{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ACUVQI7S4KEZ4WDUEY2ZFHZ7PA","short_pith_number":"pith:ACUVQI7S","schema_version":"1.0","canonical_sha256":"00a95823f2e2899e58742635929f3f780a2c2f1694fe38bf149af7239d5b72cc","source":{"kind":"arxiv","id":"1112.0812","version":1},"attestation_state":"computed","paper":{"title":"Computational complexity of topological invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"Manuel Amann","submitted_at":"2011-12-05T00:00:33Z","abstract_excerpt":"We answer the following question posed by Lechuga: Given a simply-connected space $X$ with both $H_*(X,\\qq)$ and $\\pi_*(X)\\otimes \\qq$ being finite-dimensional, what is the computational complexity of an algorithm computing the cup-length and the rational Lusternik--Schnirelmann category of $X$?\n  Basically, by a reduction from the decision problem whether a given graph is $k$-colourable (for $k\\geq 3$) we show that (even stricter versions of the) problems above are $\\mathbf{NP}$-hard."},"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":"1112.0812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-12-05T00:00:33Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"957f5f52e36ebfae21cba2a2a618c6cab930240d4114d0de995bbd8fe29f7069","abstract_canon_sha256":"0604f78d06d5a2cca136216f8a89cd236701984f29d31f5e8be15523e46631ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:57.729801Z","signature_b64":"2K8i0yL7piMTqIDgKoNvM9uSv/nWWWOfbWlxF9bSdgR3gnBTt7VaQC2e2bxk0eYXUt+o1xT3nG+BFiicYvhzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00a95823f2e2899e58742635929f3f780a2c2f1694fe38bf149af7239d5b72cc","last_reissued_at":"2026-05-18T04:06:57.729106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:57.729106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational complexity of topological invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"Manuel Amann","submitted_at":"2011-12-05T00:00:33Z","abstract_excerpt":"We answer the following question posed by Lechuga: Given a simply-connected space $X$ with both $H_*(X,\\qq)$ and $\\pi_*(X)\\otimes \\qq$ being finite-dimensional, what is the computational complexity of an algorithm computing the cup-length and the rational Lusternik--Schnirelmann category of $X$?\n  Basically, by a reduction from the decision problem whether a given graph is $k$-colourable (for $k\\geq 3$) we show that (even stricter versions of the) problems above are $\\mathbf{NP}$-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0812","kind":"arxiv","version":1},"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":"1112.0812","created_at":"2026-05-18T04:06:57.729208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0812v1","created_at":"2026-05-18T04:06:57.729208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0812","created_at":"2026-05-18T04:06:57.729208+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACUVQI7S4KEZ","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACUVQI7S4KEZ4WDU","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACUVQI7S","created_at":"2026-05-18T12:26:24.575870+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/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA","json":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA.json","graph_json":"https://pith.science/api/pith-number/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/graph.json","events_json":"https://pith.science/api/pith-number/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/events.json","paper":"https://pith.science/paper/ACUVQI7S"},"agent_actions":{"view_html":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA","download_json":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA.json","view_paper":"https://pith.science/paper/ACUVQI7S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0812&json=true","fetch_graph":"https://pith.science/api/pith-number/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/graph.json","fetch_events":"https://pith.science/api/pith-number/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/action/storage_attestation","attest_author":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/action/author_attestation","sign_citation":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/action/citation_signature","submit_replication":"https://pith.science/pith/ACUVQI7S4KEZ4WDUEY2ZFHZ7PA/action/replication_record"}},"created_at":"2026-05-18T04:06:57.729208+00:00","updated_at":"2026-05-18T04:06:57.729208+00:00"}