{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ISGDVROXIBGHZEZEO37FT5O3LI","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":"fd510a9a37331dec04a6c6da13bee79456bc6478615b969280eb3e0baf3a5f37","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-17T11:25:06Z","title_canon_sha256":"a5eafce54689ef3095455ea9cb8152e3e5d11f3cd189854eabdf518db729fa4b"},"schema_version":"1.0","source":{"id":"1302.4058","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4058","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4058v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4058","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"ISGDVROXIBGH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"ISGDVROXIBGHZEZE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"ISGDVROX","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:069375fddf607700f30d48edb6cac634c9030042464ce8bc8303b0d0111bbca9","target":"graph","created_at":"2026-05-18T01:26:03Z","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 introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance and Rieffel's proximity by making *-isomorphism a necessary condition for distance zero, while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*-algebras.","authors_text":"Frederic Latremoliere","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-17T11:25:06Z","title":"The Quantum Gromov-Hausdorff Propinquity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4058","kind":"arxiv","version":3},"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":"sha256:2e994f1f715fbd4ff4557086182ac2c5d2fb6daccdffdbec25596f9ca087edfb","target":"record","created_at":"2026-05-18T01:26:03Z","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":"fd510a9a37331dec04a6c6da13bee79456bc6478615b969280eb3e0baf3a5f37","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-17T11:25:06Z","title_canon_sha256":"a5eafce54689ef3095455ea9cb8152e3e5d11f3cd189854eabdf518db729fa4b"},"schema_version":"1.0","source":{"id":"1302.4058","kind":"arxiv","version":3}},"canonical_sha256":"448c3ac5d7404c7c932476fe59f5db5a1469c2a2018af077e278098e81a94bae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"448c3ac5d7404c7c932476fe59f5db5a1469c2a2018af077e278098e81a94bae","first_computed_at":"2026-05-18T01:26:03.230787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:03.230787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8et6yrJbucolaVgoM5AYwqdnQ7fWD70q/APSM3pCvB2hlckSW/IZcuA1SFu8GdGpmTYQR+6u71GIH4U7kCqqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:03.231378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4058","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e994f1f715fbd4ff4557086182ac2c5d2fb6daccdffdbec25596f9ca087edfb","sha256:069375fddf607700f30d48edb6cac634c9030042464ce8bc8303b0d0111bbca9"],"state_sha256":"6cb00c4b2f7daa9d52bb307ee9426848242de93d17713bdcd06ef3efdb99393d"}