{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:QM5WW5WJTLHYRI64J7V5RPPZQN","short_pith_number":"pith:QM5WW5WJ","canonical_record":{"source":{"id":"2211.00782","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-11-01T23:01:27Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f5e7ca81f8c43710a3b2be57dfde1af3ae93aa3bf9a83ed56983b1ecc13a01d4","abstract_canon_sha256":"df04f51fa26a6391ae06b2e49439f9a6f627015736ebada98df5cb5aaa74c031"},"schema_version":"1.0"},"canonical_sha256":"833b6b76c99acf88a3dc4febd8bdf9837238c2336e5da6ca4bade48e057b622a","source":{"kind":"arxiv","id":"2211.00782","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.00782","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"2211.00782v3","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.00782","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"QM5WW5WJTLHY","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"pith_short_16","alias_value":"QM5WW5WJTLHYRI64","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"pith_short_8","alias_value":"QM5WW5WJ","created_at":"2026-07-05T12:02:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:QM5WW5WJTLHYRI64J7V5RPPZQN","target":"record","payload":{"canonical_record":{"source":{"id":"2211.00782","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-11-01T23:01:27Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f5e7ca81f8c43710a3b2be57dfde1af3ae93aa3bf9a83ed56983b1ecc13a01d4","abstract_canon_sha256":"df04f51fa26a6391ae06b2e49439f9a6f627015736ebada98df5cb5aaa74c031"},"schema_version":"1.0"},"canonical_sha256":"833b6b76c99acf88a3dc4febd8bdf9837238c2336e5da6ca4bade48e057b622a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:31.246244Z","signature_b64":"KE3DzYYFDyro66IVHQ7S+2cTGQqSu5RNDjXFdRIrxlf/NmANerdNsbQZyX8oyqlGCO53frE18iztETvC4sQkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"833b6b76c99acf88a3dc4febd8bdf9837238c2336e5da6ca4bade48e057b622a","last_reissued_at":"2026-07-05T12:02:31.245719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:31.245719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.00782","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:02:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElmDBPESbW5ru/IeFN+1NnqrTdefuGznjV82Cd0IU4MgIzQcXZpWnAUf7xjy+eTm2d1RHHpiC2+kE/S3WbcrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T02:39:11.565389Z"},"content_sha256":"d69720f7916c215a3e30d750b44b2400e3349729e19a05051e4cdb7ddf91974e","schema_version":"1.0","event_id":"sha256:d69720f7916c215a3e30d750b44b2400e3349729e19a05051e4cdb7ddf91974e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:QM5WW5WJTLHYRI64J7V5RPPZQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inertia groups of $(n-1)$-connected $2n$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Adela YiYu Zhang, Andrew Senger","submitted_at":"2022-11-01T23:01:27Z","abstract_excerpt":"In this paper, we compute the inertia groups of $(n-1)$-connected, smooth, closed, oriented $2n$-manifolds where $n \\geq 3$. As a consequence, we complete the diffeomorphism classification of such manifolds, finishing a program initiated by Wall sixty years ago, with the exception of the $126$-dimensional case of the Kervaire invariant one problem.\n  In particular, we find that the inertia group always vanishes for $n \\neq 4,8,9$ -- for $n \\gg 0$, this was known by the work of several previous authors, including Wall, Stolz, and Burklund and Hahn with the first named author. When $n = 4,8,9$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.00782","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.00782/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T12:02:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xviaUzcZWkCMKNGceMdN96zLnR7cRdTaQQezlc/C4NUgQjmpTd4Tlc9Sa1AHjmHM4z2qkSA1f/D6GGvFfOg7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T02:39:11.565900Z"},"content_sha256":"723c41de6275d186452d0b8893e8d9e101bcdc86ec0e1e0b7a8dd1bba9f5a8ad","schema_version":"1.0","event_id":"sha256:723c41de6275d186452d0b8893e8d9e101bcdc86ec0e1e0b7a8dd1bba9f5a8ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QM5WW5WJTLHYRI64J7V5RPPZQN/bundle.json","state_url":"https://pith.science/pith/QM5