{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VHPRRTRWVQ2M35426LCZZSKQVX","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":"aecebb5a2bf8f53c02f8b2c0ab25039ead5a4678476cb72f502f7d79353cd525","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-20T01:19:25Z","title_canon_sha256":"d43d2887eda797059bef6faa122e91517746afc0a87afaeb43a4a1e7de3fdd48"},"schema_version":"1.0","source":{"id":"1201.4196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4196","created_at":"2026-05-18T04:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4196v1","created_at":"2026-05-18T04:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4196","created_at":"2026-05-18T04:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"VHPRRTRWVQ2M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VHPRRTRWVQ2M3542","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VHPRRTRW","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:3364dfd4a075710d3ef34ef2272bf960e3e4b68bcdbf69c23b1e994cfcf1e9bf","target":"graph","created_at":"2026-05-18T04:04:07Z","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":"For $d = 2, 3, \\ldots$ and $p \\in [1, \\infty),$ we define a class of representations $\\rho$ of the Leavitt algebra $L_d$ on spaces of the form $L^p (X, \\mu),$ which we call the spatial representations. We prove that for fixed $d$ and $p,$ the Banach algebra ${{\\mathcal{O}}_{d}^{p}}$ obtained as the closure of the image of $L_d$ under the representation $\\rho$ is the same for all spatial representations $\\rho.$ When $p = 2,$ we recover the usual Cuntz algebra ${\\mathcal{O}}_{d}.$ We give a number of equivalent conditions for a representation to be spatial. We show that for distinct $p_1$ and $p","authors_text":"N. Christopher Phillips","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-20T01:19:25Z","title":"Analogs of Cuntz algebras on $L^p$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4196","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":"sha256:4a86875b8e435a855d3beffe9d437cad51b0357006afd193bc1b455bc20e610e","target":"record","created_at":"2026-05-18T04:04:07Z","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":"aecebb5a2bf8f53c02f8b2c0ab25039ead5a4678476cb72f502f7d79353cd525","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-20T01:19:25Z","title_canon_sha256":"d43d2887eda797059bef6faa122e91517746afc0a87afaeb43a4a1e7de3fdd48"},"schema_version":"1.0","source":{"id":"1201.4196","kind":"arxiv","version":1}},"canonical_sha256":"a9df18ce36ac34cdf79af2c59cc950adc7a23ef52a573190296e0f134a41ebe8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9df18ce36ac34cdf79af2c59cc950adc7a23ef52a573190296e0f134a41ebe8","first_computed_at":"2026-05-18T04:04:07.610748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:07.610748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zCE02F+FM68080n/TjvYkIHxCKlAlAnEyQILGu7nqr7+Fpz3M9WLuErw/zWYs+59mfwpTkQjiOwmNfx8jB5yCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:07.611190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a86875b8e435a855d3beffe9d437cad51b0357006afd193bc1b455bc20e610e","sha256:3364dfd4a075710d3ef34ef2272bf960e3e4b68bcdbf69c23b1e994cfcf1e9bf"],"state_sha256":"91521c97596480da4d2e0341ef470915c2314637b1bab863b4a387ff44188d83"}