{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DQ22RYMYRPJQRZ3S2PNBOST37C","short_pith_number":"pith:DQ22RYMY","schema_version":"1.0","canonical_sha256":"1c35a8e1988bd308e772d3da174a7bf89e0ff2f08014fb68e36fb37479e909ec","source":{"kind":"arxiv","id":"1403.7501","version":3},"attestation_state":"computed","paper":{"title":"Adams filtration and generalized Hurewicz maps for infinite loopspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nicholas J. Kuhn","submitted_at":"2014-03-28T19:22:13Z","abstract_excerpt":"We study the Hurewicz map h from the homotopy groups of a spectrum X to the R-homology of its 0th space X(0), where R is a connective commutative S-algebra.\n  We prove that the decreasing filtration of the domain of h associated to an R-based Adams resolution is compatible with the augmentation ideal filtration of the range associated to the suspension spectrum of X(0)_+, an augmented commutative S-algebra. The proof makes use of the interplay of this filtration with Topological Andre Quillen Homology.\n  An application is a Connectivity Theorem: Localize at a prime p and suppose X is (c-1)-con"},"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":"1403.7501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-28T19:22:13Z","cross_cats_sorted":[],"title_canon_sha256":"80726d8230ac934bfa5867208e680dc3d88fa178b83eb5f08418ebd0a83a0168","abstract_canon_sha256":"31b2f21c1eeae20e7b96e549f0994b2b55120d361b984c79172415d4fbcd06a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:41.886443Z","signature_b64":"yfKZe1wb5rxQqS9Jz9Bkfk9aq7mA/yQsZf+iG34faYbxKGsxuaiLS08Mf4WWd34VJRr8dwFtlKP7ApaW4X2YCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c35a8e1988bd308e772d3da174a7bf89e0ff2f08014fb68e36fb37479e909ec","last_reissued_at":"2026-05-18T00:10:41.885744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:41.885744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adams filtration and generalized Hurewicz maps for infinite loopspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nicholas J. Kuhn","submitted_at":"2014-03-28T19:22:13Z","abstract_excerpt":"We study the Hurewicz map h from the homotopy groups of a spectrum X to the R-homology of its 0th space X(0), where R is a connective commutative S-algebra.\n  We prove that the decreasing filtration of the domain of h associated to an R-based Adams resolution is compatible with the augmentation ideal filtration of the range associated to the suspension spectrum of X(0)_+, an augmented commutative S-algebra. The proof makes use of the interplay of this filtration with Topological Andre Quillen Homology.\n  An application is a Connectivity Theorem: Localize at a prime p and suppose X is (c-1)-con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7501","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1403.7501","created_at":"2026-05-18T00:10:41.885848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7501v3","created_at":"2026-05-18T00:10:41.885848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7501","created_at":"2026-05-18T00:10:41.885848+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQ22RYMYRPJQ","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQ22RYMYRPJQRZ3S","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQ22RYMY","created_at":"2026-05-18T12:28:25.294606+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/DQ22RYMYRPJQRZ3S2PNBOST37C","json":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C.json","graph_json":"https://pith.science/api/pith-number/DQ22RYMYRPJQRZ3S2PNBOST37C/graph.json","events_json":"https://pith.science/api/pith-number/DQ22RYMYRPJQRZ3S2PNBOST37C/events.json","paper":"https://pith.science/paper/DQ22RYMY"},"agent_actions":{"view_html":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C","download_json":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C.json","view_paper":"https://pith.science/paper/DQ22RYMY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7501&json=true","fetch_graph":"https://pith.science/api/pith-number/DQ22RYMYRPJQRZ3S2PNBOST37C/graph.json","fetch_events":"https://pith.science/api/pith-number/DQ22RYMYRPJQRZ3S2PNBOST37C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C/action/storage_attestation","attest_author":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C/action/author_attestation","sign_citation":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C/action/citation_signature","submit_replication":"https://pith.science/pith/DQ22RYMYRPJQRZ3S2PNBOST37C/action/replication_record"}},"created_at":"2026-05-18T00:10:41.885848+00:00","updated_at":"2026-05-18T00:10:41.885848+00:00"}