{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YIHDXMXNEDDQL7TIHO7GFB4TY2","short_pith_number":"pith:YIHDXMXN","canonical_record":{"source":{"id":"1309.0938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-04T08:08:37Z","cross_cats_sorted":[],"title_canon_sha256":"b4c309b386737ec41809289679a06d04d539f09e0798650b2c1a29017ee79cd9","abstract_canon_sha256":"96c94e8d4b3c094945ffb4bfeae1ceb9bc81ed481d21f5cc2a5209ffec2f2a61"},"schema_version":"1.0"},"canonical_sha256":"c20e3bb2ed20c705fe683bbe628793c6a8f581f376c287d08e9b4183b47fc162","source":{"kind":"arxiv","id":"1309.0938","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0938","created_at":"2026-05-18T03:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0938v1","created_at":"2026-05-18T03:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0938","created_at":"2026-05-18T03:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"YIHDXMXNEDDQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YIHDXMXNEDDQL7TI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YIHDXMXN","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YIHDXMXNEDDQL7TIHO7GFB4TY2","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-04T08:08:37Z","cross_cats_sorted":[],"title_canon_sha256":"b4c309b386737ec41809289679a06d04d539f09e0798650b2c1a29017ee79cd9","abstract_canon_sha256":"96c94e8d4b3c094945ffb4bfeae1ceb9bc81ed481d21f5cc2a5209ffec2f2a61"},"schema_version":"1.0"},"canonical_sha256":"c20e3bb2ed20c705fe683bbe628793c6a8f581f376c287d08e9b4183b47fc162","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:16.395432Z","signature_b64":"qPN39jlKcdptBxXcWbpMCuul8SvmB/PhxTAhNapl9T8cEn7PIVNbjqeyDjyG4Se7ZKQCKT3UfnRcSeV8iXVIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c20e3bb2ed20c705fe683bbe628793c6a8f581f376c287d08e9b4183b47fc162","last_reissued_at":"2026-05-18T03:14:16.394860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:16.394860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0938","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9KXWi2jkteJDMlcwgX4m7KDmCDBK2nYnHWIy8CEjcCwyngzzugIcVw4rZUQu5W+gfzU1hwxS+Wb2LoxAE6LzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:03:19.860215Z"},"content_sha256":"fee7182ee28c3bcb5f1f21ec1b2b67496192e796e0e1957a66c522c85cc676c8","schema_version":"1.0","event_id":"sha256:fee7182ee28c3bcb5f1f21ec1b2b67496192e796e0e1957a66c522c85cc676c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YIHDXMXNEDDQL7TIHO7GFB4TY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension elevation in Muntz spaces: A new emergence of the Muntz condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rachid Ait-Haddou","submitted_at":"2013-09-04T08:08:37Z","abstract_excerpt":"We show that the limiting polygon generated by the dimension elevation algorithm with respect to the \\muntz space $span(1,t^{r_1},t^{r_2},...,t^{r_m},...)$, with $0 < r_1 < r_2 < ... < r_m < ...$ and $\\lim_{n\\to\\infty}r_n = \\infty$, over an interval $[a,b]\\subset]0,\\infty[$ converges to the underlying Chebyshev-B\\'ezier curve if and only if the \\muntz condition $\\sum_{i=1}^{\\infty} \\frac{1}{r_i} = \\infty$ is satisfied. The surprising emergence of the \\muntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0938","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mol/2U1iXizM3D3FMX0wmQnQOmpNi0Y2VPYpL55ITJ2NVsZhcp5f+jKj3+7r2Tvct+OMTvlgt7jE6cC8hvzMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:03:19.860575Z"},"content_sha256":"f1d9a3b93bfac82f27ef738e55fec0fd69ac1d738a64ad7492b43431cf4d965a","schema_version":"1.0","event_id":"sha256:f1d9a3b93bfac82f27ef738e55fec0fd69ac1d738a64ad7492b43431cf4d965a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2/bundle.json","state_url":"https://pith.science/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2/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":"2026-06-22T14:03:19Z","links":{"resolver":"https://pith.science/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2","bundle":"https://pith.science/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2/bundle.json","state":"https://pith.science/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIHDXMXNEDDQL7TIHO7GFB4TY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YIHDXMXNEDDQL7TIHO7GFB4TY2","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":"96c94e8d4b3c094945ffb4bfeae1ceb9bc81ed481d21f5cc2a5209ffec2f2a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-04T08:08:37Z","title_canon_sha256":"b4c309b386737ec41809289679a06d04d539f09e0798650b2c1a29017ee79cd9"},"schema_version":"1.0","source":{"id":"1309.0938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0938","created_at":"2026-05-18T03:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0938v1","created_at":"2026-05-18T03:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0938","created_at":"2026-05-18T03:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"YIHDXMXNEDDQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YIHDXMXNEDDQL7TI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YIHDXMXN","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f1d9a3b93bfac82f27ef738e55fec0fd69ac1d738a64ad7492b43431cf4d965a","target":"graph","created_at":"2026-05-18T03:14:16Z","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":"We show that the limiting polygon generated by the dimension elevation algorithm with respect to the \\muntz space $span(1,t^{r_1},t^{r_2},...,t^{r_m},...)$, with $0 < r_1 < r_2 < ... < r_m < ...$ and $\\lim_{n\\to\\infty}r_n = \\infty$, over an interval $[a,b]\\subset]0,\\infty[$ converges to the underlying Chebyshev-B\\'ezier curve if and only if the \\muntz condition $\\sum_{i=1}^{\\infty} \\frac{1}{r_i} = \\infty$ is satisfied. The surprising emergence of the \\muntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the con","authors_text":"Rachid Ait-Haddou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-04T08:08:37Z","title":"Dimension elevation in Muntz spaces: A new emergence of the Muntz condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0938","kind":"arxiv","version":1},"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:fee7182ee28c3bcb5f1f21ec1b2b67496192e796e0e1957a66c522c85cc676c8","target":"record","created_at":"2026-05-18T03:14:16Z","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":"96c94e8d4b3c094945ffb4bfeae1ceb9bc81ed481d21f5cc2a5209ffec2f2a61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-04T08:08:37Z","title_canon_sha256":"b4c309b386737ec41809289679a06d04d539f09e0798650b2c1a29017ee79cd9"},"schema_version":"1.0","source":{"id":"1309.0938","kind":"arxiv","version":1}},"canonical_sha256":"c20e3bb2ed20c705fe683bbe628793c6a8f581f376c287d08e9b4183b47fc162","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c20e3bb2ed20c705fe683bbe628793c6a8f581f376c287d08e9b4183b47fc162","first_computed_at":"2026-05-18T03:14:16.394860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:16.394860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPN39jlKcdptBxXcWbpMCuul8SvmB/PhxTAhNapl9T8cEn7PIVNbjqeyDjyG4Se7ZKQCKT3UfnRcSeV8iXVIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:16.395432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fee7182ee28c3bcb5f1f21ec1b2b67496192e796e0e1957a66c522c85cc676c8","sha256:f1d9a3b93bfac82f27ef738e55fec0fd69ac1d738a64ad7492b43431cf4d965a"],"state_sha256":"0ce21ce5bc527911bc5faa742096ea91b68b2bc8031ca36ea85949d1ce5ddd13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"De/hp0kKVbPKhjonbSHz3h2RLpHGwyGqI8miSENxl4wMMGrdi/R/LanNbGr2v4/h97glVLtHK8L/xcxHb5UeBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:03:19.862439Z","bundle_sha256":"81260121f35aae0323ba2b5009ed0bb5ac74fb80be0f5d4eebe88ec1cea6ce00"}}