","first_computed_at":"2026-05-18T01:57:41.812364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:41.812364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94Iqkr26hz7PtI/1PMiBryyWr3pA72PWaE1rfSpycUG0ayXhghGjqjYidqLQp5j95i8+4FN5fNF5aAKCv4/aBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:41.812917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4680","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e429bcdffe186de19ad203f8ea4acceca0d5df17463f1dd622dc12af60aaa88a","sha256:3e171b65cc7cf07c2425f5673042da8546e1cfec2cbaeb882280a963a54d9091"],"state_sha256":"93da93dc75e202348e53a41273cc1d368f5927281d7cc31aa104e8a4a06e344e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jjMHnYxx4Cbj2S0AV4R4SgQcQc+CInulUYF7h/w5vYZEfuqBqUBU64ILO/0kF5deQFFS9pcfaUiwhN6eCI4yBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T10:44:52.354991Z","bundle_sha256":"f85c96a03f346bab1691a11e66506416e688a5e9ccf46c20e4d8ff8e8c95896d"}}