{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6BI4EEAAOHBT35B7NKKBYECSMZ","short_pith_number":"pith:6BI4EEAA","canonical_record":{"source":{"id":"2010.09869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-10-19T21:07:41Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"29a2ddfccaa1c5cf4991456b9c5a87e3308221ab00978b28fcce71938554dcfd","abstract_canon_sha256":"5eba3351ae6948afd61d4a704747f112d9b4f699bb97c55217253cc833d8247f"},"schema_version":"1.0"},"canonical_sha256":"f051c2100071c33df43f6a941c105266455c9733228f04ee2e6c5d17b4b8d71e","source":{"kind":"arxiv","id":"2010.09869","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09869","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09869v2","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09869","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"pith_short_12","alias_value":"6BI4EEAAOHBT","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"pith_short_16","alias_value":"6BI4EEAAOHBT35B7","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"pith_short_8","alias_value":"6BI4EEAA","created_at":"2026-07-05T04:14:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6BI4EEAAOHBT35B7NKKBYECSMZ","target":"record","payload":{"canonical_record":{"source":{"id":"2010.09869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-10-19T21:07:41Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"29a2ddfccaa1c5cf4991456b9c5a87e3308221ab00978b28fcce71938554dcfd","abstract_canon_sha256":"5eba3351ae6948afd61d4a704747f112d9b4f699bb97c55217253cc833d8247f"},"schema_version":"1.0"},"canonical_sha256":"f051c2100071c33df43f6a941c105266455c9733228f04ee2e6c5d17b4b8d71e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:14:22.760775Z","signature_b64":"14fla3j6ePlzfDXG9iESPRSmofJvs5VOdKE7dc/cy4VQkXZyYq6OyhkjNgaXsPJV0TC+PVKYMyo7XMGo+LhiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f051c2100071c33df43f6a941c105266455c9733228f04ee2e6c5d17b4b8d71e","last_reissued_at":"2026-07-05T04:14:22.760330Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:14:22.760330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.09869","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":"2026-07-05T04:14:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jdjy/AoDLaeMT5IYrOgbR4XOKqK1WOz4ajfamexvRERnZVOETBQJzBiFrZX6yVyvEXdAFmB9eduUc65caItAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:30:55.338401Z"},"content_sha256":"a0a123c47b7a93c0209ccd022d19a7fe4519db60f12f8e49711333f2d337d99a","schema_version":"1.0","event_id":"sha256:a0a123c47b7a93c0209ccd022d19a7fe4519db60f12f8e49711333f2d337d99a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6BI4EEAAOHBT35B7NKKBYECSMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inertia groups in the metastable range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Andrew Senger, Jeremy Hahn, Robert Burklund","submitted_at":"2020-10-19T21:07:41Z","abstract_excerpt":"We prove that the inertia groups of all sufficiently-connected, high-dimensional $(2n)$-manifolds are trivial. This is a key step toward a general classification of manifolds in the metastable range. Specifically, for $m \\gg 0$ and $k>5/12$, suppose $M$ is a $\\lfloor km \\rfloor$-connected, smooth, closed, oriented $m$-manifold and $\\Sigma$ is an exotic $m$-sphere. We prove that, if $M \\sharp \\Sigma$ is diffeomorphic to $M$, then $\\Sigma$ bounds a parallelizable manifold. Our proof is built on an understanding of the second extended power functor in Pstr\\k{a}gowski's category of synthetic spect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09869","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.09869/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":"2026-07-05T04:14:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+6//dp1J2XA8JcJwOlhjeirSoO6jNZnminwsBJiU6j4zdIqNWCxfM3DcT7IQsjaDh46Q7+fvDRIELkZ1vwqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:30:55.338774Z"},"content_sha256":"b3e77a8a1763067afa1d2f0dce535b715fba41dfac665d677f8c276732eb072b","schema_version":"1.0","event_id":"sha256:b3e77a8a1763067afa1d2f0dce535b715fba41dfac665d677f8c276732eb072b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BI4EEAAOHBT35B7NKKBYECSMZ/bundle.json","state_url":"https://