{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:S4FAKUITYMJEFW7MTZIUFSC2VI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1d57b0e75531e36a8c454aea22e3b69343ec237fe62a4c8fb5b771c73da78a15","cross_cats_sorted":["math.AT","math.GN"],"license":"","primary_cat":"math.GT","submitted_at":"2007-01-04T08:15:48Z","title_canon_sha256":"9c1c6ea9723d78db03c751ad568169edf3d668302b6bd842e0a5f55322285c99"},"schema_version":"1.0","source":{"id":"math/0701127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701127","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701127v1","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701127","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"S4FAKUITYMJE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"S4FAKUITYMJEFW7M","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"S4FAKUIT","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:6492cca32b61dc30cfc88e84b9bd521defbbe389159a07650259ea9fea2d707f","target":"graph","created_at":"2026-05-18T02:41:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove the projective plane $\\rp^2$ is an absolute extensor of a finite-dimensional metric space $X$ if and only if the cohomological dimension mod 2 of $X$ does not exceed 1. This solves one of the remaining difficult problems (posed by A.N.Dranishnikov) in extension theory. One of the main tools is the computation of the fundamental group of the function space $\\Map(\\rp^n,\\rp^{n+1})$ (based at inclusion) as being isomorphic to either $\\Z_4$ or $\\Z_2\\oplus\\Z_2$ for $n\\ge 1$. Double surgery and the above fact yield the proof.","authors_text":"Jerzy Dydak, Michael Levin","cross_cats":["math.AT","math.GN"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-01-04T08:15:48Z","title":"Maps to the projective plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701127","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d2cd9771478bfe839175a92861b5bf5d3bdbcd839b3f81d7197b29694914a853","target":"record","created_at":"2026-05-18T02:41:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1d57b0e75531e36a8c454aea22e3b69343ec237fe62a4c8fb5b771c73da78a15","cross_cats_sorted":["math.AT","math.GN"],"license":"","primary_cat":"math.GT","submitted_at":"2007-01-04T08:15:48Z","title_canon_sha256":"9c1c6ea9723d78db03c751ad568169edf3d668302b6bd842e0a5f55322285c99"},"schema_version":"1.0","source":{"id":"math/0701127","kind":"arxiv","version":1}},"canonical_sha256":"970a055113c31242dbec9e5142c85aaa2a0858c33541981003409c75cadf57c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"970a055113c31242dbec9e5142c85aaa2a0858c33541981003409c75cadf57c1","first_computed_at":"2026-05-18T02:41:26.638832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.638832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cf8SAGFmMWFUpNtV+wWFw+M4lcLJfQD9ggT2XAmYP1DMTRRYAfFAT2DQVYA92p1yuAqWWl6TvRu9FvNT6g/1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.639383Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2cd9771478bfe839175a92861b5bf5d3bdbcd839b3f81d7197b29694914a853","sha256:6492cca32b61dc30cfc88e84b9bd521defbbe389159a07650259ea9fea2d707f"],"state_sha256":"686602c71c49990d7634aac91b85bceea460e610e69ac596888d8699bae6a23c"}