{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DOYJ2OLGFMW4DZFECH6B2DHTWE","short_pith_number":"pith:DOYJ2OLG","canonical_record":{"source":{"id":"1507.05114","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-15T21:56:19Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2ea2e654b269bf3914b4a9d67a5dfea47d0037b6bb2090860ce05476ed4fb17e","abstract_canon_sha256":"8482e3b08f23143a934cd994aed751741c0ef6675ed861e521cf2398fdf65dc0"},"schema_version":"1.0"},"canonical_sha256":"1bb09d39662b2dc1e4a411fc1d0cf3b10614b6ecef66bba2686b446f249c1df2","source":{"kind":"arxiv","id":"1507.05114","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05114","created_at":"2026-05-18T01:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05114v2","created_at":"2026-05-18T01:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05114","created_at":"2026-05-18T01:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"DOYJ2OLGFMW4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DOYJ2OLGFMW4DZFE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DOYJ2OLG","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DOYJ2OLGFMW4DZFECH6B2DHTWE","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05114","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-15T21:56:19Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2ea2e654b269bf3914b4a9d67a5dfea47d0037b6bb2090860ce05476ed4fb17e","abstract_canon_sha256":"8482e3b08f23143a934cd994aed751741c0ef6675ed861e521cf2398fdf65dc0"},"schema_version":"1.0"},"canonical_sha256":"1bb09d39662b2dc1e4a411fc1d0cf3b10614b6ecef66bba2686b446f249c1df2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:52.704234Z","signature_b64":"BM3onnHVLhJOQnxpvFStuPedV/xh4XnjknW3dlnrfveaX8u7jGtxPw4gUuxr6MNjKWQsRU9qCdseRD1jcUm9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bb09d39662b2dc1e4a411fc1d0cf3b10614b6ecef66bba2686b446f249c1df2","last_reissued_at":"2026-05-18T01:17:52.703624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:52.703624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05114","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPwWh9ZDslqsnMO+IvZ1Vjf2LilN9S7M9JNYjvPHWPmMLVV5WOIPoeL/iUinH52cJzwhLi1I4JON3d98K6qwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:43:57.119359Z"},"content_sha256":"d766b69db6862cc9014b505b31e2667bc6354daf3bd8d6b5c4efe7e4b5b018fb","schema_version":"1.0","event_id":"sha256:d766b69db6862cc9014b505b31e2667bc6354daf3bd8d6b5c4efe7e4b5b018fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DOYJ2OLGFMW4DZFECH6B2DHTWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Is it possible to determine a point lying in a simplex if we know the distances from the vertices?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","submitted_at":"2015-07-15T21:56:19Z","abstract_excerpt":"It is an elementary fact that if we fix an arbitrary set of $d+1$ affine independent points $\\{p_0,\\dots p_d\\}$ in $\\mathbb{R}^d$, then the Euclidean distances $\\{|x-p_j|\\}_{j=0}^d$ determine the point $x$ in $\\mathbb{R}^d$ uniquely. In this paper we investigate a similar problem in general normed spaces which is motivated by this known fact. Namely, we characterize those, at least $d$-dimensional, real normed spaces $(X, \\|\\cdot\\|)$ such that for every set of $d+1$ affine independent points $\\{p_0,\\dots p_d\\} \\subset X$, the distances $\\{\\|x-p_j\\|\\}_{j=0}^d$ determines the point $x$ lying in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05114","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/eTJeJwn4ShP0NaS1PKJetido53ShpksnTRBBD+BOLIe3dBlnvuajaV6W1iG700nhE3pOXt5RjOF9I2FmHqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:43:57.119726Z"},"content_sha256":"89dbe74d5be936189be7a479e1bb3fb84c6bdbc70659c210c8635fc6f2a923e6","schema_version":"1.0","event_id":"sha256:89dbe74d5be936189be7a479e1bb3fb84c6bdbc70659c210c8635fc6f2a923e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE/bundle.json","state_url":"https://pith.science/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