{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GZP2SKJTARD3ZQLUWPN2Y4VAUG","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":"2053a475c4e802ed90543c2c098a767c6feef80984441ec0b50b472e8e555278","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-10T05:35:23Z","title_canon_sha256":"3c77df3f4e4e4f8c156d524bf92021ec1e95e0a0bff1da1c96825e0d9b35c7ec"},"schema_version":"1.0","source":{"id":"1411.2330","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2330","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2330v4","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2330","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"GZP2SKJTARD3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZP2SKJTARD3ZQLU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZP2SKJT","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:587687a169c466da09912d070d25edbc08f72f297e1d4a918c512bc9eb41d2a1","target":"graph","created_at":"2026-05-18T00:44:28Z","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":"Let $n \\geq 2$. We prove a homological stability theorem for the diffeomorphism groups of $(4n+1)$-dimensional manifolds, with respect to forming the connected sum with $(2n-1)$-connected, $(4n+1)$-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold $M$, on the linking form associated to the homology groups of $M$. In particular, we construct a geometric model for the linking form using the intersections of embedded and immersed $\\mathbb{Z}/k$-manifolds. In addition to our main homological stability theo","authors_text":"Nathan Perlmutter","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-10T05:35:23Z","title":"Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2330","kind":"arxiv","version":4},"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:d4b7a14dbab5d8e2341661935e679704c6f45686a21219ea5de09795ba71db90","target":"record","created_at":"2026-05-18T00:44:28Z","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":"2053a475c4e802ed90543c2c098a767c6feef80984441ec0b50b472e8e555278","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-10T05:35:23Z","title_canon_sha256":"3c77df3f4e4e4f8c156d524bf92021ec1e95e0a0bff1da1c96825e0d9b35c7ec"},"schema_version":"1.0","source":{"id":"1411.2330","kind":"arxiv","version":4}},"canonical_sha256":"365fa929330447bcc174b3dbac72a0a18eb58d7a7c43c191415a96d86b68f1fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"365fa929330447bcc174b3dbac72a0a18eb58d7a7c43c191415a96d86b68f1fb","first_computed_at":"2026-05-18T00:44:28.706991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.706991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SK3YqoAvELdi5zZ0+jIqWRhqeRithUQM9GhY7az7VBduECvYxoBkMiucScj8W/JwIlCfjKbO0QRYoyEEPj9ZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.707628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2330","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4b7a14dbab5d8e2341661935e679704c6f45686a21219ea5de09795ba71db90","sha256:587687a169c466da09912d070d25edbc08f72f297e1d4a918c512bc9eb41d2a1"],"state_sha256":"f5ac2c930b4c18149c6141b6b011e16d8e1a67e0225d5a45be439314cdbd02f7"}