pith.science/pith/6BI4EEAAOHBT35B7NKKBYECSMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BI4EEAAOHBT35B7NKKBYECSMZ/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":"2026-07-07T10:30:55Z","links":{"resolver":"https://pith.science/pith/6BI4EEAAOHBT35B7NKKBYECSMZ","bundle":"https://pith.science/pith/6BI4EEAAOHBT35B7NKKBYECSMZ/bundle.json","state":"https://pith.science/pith/6BI4EEAAOHBT35B7NKKBYECSMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BI4EEAAOHBT35B7NKKBYECSMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6BI4EEAAOHBT35B7NKKBYECSMZ","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":"5eba3351ae6948afd61d4a704747f112d9b4f699bb97c55217253cc833d8247f","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-10-19T21:07:41Z","title_canon_sha256":"29a2ddfccaa1c5cf4991456b9c5a87e3308221ab00978b28fcce71938554dcfd"},"schema_version":"1.0","source":{"id":"2010.09869","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09869","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09869v2","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09869","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"pith_short_12","alias_value":"6BI4EEAAOHBT","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"pith_short_16","alias_value":"6BI4EEAAOHBT35B7","created_at":"2026-07-05T04:14:22Z"},{"alias_kind":"pith_short_8","alias_value":"6BI4EEAA","created_at":"2026-07-05T04:14:22Z"}],"graph_snapshots":[{"event_id":"sha256:b3e77a8a1763067afa1d2f0dce535b715fba41dfac665d677f8c276732eb072b","target":"graph","created_at":"2026-07-05T04:14:22Z","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/2010.09869/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the inertia groups of all sufficiently-connected, high-dimensional $(2n)$-manifolds are trivial. This is a key step toward a general classification of manifolds in the metastable range. Specifically, for $m \\gg 0$ and $k>5/12$, suppose $M$ is a $\\lfloor km \\rfloor$-connected, smooth, closed, oriented $m$-manifold and $\\Sigma$ is an exotic $m$-sphere. We prove that, if $M \\sharp \\Sigma$ is diffeomorphic to $M$, then $\\Sigma$ bounds a parallelizable manifold. Our proof is built on an understanding of the second extended power functor in Pstr\\k{a}gowski's category of synthetic spect","authors_text":"Andrew Senger, Jeremy Hahn, Robert Burklund","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-10-19T21:07:41Z","title":"Inertia groups in the metastable range"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09869","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:a0a123c47b7a93c0209ccd022d19a7fe4519db60f12f8e49711333f2d337d99a","target":"record","created_at":"2026-07-05T04:14:22Z","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":"5eba3351ae6948afd61d4a704747f112d9b4f699bb97c55217253cc833d8247f","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-10-19T21:07:41Z","title_canon_sha256":"29a2ddfccaa1c5cf4991456b9c5a87e3308221ab00978b28fcce71938554dcfd"},"schema_version":"1.0","source":{"id":"2010.09869","kind":"arxiv","version":2}},"canonical_sha256":"f051c2100071c33df43f6a941c105266455c9733228f04ee2e6c5d17b4b8d71e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f051c2100071c33df43f6a941c105266455c9733228f04ee2e6c5d17b4b8d71e","first_computed_at":"2026-07-05T04:14:22.760330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:14:22.760330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"14fla3j6ePlzfDXG9iESPRSmofJvs5VOdKE7dc/cy4VQkXZyYq6OyhkjNgaXsPJV0TC+PVKYMyo7XMGo+LhiBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:14:22.760775Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.09869","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0a123c47b7a93c0209ccd022d19a7fe4519db60f12f8e49711333f2d337d99a","sha256:b3e77a8a1763067afa1d2f0dce535b715fba41dfac665d677f8c276732eb072b"],"state_sha256":"bc4347fe510d491c76f0109e854dd196357f1662ab30be254ba78a77aa1a348f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntDFKZOAuc2ck13uFyI9JTBQodmG/ux8CaV4mBhttrkVxy7MQkkq/+muYk/KwJwNUOacGigs6Qez4z93DjS9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:30:55.340672Z","bundle_sha256":"9489e1381cb461122b53aeea9e30c68d4524ba612d12596d4f58724d8124c960"}}