{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6BJNFMFRIB4VTX2HPQGOPTKCFN","short_pith_number":"pith:6BJNFMFR","schema_version":"1.0","canonical_sha256":"f052d2b0b1407959df477c0ce7cd422b6093553394bebcaeca4943f6898075a9","source":{"kind":"arxiv","id":"2604.20562","version":2},"attestation_state":"computed","paper":{"title":"Submetry onto one-dimensional space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Euclidean plane and two-dimensional sphere have their equidistant decompositions fully classified.","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Darya Sukhorebska","submitted_at":"2026-04-22T13:43:33Z","abstract_excerpt":"We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2604.20562","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-04-22T13:43:33Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"8a77cdd4896aef8c196ab9d4d224bac4a3ac2a469cd9e7c20149259a889733f8","abstract_canon_sha256":"9bbc9fc135030225d49195e185fb176b092051e1b48678a1befe9af6ef5445e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:14.165390Z","signature_b64":"l+7cPhN1MgoYlfh9mkgJLjTwvr5ybn1YVUrMMxDmLzJFSuR+RNgqveDFPuxLltX5cNyOuwhLqGKJ5kbzptjyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f052d2b0b1407959df477c0ce7cd422b6093553394bebcaeca4943f6898075a9","last_reissued_at":"2026-05-20T01:05:14.164412Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:14.164412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Submetry onto one-dimensional space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Euclidean plane and two-dimensional sphere have their equidistant decompositions fully classified.","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Darya Sukhorebska","submitted_at":"2026-04-22T13:43:33Z","abstract_excerpt":"We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The abstract assumes standard definitions of equidistant decomposition and the usual metrics on the plane and sphere suffice for a complete classification without additional constraints or exceptions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Full classification of equidistant decompositions of the 2D Euclidean plane and 2D sphere is provided.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Euclidean plane and two-dimensional sphere have their equidistant decompositions fully classified.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"752ee493420230e21f0f48c15f8c6475bceee1533977ea1d171b6acd984dcda6"},"source":{"id":"2604.20562","kind":"arxiv","version":2},"verdict":{"id":"12072537-82f0-4a60-afcb-af5d29de1f09","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T21:14:30.308069Z","strongest_claim":"We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere.","one_line_summary":"Full classification of equidistant decompositions of the 2D Euclidean plane and 2D sphere is provided.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The abstract assumes standard definitions of equidistant decomposition and the usual metrics on the plane and sphere suffice for a complete classification without additional constraints or exceptions.","pith_extraction_headline":"The Euclidean plane and two-dimensional sphere have their equidistant decompositions fully classified."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.20562/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":1,"sample":[{"doi":"","year":1982,"title":"[Ban82] V. Bangert. Sets with positive reach.Arch. Math., 38(1):54–57, 1982. [BBI01] D. Burago, Yu. Burago, and S. Ivanov.A Course in Metric Geometry, volume 33 Gradu- ate Studies in Mathematics.A Cou","work_id":"e870f0bd-15bd-48a8-af1a-6e65454ced6a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":1,"snapshot_sha256":"2588787a149c56632eaaddfd0d6667c5d33fd40e68102bcba15677b9ada6cfd4","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6f177a36a402aac090d86e6fab6ece764bc81963f6647ff7b347cc65df76c28c"},"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":"2604.20562","created_at":"2026-05-20T01:05:14.164539+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.20562v2","created_at":"2026-05-20T01:05:14.164539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.20562","created_at":"2026-05-20T01:05:14.164539+00:00"},{"alias_kind":"pith_short_12","alias_value":"6BJNFMFRIB4V","created_at":"2026-05-20T01:05:14.164539+00:00"},{"alias_kind":"pith_short_16","alias_value":"6BJNFMFRIB4VTX2H","created_at":"2026-05-20T01:05:14.164539+00:00"},{"alias_kind":"pith_short_8","alias_value":"6BJNFMFR","created_at":"2026-05-20T01:05:14.164539+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN","json":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN.json","graph_json":"https://pith.science/api/pith-number/6BJNFMFRIB4VTX2HPQGOPTKCFN/graph.json","events_json":"https://pith.science/api/pith-number/6BJNFMFRIB4VTX2HPQGOPTKCFN/events.json","paper":"https://pith.science/paper/6BJNFMFR"},"agent_actions":{"view_html":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN","download_json":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN.json","view_paper":"https://pith.science/paper/6BJNFMFR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.20562&json=true","fetch_graph":"https://pith.science/api/pith-number/6BJNFMFRIB4VTX2HPQGOPTKCFN/graph.json","fetch_events":"https://pith.science/api/pith-number/6BJNFMFRIB4VTX2HPQGOPTKCFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN/action/storage_attestation","attest_author":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN/action/author_attestation","sign_citation":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN/action/citation_signature","submit_replication":"https://pith.science/pith/6BJNFMFRIB4VTX2HPQGOPTKCFN/action/replication_record"}},"created_at":"2026-05-20T01:05:14.164539+00:00","updated_at":"2026-05-20T01:05:14.164539+00:00"}