{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UQTDXMY4PBK4TV7W4THMEFEXVA","short_pith_number":"pith:UQTDXMY4","schema_version":"1.0","canonical_sha256":"a4263bb31c7855c9d7f6e4cec21497a83498674e8e2873d09d539a74e770620f","source":{"kind":"arxiv","id":"1512.06579","version":3},"attestation_state":"computed","paper":{"title":"Assignments for topological group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AT","authors_text":"Augustin-Liviu Mare, Oliver Goertsches","submitted_at":"2015-12-21T11:03:01Z","abstract_excerpt":"A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $p\\in X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility condition is satisfied. The space ${\\mathcal{A}}_T(X)$ of all polynomial assignments has a natural structure of an algebra over the polynomial ring of ${\\rm Lie}(T)$. It is an equivariant homotopy invariant, canonically related to the equivariant cohomology algebra. In this paper we prove various properties of ${\\mathcal{A}}_T(X)$ such as Borel localization, a C"},"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":"1512.06579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-12-21T11:03:01Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"784aa8ede9b551bea4c0b0ac954434a655c62eb1d6ac19815a479f7c133f2cdd","abstract_canon_sha256":"e5c8382ae181b15f0f0982e4d2f7abf60e8c645975c78ce9b8855e99d9578f89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.949444Z","signature_b64":"KvNYrWmNnRx1e/mHU5cegb7BJuf2Kxu6OLiDkwVWcGLqbp1DISDRHeB00NKYWl3QlQlizE29DSuRy0ofA6GrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4263bb31c7855c9d7f6e4cec21497a83498674e8e2873d09d539a74e770620f","last_reissued_at":"2026-05-18T00:20:59.948927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.948927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Assignments for topological group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AT","authors_text":"Augustin-Liviu Mare, Oliver Goertsches","submitted_at":"2015-12-21T11:03:01Z","abstract_excerpt":"A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $p\\in X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility condition is satisfied. The space ${\\mathcal{A}}_T(X)$ of all polynomial assignments has a natural structure of an algebra over the polynomial ring of ${\\rm Lie}(T)$. It is an equivariant homotopy invariant, canonically related to the equivariant cohomology algebra. In this paper we prove various properties of ${\\mathcal{A}}_T(X)$ such as Borel localization, a C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06579","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":"1512.06579","created_at":"2026-05-18T00:20:59.949008+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06579v3","created_at":"2026-05-18T00:20:59.949008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06579","created_at":"2026-05-18T00:20:59.949008+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQTDXMY4PBK4","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQTDXMY4PBK4TV7W","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQTDXMY4","created_at":"2026-05-18T12:29:44.643036+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/UQTDXMY4PBK4TV7W4THMEFEXVA","json":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA.json","graph_json":"https://pith.science/api/pith-number/UQTDXMY4PBK4TV7W4THMEFEXVA/graph.json","events_json":"https://pith.science/api/pith-number/UQTDXMY4PBK4TV7W4THMEFEXVA/events.json","paper":"https://pith.science/paper/UQTDXMY4"},"agent_actions":{"view_html":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA","download_json":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA.json","view_paper":"https://pith.science/paper/UQTDXMY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06579&json=true","fetch_graph":"https://pith.science/api/pith-number/UQTDXMY4PBK4TV7W4THMEFEXVA/graph.json","fetch_events":"https://pith.science/api/pith-number/UQTDXMY4PBK4TV7W4THMEFEXVA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA/action/storage_attestation","attest_author":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA/action/author_attestation","sign_citation":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA/action/citation_signature","submit_replication":"https://pith.science/pith/UQTDXMY4PBK4TV7W4THMEFEXVA/action/replication_record"}},"created_at":"2026-05-18T00:20:59.949008+00:00","updated_at":"2026-05-18T00:20:59.949008+00:00"}