{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OQOIOLDFT3B5OS5SS5I43QBUNX","short_pith_number":"pith:OQOIOLDF","schema_version":"1.0","canonical_sha256":"741c872c659ec3d74bb29751cdc0346de1b3e5d694e7222127ee59b53b9e2acb","source":{"kind":"arxiv","id":"1808.06620","version":1},"attestation_state":"computed","paper":{"title":"Cayley graphs and complexity geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Henry W. Lin","submitted_at":"2018-08-20T18:00:09Z","abstract_excerpt":"The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of the unitary group, we observe that this idea can be made rigorous: the complexity geometry becomes what is known as a Cayley graph. This connection allows us to translate results from the geometrical group theory literature into statements about complexity. For example, the notion of $\\delta$-hyperbolicity makes precise the idea that complexity geometry is "},"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":"1808.06620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-20T18:00:09Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"8bde130d79f2e40a2d9586cbe4ca49e77c62a8ce5279b8c0de464103c315ed4e","abstract_canon_sha256":"c92dd16b869d36c7dc5884f0a8527be0a8c6380e09e54ef9c481be014677b897"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:42.177560Z","signature_b64":"2vBBh/5hO/k38EecaKqckpgqyGnj3iBpQ6lR/VruiYrvJFlzsZgrhNqmD/3Jkux12X2fODObhfbiA3qAFOvjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"741c872c659ec3d74bb29751cdc0346de1b3e5d694e7222127ee59b53b9e2acb","last_reissued_at":"2026-05-17T23:53:42.177067Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:42.177067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cayley graphs and complexity geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Henry W. Lin","submitted_at":"2018-08-20T18:00:09Z","abstract_excerpt":"The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of the unitary group, we observe that this idea can be made rigorous: the complexity geometry becomes what is known as a Cayley graph. This connection allows us to translate results from the geometrical group theory literature into statements about complexity. For example, the notion of $\\delta$-hyperbolicity makes precise the idea that complexity geometry is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06620","kind":"arxiv","version":1},"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":"1808.06620","created_at":"2026-05-17T23:53:42.177130+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.06620v1","created_at":"2026-05-17T23:53:42.177130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06620","created_at":"2026-05-17T23:53:42.177130+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQOIOLDFT3B5","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQOIOLDFT3B5OS5S","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQOIOLDF","created_at":"2026-05-18T12:32:43.782077+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/OQOIOLDFT3B5OS5SS5I43QBUNX","json":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX.json","graph_json":"https://pith.science/api/pith-number/OQOIOLDFT3B5OS5SS5I43QBUNX/graph.json","events_json":"https://pith.science/api/pith-number/OQOIOLDFT3B5OS5SS5I43QBUNX/events.json","paper":"https://pith.science/paper/OQOIOLDF"},"agent_actions":{"view_html":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX","download_json":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX.json","view_paper":"https://pith.science/paper/OQOIOLDF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.06620&json=true","fetch_graph":"https://pith.science/api/pith-number/OQOIOLDFT3B5OS5SS5I43QBUNX/graph.json","fetch_events":"https://pith.science/api/pith-number/OQOIOLDFT3B5OS5SS5I43QBUNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX/action/storage_attestation","attest_author":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX/action/author_attestation","sign_citation":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX/action/citation_signature","submit_replication":"https://pith.science/pith/OQOIOLDFT3B5OS5SS5I43QBUNX/action/replication_record"}},"created_at":"2026-05-17T23:53:42.177130+00:00","updated_at":"2026-05-17T23:53:42.177130+00:00"}