{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:MQZ74MZYZV7KZDNHDHIQWGO4FN","short_pith_number":"pith:MQZ74MZY","schema_version":"1.0","canonical_sha256":"6433fe3338cd7eac8da719d10b19dc2b41ec2c7f0782ec7c310e34934ff73809","source":{"kind":"arxiv","id":"math/0703673","version":3},"attestation_state":"computed","paper":{"title":"Strong Singularity for Subfactors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Alan Wiggins, Pinhas Grossman","submitted_at":"2007-03-22T17:14:34Z","abstract_excerpt":"We examine the notion of $\\alpha$-strong singularity for subfactors of a \\IIi factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its unitary conjugate. Through planar algebra techniques, we demonstrate the existence of a finite index singular subfactor of the hyperfinite \\IIi factor that cannot be strongly singular with $\\alpha=1$, in contrast to the case for masas. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant $0<c<1$ such that all singular subfact"},"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":"math/0703673","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2007-03-22T17:14:34Z","cross_cats_sorted":[],"title_canon_sha256":"7943f17f81190b14101ab162099562fe2c270ff16d2bd07c28a27aeb6d2820d6","abstract_canon_sha256":"d1b3771590db748449a12e473795ce04d6b6cb29e1067c450c2735331094e1bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.190752Z","signature_b64":"qv1uaXfnamMdccAiygTF6dnDMmBMss/Qez5NS3ukjDDLO+xCuNcqsWRN/d2Gd0tCQjTkdJR4e8rTfnXdRQcsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6433fe3338cd7eac8da719d10b19dc2b41ec2c7f0782ec7c310e34934ff73809","last_reissued_at":"2026-05-18T02:57:45.190379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.190379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Singularity for Subfactors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Alan Wiggins, Pinhas Grossman","submitted_at":"2007-03-22T17:14:34Z","abstract_excerpt":"We examine the notion of $\\alpha$-strong singularity for subfactors of a \\IIi factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its unitary conjugate. Through planar algebra techniques, we demonstrate the existence of a finite index singular subfactor of the hyperfinite \\IIi factor that cannot be strongly singular with $\\alpha=1$, in contrast to the case for masas. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant $0<c<1$ such that all singular subfact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703673","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":"math/0703673","created_at":"2026-05-18T02:57:45.190435+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0703673v3","created_at":"2026-05-18T02:57:45.190435+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703673","created_at":"2026-05-18T02:57:45.190435+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQZ74MZYZV7K","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQZ74MZYZV7KZDNH","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQZ74MZY","created_at":"2026-05-18T12:25:55.427421+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/MQZ74MZYZV7KZDNHDHIQWGO4FN","json":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN.json","graph_json":"https://pith.science/api/pith-number/MQZ74MZYZV7KZDNHDHIQWGO4FN/graph.json","events_json":"https://pith.science/api/pith-number/MQZ74MZYZV7KZDNHDHIQWGO4FN/events.json","paper":"https://pith.science/paper/MQZ74MZY"},"agent_actions":{"view_html":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN","download_json":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN.json","view_paper":"https://pith.science/paper/MQZ74MZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0703673&json=true","fetch_graph":"https://pith.science/api/pith-number/MQZ74MZYZV7KZDNHDHIQWGO4FN/graph.json","fetch_events":"https://pith.science/api/pith-number/MQZ74MZYZV7KZDNHDHIQWGO4FN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN/action/storage_attestation","attest_author":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN/action/author_attestation","sign_citation":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN/action/citation_signature","submit_replication":"https://pith.science/pith/MQZ74MZYZV7KZDNHDHIQWGO4FN/action/replication_record"}},"created_at":"2026-05-18T02:57:45.190435+00:00","updated_at":"2026-05-18T02:57:45.190435+00:00"}