T18:43:57Z","links":{"resolver":"https://pith.science/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE","bundle":"https://pith.science/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE/bundle.json","state":"https://pith.science/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOYJ2OLGFMW4DZFECH6B2DHTWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DOYJ2OLGFMW4DZFECH6B2DHTWE","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":"8482e3b08f23143a934cd994aed751741c0ef6675ed861e521cf2398fdf65dc0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-15T21:56:19Z","title_canon_sha256":"2ea2e654b269bf3914b4a9d67a5dfea47d0037b6bb2090860ce05476ed4fb17e"},"schema_version":"1.0","source":{"id":"1507.05114","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05114","created_at":"2026-05-18T01:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05114v2","created_at":"2026-05-18T01:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05114","created_at":"2026-05-18T01:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"DOYJ2OLGFMW4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DOYJ2OLGFMW4DZFE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DOYJ2OLG","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:89dbe74d5be936189be7a479e1bb3fb84c6bdbc70659c210c8635fc6f2a923e6","target":"graph","created_at":"2026-05-18T01:17:52Z","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"},"paper":{"abstract_excerpt":"It is an elementary fact that if we fix an arbitrary set of $d+1$ affine independent points $\\{p_0,\\dots p_d\\}$ in $\\mathbb{R}^d$, then the Euclidean distances $\\{|x-p_j|\\}_{j=0}^d$ determine the point $x$ in $\\mathbb{R}^d$ uniquely. In this paper we investigate a similar problem in general normed spaces which is motivated by this known fact. Namely, we characterize those, at least $d$-dimensional, real normed spaces $(X, \\|\\cdot\\|)$ such that for every set of $d+1$ affine independent points $\\{p_0,\\dots p_d\\} \\subset X$, the distances $\\{\\|x-p_j\\|\\}_{j=0}^d$ determines the point $x$ lying in ","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-15T21:56:19Z","title":"Is it possible to determine a point lying in a simplex if we know the distances from the vertices?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05114","kind":"arxiv","version":2},"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:d766b69db6862cc9014b505b31e2667bc6354daf3bd8d6b5c4efe7e4b5b018fb","target":"record","created_at":"2026-05-18T01:17:52Z","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":"8482e3b08f23143a934cd994aed751741c0ef6675ed861e521cf2398fdf65dc0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-15T21:56:19Z","title_canon_sha256":"2ea2e654b269bf3914b4a9d67a5dfea47d0037b6bb2090860ce05476ed4fb17e"},"schema_version":"1.0","source":{"id":"1507.05114","kind":"arxiv","version":2}},"canonical_sha256":"1bb09d39662b2dc1e4a411fc1d0cf3b10614b6ecef66bba2686b446f249c1df2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bb09d39662b2dc1e4a411fc1d0cf3b10614b6ecef66bba2686b446f249c1df2","first_computed_at":"2026-05-18T01:17:52.703624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:52.703624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BM3onnHVLhJOQnxpvFStuPedV/xh4XnjknW3dlnrfveaX8u7jGtxPw4gUuxr6MNjKWQsRU9qCdseRD1jcUm9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:52.704234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05114","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d766b69db6862cc9014b505b31e2667bc6354daf3bd8d6b5c4efe7e4b5b018fb","sha256:89dbe74d5be936189be7a479e1bb3fb84c6bdbc70659c210c8635fc6f2a923e6"],"state_sha256":"6e43da0880a7c93c5781802d474b814d843a7333d698b103eaa1ff595f5cbe0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSzRGFG5cSDodNa5/LPoyfs6l+7A1MkqtXkJyAC5PEF4Ice9tYlYo5uHC7UpedcKxHbVuuZuxlCIxX8aO1FrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:43:57.121821Z","bundle_sha256":"8a8258aa511c999bd67cdd9d75c49ebdb74feaead94596558e8515195f568783"}}