{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:UWEWYWVG6SMS5AYISTNKDZTAPJ","short_pith_number":"pith:UWEWYWVG","schema_version":"1.0","canonical_sha256":"a5896c5aa6f4992e830894daa1e6607a5c0959c745040d90272710ad8904b023","source":{"kind":"arxiv","id":"2110.09686","version":2},"attestation_state":"computed","paper":{"title":"Family Bauer--Furuta invariant, Exotic Surfaces and Smale conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.GT","authors_text":"Anubhav Mukherjee, Jianfeng Lin","submitted_at":"2021-10-19T01:34:11Z","abstract_excerpt":"We establish the existence of a pair of exotic surfaces in a punctured $K3$ which remains exotic after one external stabilization and have diffeomorphic complements. A key ingredient in the proof is a vanishing theorem of the family Bauer--Furuta invariant for diffeomorphisms on a large family of spin 4-manifolds, which is proved using the tom Dieck splitting theorem in equivariant stable homotopy theory. In particular, we prove that the $S^{1}$-equivariant family Bauer--Furuta invariant of any orientation-preserving diffeomorphism on $S^{4}$ is trivial and that the $\\mathrm{Pin}(2)$-equivaria"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.09686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-10-19T01:34:11Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"1d26f9377b648d24e5ed1a91df8f35895a96976ec87b82124672d1488a9b893e","abstract_canon_sha256":"4fd08d018e0377f3670178550076dc9a7cae373761a34567b9d2cc0272d79724"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:31.504016Z","signature_b64":"LdgyaDrEbXZ+2DOE7oMHkX+1L64XVH6EY9N+Sg4/fH0gDWOdUoxYxb+2UuSVtQjk/gZQuku2dz6beS8Fqup8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5896c5aa6f4992e830894daa1e6607a5c0959c745040d90272710ad8904b023","last_reissued_at":"2026-07-05T03:31:31.503507Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:31.503507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Family Bauer--Furuta invariant, Exotic Surfaces and Smale conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.GT","authors_text":"Anubhav Mukherjee, Jianfeng Lin","submitted_at":"2021-10-19T01:34:11Z","abstract_excerpt":"We establish the existence of a pair of exotic surfaces in a punctured $K3$ which remains exotic after one external stabilization and have diffeomorphic complements. A key ingredient in the proof is a vanishing theorem of the family Bauer--Furuta invariant for diffeomorphisms on a large family of spin 4-manifolds, which is proved using the tom Dieck splitting theorem in equivariant stable homotopy theory. In particular, we prove that the $S^{1}$-equivariant family Bauer--Furuta invariant of any orientation-preserving diffeomorphism on $S^{4}$ is trivial and that the $\\mathrm{Pin}(2)$-equivaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09686","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/2110.09686/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.09686","created_at":"2026-07-05T03:31:31.503575+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.09686v2","created_at":"2026-07-05T03:31:31.503575+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.09686","created_at":"2026-07-05T03:31:31.503575+00:00"},{"alias_kind":"pith_short_12","alias_value":"UWEWYWVG6SMS","created_at":"2026-07-05T03:31:31.503575+00:00"},{"alias_kind":"pith_short_16","alias_value":"UWEWYWVG6SMS5AYI","created_at":"2026-07-05T03:31:31.503575+00:00"},{"alias_kind":"pith_short_8","alias_value":"UWEWYWVG","created_at":"2026-07-05T03:31:31.503575+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.29452","citing_title":"Handle decompositions and the 1-dimensional inputs skein lasagna module","ref_index":58,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ","json":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ.json","graph_json":"https://pith.science/api/pith-number/UWEWYWVG6SMS5AYISTNKDZTAPJ/graph.json","events_json":"https://pith.science/api/pith-number/UWEWYWVG6SMS5AYISTNKDZTAPJ/events.json","paper":"https://pith.science/paper/UWEWYWVG"},"agent_actions":{"view_html":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ","download_json":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ.json","view_paper":"https://pith.science/paper/UWEWYWVG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.09686&json=true","fetch_graph":"https://pith.science/api/pith-number/UWEWYWVG6SMS5AYISTNKDZTAPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/UWEWYWVG6SMS5AYISTNKDZTAPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ/action/storage_attestation","attest_author":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ/action/author_attestation","sign_citation":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ/action/citation_signature","submit_replication":"https://pith.science/pith/UWEWYWVG6SMS5AYISTNKDZTAPJ/action/replication_record"}},"created_at":"2026-07-05T03:31:31.503575+00:00","updated_at":"2026-07-05T03:31:31.503575+00:00"}