{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZELLILRP4SIUZUB2WZI7ONGAFV","short_pith_number":"pith:ZELLILRP","canonical_record":{"source":{"id":"1511.06445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T23:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"0b86f7ace1fb299f870a89340677603e80ca11aeef85f75d6230e96db644b845","abstract_canon_sha256":"1af57a0ae4c5e53702c1f1e39ae0059ed1557e45660aaed9109742bcc8c02af6"},"schema_version":"1.0"},"canonical_sha256":"c916b42e2fe4914cd03ab651f734c02d70b9d3f62b44c82fa2cd09ff377aed9b","source":{"kind":"arxiv","id":"1511.06445","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06445","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06445v1","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06445","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZELLILRP4SIU","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZELLILRP4SIUZUB2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZELLILRP","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZELLILRP4SIUZUB2WZI7ONGAFV","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T23:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"0b86f7ace1fb299f870a89340677603e80ca11aeef85f75d6230e96db644b845","abstract_canon_sha256":"1af57a0ae4c5e53702c1f1e39ae0059ed1557e45660aaed9109742bcc8c02af6"},"schema_version":"1.0"},"canonical_sha256":"c916b42e2fe4914cd03ab651f734c02d70b9d3f62b44c82fa2cd09ff377aed9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.319569Z","signature_b64":"qVgpTEklO+jetmy0BfhAiRlnQ82kX/EG6hYX3dKf/FahTtm94HFNpBv2WKRvFES6UwmkUOPSg3ZKAuI4oWi/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c916b42e2fe4914cd03ab651f734c02d70b9d3f62b44c82fa2cd09ff377aed9b","last_reissued_at":"2026-05-17T23:53:34.318857Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.318857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06445","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FPKcGO9uWLmTW5LA/EnOdjRu72p5+Ty5AJ/upgwJuB7I4mVemuZRJ2Lg3xME4IQszvX0tG0+7n7gc6mYFcOoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:40:29.802030Z"},"content_sha256":"67991441f3692d64bd311ea79592ac5e22e0f79be7b47921d9d683c4fe1b27e9","schema_version":"1.0","event_id":"sha256:67991441f3692d64bd311ea79592ac5e22e0f79be7b47921d9d683c4fe1b27e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZELLILRP4SIUZUB2WZI7ONGAFV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tautological rings for high dimensional manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ilya Grigoriev, Oscar Randal-Williams, Soren Galatius","submitted_at":"2015-11-19T23:21:29Z","abstract_excerpt":"We study tautological rings for high dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*(M)$ of those of characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised Miller--Morita--Mumford classes. We completely describe these rings modulo nilpotent elements, when $M$ is a connected sum of copies of $S^n \\times S^n$ for $n$ odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06445","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YkoHfsKqlUM/LZdyey6AW5b18LT+aDl8BlasETrM0gI9IF1odLzx2PPsF4I8eJ305tx7XJM6ux2lTgLtL0b3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:40:29.802392Z"},"content_sha256":"c2cfe632b8a2ece0a8eadc8a521cca2730150b72aeddfb0e572e322f00cb4233","schema_version":"1.0","event_id":"sha256:c2cfe632b8a2ece0a8eadc8a521cca2730150b72aeddfb0e572e322f00cb4233"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZELLILRP4SIUZUB2WZI7ONGAFV/bundle.json","state_url":"https://pith.science/pith/ZELLILRP4SIUZUB2WZI7ONGAFV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZELLILRP4SIUZUB2WZI7ONGAFV/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":"2026-05-28T16:40:29Z","links":{"resolver":"https://pith.science/pith/ZELLILRP4SIUZUB2WZI7ONGAFV","bundle":"https://pith.science/pith/ZELLILRP4SIUZUB2WZI7ONGAFV/bundle.json","state":"https://pith.science/pith/ZELLILRP4SIUZUB2WZI7ONGAFV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZELLILRP4SIUZUB2WZI7ONGAFV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZELLILRP4SIUZUB2WZI7ONGAFV","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":"1af57a0ae4c5e53702c1f1e39ae0059ed1557e45660aaed9109742bcc8c02af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T23:21:29Z","title_canon_sha256":"0b86f7ace1fb299f870a89340677603e80ca11aeef85f75d6230e96db644b845"},"schema_version":"1.0","source":{"id":"1511.06445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06445","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06445v1","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06445","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZELLILRP4SIU","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZELLILRP4SIUZUB2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZELLILRP","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:c2cfe632b8a2ece0a8eadc8a521cca2730150b72aeddfb0e572e322f00cb4233","target":"graph","created_at":"2026-05-17T23:53:34Z","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":"We study tautological rings for high dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*(M)$ of those of characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised Miller--Morita--Mumford classes. We completely describe these rings modulo nilpotent elements, when $M$ is a connected sum of copies of $S^n \\times S^n$ for $n$ odd.","authors_text":"Ilya Grigoriev, Oscar Randal-Williams, Soren Galatius","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T23:21:29Z","title":"Tautological rings for high dimensional manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06445","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":"sha256:67991441f3692d64bd311ea79592ac5e22e0f79be7b47921d9d683c4fe1b27e9","target":"record","created_at":"2026-05-17T23:53:34Z","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":"1af57a0ae4c5e53702c1f1e39ae0059ed1557e45660aaed9109742bcc8c02af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-19T23:21:29Z","title_canon_sha256":"0b86f7ace1fb299f870a89340677603e80ca11aeef85f75d6230e96db644b845"},"schema_version":"1.0","source":{"id":"1511.06445","kind":"arxiv","version":1}},"canonical_sha256":"c916b42e2fe4914cd03ab651f734c02d70b9d3f62b44c82fa2cd09ff377aed9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c916b42e2fe4914cd03ab651f734c02d70b9d3f62b44c82fa2cd09ff377aed9b","first_computed_at":"2026-05-17T23:53:34.318857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:34.318857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qVgpTEklO+jetmy0BfhAiRlnQ82kX/EG6hYX3dKf/FahTtm94HFNpBv2WKRvFES6UwmkUOPSg3ZKAuI4oWi/DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:34.319569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67991441f3692d64bd311ea79592ac5e22e0f79be7b47921d9d683c4fe1b27e9","sha256:c2cfe632b8a2ece0a8eadc8a521cca2730150b72aeddfb0e572e322f00cb4233"],"state_sha256":"e4f47d4f0979fc66195428baffff254522b07bd110e63de1e146bd40de531891"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQeuaW1LbELy441h1Urt+ogmod6Qj2Z4frShVYQaDeNqJVMLv/YxFoqVhX1AD2RYcDag8dCc3Az2CvOulQs2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:40:29.804563Z","bundle_sha256":"d95ea8888b679efb34315dba36fddfe40505ceaa3ddfe4195c0e52445b82797b"}}