WW5WJTLHYRI64J7V5RPPZQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QM5WW5WJTLHYRI64J7V5RPPZQN/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":"2026-08-24T02:39:11Z","links":{"resolver":"https://pith.science/pith/QM5WW5WJTLHYRI64J7V5RPPZQN","bundle":"https://pith.science/pith/QM5WW5WJTLHYRI64J7V5RPPZQN/bundle.json","state":"https://pith.science/pith/QM5WW5WJTLHYRI64J7V5RPPZQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QM5WW5WJTLHYRI64J7V5RPPZQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QM5WW5WJTLHYRI64J7V5RPPZQN","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":"df04f51fa26a6391ae06b2e49439f9a6f627015736ebada98df5cb5aaa74c031","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-11-01T23:01:27Z","title_canon_sha256":"f5e7ca81f8c43710a3b2be57dfde1af3ae93aa3bf9a83ed56983b1ecc13a01d4"},"schema_version":"1.0","source":{"id":"2211.00782","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.00782","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"2211.00782v3","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.00782","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"QM5WW5WJTLHY","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"pith_short_16","alias_value":"QM5WW5WJTLHYRI64","created_at":"2026-07-05T12:02:31Z"},{"alias_kind":"pith_short_8","alias_value":"QM5WW5WJ","created_at":"2026-07-05T12:02:31Z"}],"graph_snapshots":[{"event_id":"sha256:723c41de6275d186452d0b8893e8d9e101bcdc86ec0e1e0b7a8dd1bba9f5a8ad","target":"graph","created_at":"2026-07-05T12:02:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.00782/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we compute the inertia groups of $(n-1)$-connected, smooth, closed, oriented $2n$-manifolds where $n \\geq 3$. As a consequence, we complete the diffeomorphism classification of such manifolds, finishing a program initiated by Wall sixty years ago, with the exception of the $126$-dimensional case of the Kervaire invariant one problem.\n  In particular, we find that the inertia group always vanishes for $n \\neq 4,8,9$ -- for $n \\gg 0$, this was known by the work of several previous authors, including Wall, Stolz, and Burklund and Hahn with the first named author. When $n = 4,8,9$, ","authors_text":"Adela YiYu Zhang, Andrew Senger","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-11-01T23:01:27Z","title":"Inertia groups of $(n-1)$-connected $2n$-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.00782","kind":"arxiv","version":3},"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:d69720f7916c215a3e30d750b44b2400e3349729e19a05051e4cdb7ddf91974e","target":"record","created_at":"2026-07-05T12:02:31Z","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":"df04f51fa26a6391ae06b2e49439f9a6f627015736ebada98df5cb5aaa74c031","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-11-01T23:01:27Z","title_canon_sha256":"f5e7ca81f8c43710a3b2be57dfde1af3ae93aa3bf9a83ed56983b1ecc13a01d4"},"schema_version":"1.0","source":{"id":"2211.00782","kind":"arxiv","version":3}},"canonical_sha256":"833b6b76c99acf88a3dc4febd8bdf9837238c2336e5da6ca4bade48e057b622a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"833b6b76c99acf88a3dc4febd8bdf9837238c2336e5da6ca4bade48e057b622a","first_computed_at":"2026-07-05T12:02:31.245719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:02:31.245719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KE3DzYYFDyro66IVHQ7S+2cTGQqSu5RNDjXFdRIrxlf/NmANerdNsbQZyX8oyqlGCO53frE18iztETvC4sQkAA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:02:31.246244Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.00782","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d69720f7916c215a3e30d750b44b2400e3349729e19a05051e4cdb7ddf91974e","sha256:723c41de6275d186452d0b8893e8d9e101bcdc86ec0e1e0b7a8dd1bba9f5a8ad"],"state_sha256":"9f796f9939a54988f9cc4c9d743e1594a50b37156217b029d981d70f2ec6ebb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9Xi50oEOTYtkH14o7HCPFpPH4Zc1YDru5JFSDL3eatv88pPyVNjct/ERDzRj8gvGsgeABT8zSXQ+fS11QIDCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T02:39:11.570241Z","bundle_sha256":"3cdc269aa5d8cab941e4c92e9512d39f359c8e94b792120463541191be2d5c16"}}