{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EHT7RBWWB4RGDPZGL4KPDTVWZH","short_pith_number":"pith:EHT7RBWW","schema_version":"1.0","canonical_sha256":"21e7f886d60f2261bf265f14f1ceb6c9f99dee3c81175024628f008086949ce0","source":{"kind":"arxiv","id":"1707.08370","version":1},"attestation_state":"computed","paper":{"title":"High-Dimensional Simplexes for Supermetric Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.IR","authors_text":"Fausto Rabitti, Lucia Vadicamo, Richard Connor","submitted_at":"2017-07-26T10:52:28Z","abstract_excerpt":"In 1953, Blumenthal showed that every semi-metric space that is isometrically embeddable in a Hilbert space has the n-point property; we have previously called such spaces supermetric spaces. Although this is a strictly stronger property than triangle inequality, it is nonetheless closely related and many useful metric spaces possess it. These include Euclidean, Cosine and Jensen-Shannon spaces of any dimension. A simple corollary of the n-point property is that, for any (n+1) objects sampled from the space, there exists an n-dimensional simplex in Euclidean space whose edge lengths correspond"},"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":"1707.08370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IR","submitted_at":"2017-07-26T10:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"053b41e4ac4200658c99ce5f6c12808070fac0ab174f33ee2988746f4458134f","abstract_canon_sha256":"79f8d61e962b3dd3d20921e13b89357700f1b304c20bb181d7172bff135d48a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:24.402520Z","signature_b64":"xy0kweB8KChQeP+TceLsPANDUdrnioD3pf56q691Sal+rJu4tbuNwq90Y9Isd4iS/2Bu87K1aii1lBPHhJ9SBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21e7f886d60f2261bf265f14f1ceb6c9f99dee3c81175024628f008086949ce0","last_reissued_at":"2026-05-18T00:39:24.401841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:24.401841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-Dimensional Simplexes for Supermetric Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.IR","authors_text":"Fausto Rabitti, Lucia Vadicamo, Richard Connor","submitted_at":"2017-07-26T10:52:28Z","abstract_excerpt":"In 1953, Blumenthal showed that every semi-metric space that is isometrically embeddable in a Hilbert space has the n-point property; we have previously called such spaces supermetric spaces. Although this is a strictly stronger property than triangle inequality, it is nonetheless closely related and many useful metric spaces possess it. These include Euclidean, Cosine and Jensen-Shannon spaces of any dimension. A simple corollary of the n-point property is that, for any (n+1) objects sampled from the space, there exists an n-dimensional simplex in Euclidean space whose edge lengths correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08370","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":"1707.08370","created_at":"2026-05-18T00:39:24.401930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.08370v1","created_at":"2026-05-18T00:39:24.401930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08370","created_at":"2026-05-18T00:39:24.401930+00:00"},{"alias_kind":"pith_short_12","alias_value":"EHT7RBWWB4RG","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EHT7RBWWB4RGDPZG","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EHT7RBWW","created_at":"2026-05-18T12:31:12.930513+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/EHT7RBWWB4RGDPZGL4KPDTVWZH","json":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH.json","graph_json":"https://pith.science/api/pith-number/EHT7RBWWB4RGDPZGL4KPDTVWZH/graph.json","events_json":"https://pith.science/api/pith-number/EHT7RBWWB4RGDPZGL4KPDTVWZH/events.json","paper":"https://pith.science/paper/EHT7RBWW"},"agent_actions":{"view_html":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH","download_json":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH.json","view_paper":"https://pith.science/paper/EHT7RBWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.08370&json=true","fetch_graph":"https://pith.science/api/pith-number/EHT7RBWWB4RGDPZGL4KPDTVWZH/graph.json","fetch_events":"https://pith.science/api/pith-number/EHT7RBWWB4RGDPZGL4KPDTVWZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH/action/storage_attestation","attest_author":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH/action/author_attestation","sign_citation":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH/action/citation_signature","submit_replication":"https://pith.science/pith/EHT7RBWWB4RGDPZGL4KPDTVWZH/action/replication_record"}},"created_at":"2026-05-18T00:39:24.401930+00:00","updated_at":"2026-05-18T00:39:24.401930+00:00"}