{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J43K72CJAWKWXOXF22F3C7W2JD","short_pith_number":"pith:J43K72CJ","canonical_record":{"source":{"id":"1405.5713","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-22T11:22:24Z","cross_cats_sorted":[],"title_canon_sha256":"54bd5c8e2f55e686998eb8a6ed5fe6b00dcbb6d0162bc914f597b28334d9efc3","abstract_canon_sha256":"c2ce319f3e6e018c39c0a6a2ce910cd218a22a374034046e153b2d0582b3cf28"},"schema_version":"1.0"},"canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","source":{"kind":"arxiv","id":"1405.5713","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5713","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5713v4","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5713","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"J43K72CJAWKW","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J43K72CJAWKWXOXF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J43K72CJ","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J43K72CJAWKWXOXF22F3C7W2JD","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5713","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-22T11:22:24Z","cross_cats_sorted":[],"title_canon_sha256":"54bd5c8e2f55e686998eb8a6ed5fe6b00dcbb6d0162bc914f597b28334d9efc3","abstract_canon_sha256":"c2ce319f3e6e018c39c0a6a2ce910cd218a22a374034046e153b2d0582b3cf28"},"schema_version":"1.0"},"canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.479355Z","signature_b64":"XLZiDaLYrzss3KefSiIhEM6Lx1GZrQHnl0eAaYzkEixCryyc84qHd7bwRce43XFhqEf14PXEfdGnt1dIje2XDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","last_reissued_at":"2026-05-18T01:04:30.478765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.478765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5713","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X4jgriyc1Nlsq6JPOxybYT0xUKpJkjTQb1l9m2Vn8aXusXIMrm9TVC7br5CudpAKMBVsluTFCD6lTPRuHYY3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T19:28:18.492408Z"},"content_sha256":"135f04eab449f01e6e019d2cc7464aeec39882270cd2bd52a4b7c198163eef04","schema_version":"1.0","event_id":"sha256:135f04eab449f01e6e019d2cc7464aeec39882270cd2bd52a4b7c198163eef04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J43K72CJAWKWXOXF22F3C7W2JD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral tensor-train decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Allan P. Engsig-Karup, Daniele Bigoni, Youssef M. Marzouk","submitted_at":"2014-05-22T11:22:24Z","abstract_excerpt":"The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results on the convergence of the decomposition, revealing links between the regularity of the function, the dimension of the input space, and the TT ranks. We also show that the regularity of the target function is preserved by the univariate functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5713","kind":"arxiv","version":4},"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":"2026-05-18T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghTvc0cyi9GefbS7z+nFX04waCqMdwq5FyDfNliD6lKN9ERJtpslIE3S/o5wWFG/1t0SUb04FPi6/ukCUJ7NCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T19:28:18.492770Z"},"content_sha256":"d772a028b9a06b15af0af8edf3ce49af0577516c19ade2e09d9f7123297b7a70","schema_version":"1.0","event_id":"sha256:d772a028b9a06b15af0af8edf3ce49af0577516c19ade2e09d9f7123297b7a70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/bundle.json","state_url":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J43K72CJAWKWXOXF22F3C7W2JD/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":"2026-05-20T19:28:18Z","links":{"resolver":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD","bundle":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/bundle.json","state":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J43K72CJAWKWXOXF22F3C7W2JD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J43K72CJAWKWXOXF22F3C7W2JD","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":"c2ce319f3e6e018c39c0a6a2ce910cd218a22a374034046e153b2d0582b3cf28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-22T11:22:24Z","title_canon_sha256":"54bd5c8e2f55e686998eb8a6ed5fe6b00dcbb6d0162bc914f597b28334d9efc3"},"schema_version":"1.0","source":{"id":"1405.5713","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5713","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5713v4","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5713","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"J43K72CJAWKW","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J43K72CJAWKWXOXF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J43K72CJ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d772a028b9a06b15af0af8edf3ce49af0577516c19ade2e09d9f7123297b7a70","target":"graph","created_at":"2026-05-18T01:04:30Z","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":"The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results on the convergence of the decomposition, revealing links between the regularity of the function, the dimension of the input space, and the TT ranks. We also show that the regularity of the target function is preserved by the univariate functions","authors_text":"Allan P. Engsig-Karup, Daniele Bigoni, Youssef M. Marzouk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-22T11:22:24Z","title":"Spectral tensor-train decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5713","kind":"arxiv","version":4},"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":"sha256:135f04eab449f01e6e019d2cc7464aeec39882270cd2bd52a4b7c198163eef04","target":"record","created_at":"2026-05-18T01:04:30Z","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":"c2ce319f3e6e018c39c0a6a2ce910cd218a22a374034046e153b2d0582b3cf28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-22T11:22:24Z","title_canon_sha256":"54bd5c8e2f55e686998eb8a6ed5fe6b00dcbb6d0162bc914f597b28334d9efc3"},"schema_version":"1.0","source":{"id":"1405.5713","kind":"arxiv","version":4}},"canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","first_computed_at":"2026-05-18T01:04:30.478765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:30.478765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLZiDaLYrzss3KefSiIhEM6Lx1GZrQHnl0eAaYzkEixCryyc84qHd7bwRce43XFhqEf14PXEfdGnt1dIje2XDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:30.479355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5713","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:135f04eab449f01e6e019d2cc7464aeec39882270cd2bd52a4b7c198163eef04","sha256:d772a028b9a06b15af0af8edf3ce49af0577516c19ade2e09d9f7123297b7a70"],"state_sha256":"529b7e0ef44ed9dbb2940550e385ad30255b513b0be4ca8159e0985953d97b1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lAwRnBT7AI5yEu3E7YDGNRB0zpXePIUYl64XdMZBo2lgMB/LbuHW09PgwkO9/ULYZAs1zFy1ohExxpZdqdHDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T19:28:18.494926Z","bundle_sha256":"860a61a966ef634a35973f230a55c3fb7b172ab73d0714c99807cfb7c6489eeb"}}