{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CSRYQTPBUHA25BLXFZB3DPSUAL","short_pith_number":"pith:CSRYQTPB","schema_version":"1.0","canonical_sha256":"14a3884de1a1c1ae85772e43b1be5402dcabf398a3036fffd5057fe2686326c4","source":{"kind":"arxiv","id":"2605.19243","version":1},"attestation_state":"computed","paper":{"title":"Euclidean Embedding of Data Using Local Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CG"],"primary_cat":"cs.LG","authors_text":"Dimitris Arabadjis","submitted_at":"2026-05-19T01:31:53Z","abstract_excerpt":"We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph weighted by pairwise distances, without requiring any prior vector representation of the data. The embedding is obtained by solving a variational problem that matches local, on-graph distances to the Euclidean metric, induced by the differentials of the embedding functions. The resulting Euler-Lagrange equations are derived in a coordinate-free form, enabling dir"},"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":"2605.19243","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T01:31:53Z","cross_cats_sorted":["cs.AI","cs.CG"],"title_canon_sha256":"6ed5806a95b84d999a75d2238aabe2e566cec93684c027a0fd973c417820df81","abstract_canon_sha256":"d071e90b9cae580049634b89e262a97a1833afb7f6c3c8a69eef83e1f88d661f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:35.555762Z","signature_b64":"ZUsWFntHac9HWj0EZzxCnedVkelHiASsLIsM6Inc+VBK/xGCASVlJpkTID2ZjpHLX/QZrDu6IRQvZVcfesGJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14a3884de1a1c1ae85772e43b1be5402dcabf398a3036fffd5057fe2686326c4","last_reissued_at":"2026-05-20T01:05:35.554953Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:35.554953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Euclidean Embedding of Data Using Local Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CG"],"primary_cat":"cs.LG","authors_text":"Dimitris Arabadjis","submitted_at":"2026-05-19T01:31:53Z","abstract_excerpt":"We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph weighted by pairwise distances, without requiring any prior vector representation of the data. The embedding is obtained by solving a variational problem that matches local, on-graph distances to the Euclidean metric, induced by the differentials of the embedding functions. The resulting Euler-Lagrange equations are derived in a coordinate-free form, enabling dir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19243","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19243/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.19243","created_at":"2026-05-20T01:05:35.555076+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.19243v1","created_at":"2026-05-20T01:05:35.555076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19243","created_at":"2026-05-20T01:05:35.555076+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSRYQTPBUHA2","created_at":"2026-05-20T01:05:35.555076+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSRYQTPBUHA25BLX","created_at":"2026-05-20T01:05:35.555076+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSRYQTPB","created_at":"2026-05-20T01:05:35.555076+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/CSRYQTPBUHA25BLXFZB3DPSUAL","json":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL.json","graph_json":"https://pith.science/api/pith-number/CSRYQTPBUHA25BLXFZB3DPSUAL/graph.json","events_json":"https://pith.science/api/pith-number/CSRYQTPBUHA25BLXFZB3DPSUAL/events.json","paper":"https://pith.science/paper/CSRYQTPB"},"agent_actions":{"view_html":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL","download_json":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL.json","view_paper":"https://pith.science/paper/CSRYQTPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.19243&json=true","fetch_graph":"https://pith.science/api/pith-number/CSRYQTPBUHA25BLXFZB3DPSUAL/graph.json","fetch_events":"https://pith.science/api/pith-number/CSRYQTPBUHA25BLXFZB3DPSUAL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL/action/storage_attestation","attest_author":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL/action/author_attestation","sign_citation":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL/action/citation_signature","submit_replication":"https://pith.science/pith/CSRYQTPBUHA25BLXFZB3DPSUAL/action/replication_record"}},"created_at":"2026-05-20T01:05:35.555076+00:00","updated_at":"2026-05-20T01:05:35.555076+00:00"}