{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F2RGEWC6XYUHAXYMYUSMVNQZ3E","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":"b0acf7fd7be37d4da65949829f4b31e88ab0594ce5ebd3f7a9dd75a0ae77b3d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T12:25:08Z","title_canon_sha256":"99d43d2779f7423c7ecc792a94c09411f69ef877df47130f0ac2ebf9554d68e5"},"schema_version":"1.0","source":{"id":"1304.5928","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5928","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5928v2","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5928","created_at":"2026-05-18T03:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"F2RGEWC6XYUH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F2RGEWC6XYUHAXYM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F2RGEWC6","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:ce4c05f7b54c68052ea2b0eb0a07b39b3540397c268cfc49db3fb5b6dce33b1e","target":"graph","created_at":"2026-05-18T03:02:21Z","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 study the questions of how to recognize when a simplicial set X is of the form X=map(Y,A) for a given space A, and how to recover Y from X, if so. A full answer is provided when A=K(R,n), for $R=\\mathbb{F}_p$ or $\\mathbb{Q}$, in terms of a mapping algebra structure on X (defined in terms of product-preserving simplicial functors out of a certain simplicially-enriched sketch). In addition, when A is a suitable infinite loop space for a suitable connective ring spectrum, we can recover Y from map(Y,A) given such a mapping algebra structure. Most importantly, our methods provide a new way of l","authors_text":"David Blanc, Debasis Sen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T12:25:08Z","title":"Mapping spaces and R-completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5928","kind":"arxiv","version":2},"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":"sha256:7df2e8a1529b640f13bc2075053c03e12e2e0b4353a6c2dd932bbbd3e2bf2cb1","target":"record","created_at":"2026-05-18T03:02:21Z","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":"b0acf7fd7be37d4da65949829f4b31e88ab0594ce5ebd3f7a9dd75a0ae77b3d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-22T12:25:08Z","title_canon_sha256":"99d43d2779f7423c7ecc792a94c09411f69ef877df47130f0ac2ebf9554d68e5"},"schema_version":"1.0","source":{"id":"1304.5928","kind":"arxiv","version":2}},"canonical_sha256":"2ea262585ebe28705f0cc524cab619d90e83bc2a87683c53b743920dace23fb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ea262585ebe28705f0cc524cab619d90e83bc2a87683c53b743920dace23fb6","first_computed_at":"2026-05-18T03:02:21.089789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:21.089789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HpxI/xb0IWXKUTOwN28v4u03XpX3W2jIs4Mak4Ep0IIYXz8QIyDFV7fqAOqYr52rtcqmjh7IhTgPM9f6j9EuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:21.090570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5928","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7df2e8a1529b640f13bc2075053c03e12e2e0b4353a6c2dd932bbbd3e2bf2cb1","sha256:ce4c05f7b54c68052ea2b0eb0a07b39b3540397c268cfc49db3fb5b6dce33b1e"],"state_sha256":"0df2749550e37b2727ef256cdbb69599bb07293ba1dfb4ee08db0dfbf939a232"}