{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:J6POT5FY7EWULSHX4AQEX45KPI","short_pith_number":"pith:J6POT5FY","schema_version":"1.0","canonical_sha256":"4f9ee9f4b8f92d45c8f7e0204bf3aa7a2bf025d050c52eea0d2741c5733570d6","source":{"kind":"arxiv","id":"2505.23665","version":1},"attestation_state":"computed","paper":{"title":"Higher homotopy wild sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"Atish Mitra, Jeremy Brazas","submitted_at":"2025-05-29T17:12:41Z","abstract_excerpt":"The $\\pi_n$-wild set $\\mathbf{w}_{n}(X)$ of a topological space $X$ is the subspace of $X$ consisting of the points at which there exists a shrinking sequence of essential based maps $S^n\\to X$. In this paper, we show that the homotopy type of $\\mathbf{w}_{n}(X)$ is a homotopy invariant of $X$ and, in analogy to the known one-dimensional case, we show that for certain $n$-dimensional $\\pi_n$-shape injective metric spaces, the homeomorphism type of $\\mathbf{w}_{n}(X)$ is a homotopy invariant of $X$. We also prove that the $\\pi_n$-wild set of a Peano continuum can be homeomorphic to any compact "},"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":"2505.23665","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-05-29T17:12:41Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"95f5195c21be3ad7e8b9166a435c04b9c126a577faa28e470421528749a23f76","abstract_canon_sha256":"4c4248d7d0d520d9e6b7e955779b4e843ade4293a29c66a9835d072cdd9f61a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:05.721082Z","signature_b64":"Jai8Zht5Ozqd1ixBhFfT829+IRc1V+3OgPQ756yFksyu8kGrEb6Qnbh9W+7rd9htdvpJpN5JDg2n8aM4g8ZmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f9ee9f4b8f92d45c8f7e0204bf3aa7a2bf025d050c52eea0d2741c5733570d6","last_reissued_at":"2026-07-05T11:12:05.720597Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:05.720597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher homotopy wild sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"Atish Mitra, Jeremy Brazas","submitted_at":"2025-05-29T17:12:41Z","abstract_excerpt":"The $\\pi_n$-wild set $\\mathbf{w}_{n}(X)$ of a topological space $X$ is the subspace of $X$ consisting of the points at which there exists a shrinking sequence of essential based maps $S^n\\to X$. In this paper, we show that the homotopy type of $\\mathbf{w}_{n}(X)$ is a homotopy invariant of $X$ and, in analogy to the known one-dimensional case, we show that for certain $n$-dimensional $\\pi_n$-shape injective metric spaces, the homeomorphism type of $\\mathbf{w}_{n}(X)$ is a homotopy invariant of $X$. We also prove that the $\\pi_n$-wild set of a Peano continuum can be homeomorphic to any compact "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23665","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.23665/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":"2505.23665","created_at":"2026-07-05T11:12:05.720654+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.23665v1","created_at":"2026-07-05T11:12:05.720654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23665","created_at":"2026-07-05T11:12:05.720654+00:00"},{"alias_kind":"pith_short_12","alias_value":"J6POT5FY7EWU","created_at":"2026-07-05T11:12:05.720654+00:00"},{"alias_kind":"pith_short_16","alias_value":"J6POT5FY7EWULSHX","created_at":"2026-07-05T11:12:05.720654+00:00"},{"alias_kind":"pith_short_8","alias_value":"J6POT5FY","created_at":"2026-07-05T11:12:05.720654+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.14929","citing_title":"Transfinitely iterated wild sets","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI","json":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI.json","graph_json":"https://pith.science/api/pith-number/J6POT5FY7EWULSHX4AQEX45KPI/graph.json","events_json":"https://pith.science/api/pith-number/J6POT5FY7EWULSHX4AQEX45KPI/events.json","paper":"https://pith.science/paper/J6POT5FY"},"agent_actions":{"view_html":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI","download_json":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI.json","view_paper":"https://pith.science/paper/J6POT5FY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.23665&json=true","fetch_graph":"https://pith.science/api/pith-number/J6POT5FY7EWULSHX4AQEX45KPI/graph.json","fetch_events":"https://pith.science/api/pith-number/J6POT5FY7EWULSHX4AQEX45KPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI/action/storage_attestation","attest_author":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI/action/author_attestation","sign_citation":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI/action/citation_signature","submit_replication":"https://pith.science/pith/J6POT5FY7EWULSHX4AQEX45KPI/action/replication_record"}},"created_at":"2026-07-05T11:12:05.720654+00:00","updated_at":"2026-07-05T11:12:05.720654+00:00"}