{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NIHFMXE24IVNP5GISMNS5JVF3C","short_pith_number":"pith:NIHFMXE2","schema_version":"1.0","canonical_sha256":"6a0e565c9ae22ad7f4c8931b2ea6a5d89d3a760b7f2becbcd4f0215303f8df79","source":{"kind":"arxiv","id":"1705.09365","version":3},"attestation_state":"computed","paper":{"title":"Four approaches to cohomology theories with reality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"J.P.C. Greenlees","submitted_at":"2017-05-25T21:13:42Z","abstract_excerpt":"We give an account of well known calculations of the RO(Q)-graded coefficient rings of some of the most basic Q-equivariant cohomology theories, where Q is a group of order 2. One purpose is to advertise the effectiveness of the Tate square, showing it has advantages over the slice spectral sequences in algebraically simple cases. A second purpose is to give a single account showing how to translate between the languages of different approaches. [v2 corrects some typos and adds some thanks and references, v3 corrects a few more typos]."},"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":"1705.09365","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-25T21:13:42Z","cross_cats_sorted":[],"title_canon_sha256":"669bb45f9462d15361b5dec822bfe1dd101bbd2e3dc67e341a748b1d465b8191","abstract_canon_sha256":"b507447b88d67b54ead0dd708115ee90c0c6cae3df454a7b483df3e0477a1d60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:20.510885Z","signature_b64":"8Oe0FmD1GzuOylFPaSdY3Rbllh+riXERArxRReKv9vVN6XwvDXfaxzmkmy5fGT0pNcwsW2cOwmoeM60uOGOpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a0e565c9ae22ad7f4c8931b2ea6a5d89d3a760b7f2becbcd4f0215303f8df79","last_reissued_at":"2026-05-18T00:32:20.510382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:20.510382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Four approaches to cohomology theories with reality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"J.P.C. Greenlees","submitted_at":"2017-05-25T21:13:42Z","abstract_excerpt":"We give an account of well known calculations of the RO(Q)-graded coefficient rings of some of the most basic Q-equivariant cohomology theories, where Q is a group of order 2. One purpose is to advertise the effectiveness of the Tate square, showing it has advantages over the slice spectral sequences in algebraically simple cases. A second purpose is to give a single account showing how to translate between the languages of different approaches. [v2 corrects some typos and adds some thanks and references, v3 corrects a few more typos]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09365","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":"1705.09365","created_at":"2026-05-18T00:32:20.510444+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.09365v3","created_at":"2026-05-18T00:32:20.510444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09365","created_at":"2026-05-18T00:32:20.510444+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIHFMXE24IVN","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIHFMXE24IVNP5GI","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIHFMXE2","created_at":"2026-05-18T12:31:31.346846+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/NIHFMXE24IVNP5GISMNS5JVF3C","json":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C.json","graph_json":"https://pith.science/api/pith-number/NIHFMXE24IVNP5GISMNS5JVF3C/graph.json","events_json":"https://pith.science/api/pith-number/NIHFMXE24IVNP5GISMNS5JVF3C/events.json","paper":"https://pith.science/paper/NIHFMXE2"},"agent_actions":{"view_html":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C","download_json":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C.json","view_paper":"https://pith.science/paper/NIHFMXE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.09365&json=true","fetch_graph":"https://pith.science/api/pith-number/NIHFMXE24IVNP5GISMNS5JVF3C/graph.json","fetch_events":"https://pith.science/api/pith-number/NIHFMXE24IVNP5GISMNS5JVF3C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C/action/storage_attestation","attest_author":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C/action/author_attestation","sign_citation":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C/action/citation_signature","submit_replication":"https://pith.science/pith/NIHFMXE24IVNP5GISMNS5JVF3C/action/replication_record"}},"created_at":"2026-05-18T00:32:20.510444+00:00","updated_at":"2026-05-18T00:32:20.510444+00:00"}