{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JQ2BF73YHCMNCL4O6W46R6LBFQ","short_pith_number":"pith:JQ2BF73Y","schema_version":"1.0","canonical_sha256":"4c3412ff783898d12f8ef5b9e8f9612c18ecc192f685a5f7774d6017a2ca1fd1","source":{"kind":"arxiv","id":"1612.07762","version":2},"attestation_state":"computed","paper":{"title":"Algebraic Hopf invariants and rational models for mapping spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Felix Wierstra","submitted_at":"2016-12-22T19:28:44Z","abstract_excerpt":"In this paper we will define an invariant $mc_{\\infty}(f)$ of maps $f:X \\rightarrow Y_{\\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\\mathbb{Q}}$. We prove that this invariant is complete, i.e. $mc_{\\infty}(f)=mc_{\\infty}(g)$ if an only if $f$ and $g$ are homotopic. We will also construct an $L_{\\infty}$-model for the based mapping space $Map_*(X,Y_{\\mathbb{Q}})$ from a $C_{\\infty}$-coalgebra and an $L_{\\infty}$-algebra."},"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":"1612.07762","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-12-22T19:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"5eb7ec7f55513bcdfae16d6c64a1ff5e0c7ec07ff5c03d172c10953edeeec29d","abstract_canon_sha256":"845d5c1eab4a86867171b0c869022b6a106946f45753fbde8b3f9af12269d9da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:42.580269Z","signature_b64":"fcKldm7jAWrvHeNL1bswsd2p/JmHfESIGJ07LepwdxLP8+/CqihZKg1lggpEv+j+VFQNsG45RO/1naHW0vVJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c3412ff783898d12f8ef5b9e8f9612c18ecc192f685a5f7774d6017a2ca1fd1","last_reissued_at":"2026-05-17T23:58:42.579822Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:42.579822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Hopf invariants and rational models for mapping spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Felix Wierstra","submitted_at":"2016-12-22T19:28:44Z","abstract_excerpt":"In this paper we will define an invariant $mc_{\\infty}(f)$ of maps $f:X \\rightarrow Y_{\\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\\mathbb{Q}}$. We prove that this invariant is complete, i.e. $mc_{\\infty}(f)=mc_{\\infty}(g)$ if an only if $f$ and $g$ are homotopic. We will also construct an $L_{\\infty}$-model for the based mapping space $Map_*(X,Y_{\\mathbb{Q}})$ from a $C_{\\infty}$-coalgebra and an $L_{\\infty}$-algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07762","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":""},"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":"1612.07762","created_at":"2026-05-17T23:58:42.579883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.07762v2","created_at":"2026-05-17T23:58:42.579883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07762","created_at":"2026-05-17T23:58:42.579883+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQ2BF73YHCMN","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQ2BF73YHCMNCL4O","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQ2BF73Y","created_at":"2026-05-18T12:30:25.849896+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/JQ2BF73YHCMNCL4O6W46R6LBFQ","json":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ.json","graph_json":"https://pith.science/api/pith-number/JQ2BF73YHCMNCL4O6W46R6LBFQ/graph.json","events_json":"https://pith.science/api/pith-number/JQ2BF73YHCMNCL4O6W46R6LBFQ/events.json","paper":"https://pith.science/paper/JQ2BF73Y"},"agent_actions":{"view_html":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ","download_json":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ.json","view_paper":"https://pith.science/paper/JQ2BF73Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.07762&json=true","fetch_graph":"https://pith.science/api/pith-number/JQ2BF73YHCMNCL4O6W46R6LBFQ/graph.json","fetch_events":"https://pith.science/api/pith-number/JQ2BF73YHCMNCL4O6W46R6LBFQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ/action/storage_attestation","attest_author":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ/action/author_attestation","sign_citation":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ/action/citation_signature","submit_replication":"https://pith.science/pith/JQ2BF73YHCMNCL4O6W46R6LBFQ/action/replication_record"}},"created_at":"2026-05-17T23:58:42.579883+00:00","updated_at":"2026-05-17T23:58:42.579883+00:00"}