{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2I36DCA7ASBCDS4UZZZHU3P2XH","short_pith_number":"pith:2I36DCA7","schema_version":"1.0","canonical_sha256":"d237e1881f048221cb94ce727a6dfab9f6963626d2b982fb4503f78515650d71","source":{"kind":"arxiv","id":"2509.19074","version":2},"attestation_state":"computed","paper":{"title":"Framed configuration spaces and exotic spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Alexander Kupers, Fadi Mezher, Manuel Krannich","submitted_at":"2025-09-23T14:34:32Z","abstract_excerpt":"We determine when an exotic sphere $\\Sigma$ of dimension $d\\not \\equiv 1 (4)$ can be detected through the homotopy type of its truncated Disc-presheaf. The latter records the diagram of framed configuration spaces of bounded cardinality in $\\Sigma$ with natural point-forgetting and -splitting maps between them, and it gives rise to the finite stages in Goodwillie--Weiss' embedding calculus tower. Our proof involves three ingredients that could be of independent interest: a gluing result for Disc-presheaves of manifolds divided into two codimension zero submanifolds, a version of Atiyah duality"},"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":"2509.19074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-23T14:34:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7c3e8ad232d40007b130fbec5105b66db0ba49c134361b984aabac30982b7a89","abstract_canon_sha256":"9215078db728120cb5961140220e66d96e314936f793cbcc314f33a4b5157682"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:04:57.971287Z","signature_b64":"zQ8iEF0BNRINnm4ZuSPjj1Mf10VfOVmTyjHmLlXc6dHWFO7aZBS0wcTHQcO5x1jIryaPnXhWT0hVhJQ51vYEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d237e1881f048221cb94ce727a6dfab9f6963626d2b982fb4503f78515650d71","last_reissued_at":"2026-05-20T01:04:57.970502Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:04:57.970502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Framed configuration spaces and exotic spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Alexander Kupers, Fadi Mezher, Manuel Krannich","submitted_at":"2025-09-23T14:34:32Z","abstract_excerpt":"We determine when an exotic sphere $\\Sigma$ of dimension $d\\not \\equiv 1 (4)$ can be detected through the homotopy type of its truncated Disc-presheaf. The latter records the diagram of framed configuration spaces of bounded cardinality in $\\Sigma$ with natural point-forgetting and -splitting maps between them, and it gives rise to the finite stages in Goodwillie--Weiss' embedding calculus tower. Our proof involves three ingredients that could be of independent interest: a gluing result for Disc-presheaves of manifolds divided into two codimension zero submanifolds, a version of Atiyah duality"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.19074","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/2509.19074/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":"2509.19074","created_at":"2026-05-20T01:04:57.970627+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.19074v2","created_at":"2026-05-20T01:04:57.970627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.19074","created_at":"2026-05-20T01:04:57.970627+00:00"},{"alias_kind":"pith_short_12","alias_value":"2I36DCA7ASBC","created_at":"2026-05-20T01:04:57.970627+00:00"},{"alias_kind":"pith_short_16","alias_value":"2I36DCA7ASBCDS4U","created_at":"2026-05-20T01:04:57.970627+00:00"},{"alias_kind":"pith_short_8","alias_value":"2I36DCA7","created_at":"2026-05-20T01:04:57.970627+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH","json":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH.json","graph_json":"https://pith.science/api/pith-number/2I36DCA7ASBCDS4UZZZHU3P2XH/graph.json","events_json":"https://pith.science/api/pith-number/2I36DCA7ASBCDS4UZZZHU3P2XH/events.json","paper":"https://pith.science/paper/2I36DCA7"},"agent_actions":{"view_html":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH","download_json":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH.json","view_paper":"https://pith.science/paper/2I36DCA7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.19074&json=true","fetch_graph":"https://pith.science/api/pith-number/2I36DCA7ASBCDS4UZZZHU3P2XH/graph.json","fetch_events":"https://pith.science/api/pith-number/2I36DCA7ASBCDS4UZZZHU3P2XH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH/action/storage_attestation","attest_author":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH/action/author_attestation","sign_citation":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH/action/citation_signature","submit_replication":"https://pith.science/pith/2I36DCA7ASBCDS4UZZZHU3P2XH/action/replication_record"}},"created_at":"2026-05-20T01:04:57.970627+00:00","updated_at":"2026-05-20T01:04:57.970627+00:00"}