{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3ITEFUVS5XKCGPPRPSQBDXFGAE","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":"83ab2b10c191047feb86757b8cbcaacf5c74aaea199f463653a97e69066653e9","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-09-18T08:23:33Z","title_canon_sha256":"bad9d8b2e5ba73f7727a4a8cde47a228dbbbdf6ea1a7d6d7daa13d5227a759d2"},"schema_version":"1.0","source":{"id":"2509.14727","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.14727","created_at":"2026-06-30T02:17:09Z"},{"alias_kind":"arxiv_version","alias_value":"2509.14727v3","created_at":"2026-06-30T02:17:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.14727","created_at":"2026-06-30T02:17:09Z"},{"alias_kind":"pith_short_12","alias_value":"3ITEFUVS5XKC","created_at":"2026-06-30T02:17:09Z"},{"alias_kind":"pith_short_16","alias_value":"3ITEFUVS5XKCGPPR","created_at":"2026-06-30T02:17:09Z"},{"alias_kind":"pith_short_8","alias_value":"3ITEFUVS","created_at":"2026-06-30T02:17:09Z"}],"graph_snapshots":[{"event_id":"sha256:637a895826ced1b8074c092a21a4e410478ecbc4f2f96a26fdb8a96d786b0e14","target":"graph","created_at":"2026-06-30T02:17:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.14727/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \\geq 2$) on the complex projective space $\\mathbb{P}(\\mathbb{C}^n)$ modelling the space of pure states of an $n$-level quantum system. The construction can be seen as providing a natural way to isometrically embed any given finite metric space into the space of pure quantum states 'spanned' upon it. In order to show that the maps $d_p$ are indeed distance functions -- in particular, that they satisfy the triangle inequality -- we employ methods of analysis, multilinear algebra and","authors_text":"Rafa{\\l} Bistro\\'n, Tomasz Miller","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-09-18T08:23:33Z","title":"Distances between pure quantum states induced by a distance matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.14727","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:eab5931d722488ad85164d20bfecee7fdf6fe75857318aa912d431407c3055b3","target":"record","created_at":"2026-06-30T02:17:09Z","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":"83ab2b10c191047feb86757b8cbcaacf5c74aaea199f463653a97e69066653e9","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-09-18T08:23:33Z","title_canon_sha256":"bad9d8b2e5ba73f7727a4a8cde47a228dbbbdf6ea1a7d6d7daa13d5227a759d2"},"schema_version":"1.0","source":{"id":"2509.14727","kind":"arxiv","version":3}},"canonical_sha256":"da2642d2b2edd4233df17ca011dca60114ec604bd4fd3542756e64b90755198d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da2642d2b2edd4233df17ca011dca60114ec604bd4fd3542756e64b90755198d","first_computed_at":"2026-06-30T02:17:09.480756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:09.480756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BGXoo/UY3BYB9COLE9BEfuF5nPb4luzMZlSrdYopgIi9hv1PJYSOH5BPt11VY6S3CRYGoN1h4edxPVCOxGl8DQ==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:09.481427Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.14727","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eab5931d722488ad85164d20bfecee7fdf6fe75857318aa912d431407c3055b3","sha256:637a895826ced1b8074c092a21a4e410478ecbc4f2f96a26fdb8a96d786b0e14"],"state_sha256":"06b9db894a147b8aa6cb41991e277a5541ed0626f78575f863d9b44c4483c65c"}