{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RWDJBTTNBQ7WVIRGOJL2DWVISU","short_pith_number":"pith:RWDJBTTN","canonical_record":{"source":{"id":"2408.05677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-11T02:58:28Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"71efeea36f1495d72dc1a89e5afeb23994ef8c042630e86e7a5893db8661b765","abstract_canon_sha256":"faa034f2167259f7095cd6cd0aed7737e90c88fcd4c3fa72d3b6f7fc900ab760"},"schema_version":"1.0"},"canonical_sha256":"8d8690ce6d0c3f6aa2267257a1daa895388bd734bd597efafe3487bed1a40f72","source":{"kind":"arxiv","id":"2408.05677","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.05677","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"arxiv_version","alias_value":"2408.05677v1","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.05677","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"pith_short_12","alias_value":"RWDJBTTNBQ7W","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"pith_short_16","alias_value":"RWDJBTTNBQ7WVIRG","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"pith_short_8","alias_value":"RWDJBTTN","created_at":"2026-07-05T08:54:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RWDJBTTNBQ7WVIRGOJL2DWVISU","target":"record","payload":{"canonical_record":{"source":{"id":"2408.05677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-11T02:58:28Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"71efeea36f1495d72dc1a89e5afeb23994ef8c042630e86e7a5893db8661b765","abstract_canon_sha256":"faa034f2167259f7095cd6cd0aed7737e90c88fcd4c3fa72d3b6f7fc900ab760"},"schema_version":"1.0"},"canonical_sha256":"8d8690ce6d0c3f6aa2267257a1daa895388bd734bd597efafe3487bed1a40f72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:54:23.494709Z","signature_b64":"fG8Sm0K3eyFyAtC0ir5MBpjvViajDfNCm3p3LFPeSYbxfsuCd6z558R0a/iOLHYgsZn0ttedhUf/T6hOU29UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8690ce6d0c3f6aa2267257a1daa895388bd734bd597efafe3487bed1a40f72","last_reissued_at":"2026-07-05T08:54:23.494293Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:54:23.494293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.05677","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":"2026-07-05T08:54:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmPX1wJiBhGeTcS1noaESNzlqWhR3MWtShy+sfIdVbmi+n41/GQ6eYRN6HfPPQPlRKSd6m05CAMUnJbA1AW0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T21:39:44.182131Z"},"content_sha256":"8fffefa61c2f21c46a048b4ffff21e9e330049c1a0fd00f94c899919cde2e76f","schema_version":"1.0","event_id":"sha256:8fffefa61c2f21c46a048b4ffff21e9e330049c1a0fd00f94c899919cde2e76f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RWDJBTTNBQ7WVIRGOJL2DWVISU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Alex H. Williams, Anru R. Zhang, Brett W. Larsen, Tamara G. Kolda","submitted_at":"2024-08-11T02:58:28Z","abstract_excerpt":"The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions (infinite-dimensional vectors) from a reproducing kernel Hilbert space (RKHS). We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition. An advantage of CP-HiFi is that it can enforce smoothness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05677","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/2408.05677/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:54:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdXhrqp03DDgKniREtmOakxNH2r3jE6TpKdXRc/PO4SJMr+5uShoFEraCtRwO2wtjqybv9rkgSLyXp3KGbRICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T21:39:44.182529Z"},"content_sha256":"edd29d75e7c15f5070c642d4842df9ce1c57e7b5f84d289a8cfa59505df4c94a","schema_version":"1.0","event_id":"sha256:edd29d75e7c15f5070c642d4842df9ce1c57e7b5f84d289a8cfa59505df4c94a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU/bundle.json","state_url":"https://pith.science/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU/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":"2026-07-15T21:39:44Z","links":{"resolver":"https://pith.science/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU","bundle":"https://pith.science/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU/bundle.json","state":"https://pith.science/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWDJBTTNBQ7WVIRGOJL2DWVISU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RWDJBTTNBQ7WVIRGOJL2DWVISU","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":"faa034f2167259f7095cd6cd0aed7737e90c88fcd4c3fa72d3b6f7fc900ab760","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-11T02:58:28Z","title_canon_sha256":"71efeea36f1495d72dc1a89e5afeb23994ef8c042630e86e7a5893db8661b765"},"schema_version":"1.0","source":{"id":"2408.05677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.05677","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"arxiv_version","alias_value":"2408.05677v1","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.05677","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"pith_short_12","alias_value":"RWDJBTTNBQ7W","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"pith_short_16","alias_value":"RWDJBTTNBQ7WVIRG","created_at":"2026-07-05T08:54:23Z"},{"alias_kind":"pith_short_8","alias_value":"RWDJBTTN","created_at":"2026-07-05T08:54:23Z"}],"graph_snapshots":[{"event_id":"sha256:edd29d75e7c15f5070c642d4842df9ce1c57e7b5f84d289a8cfa59505df4c94a","target":"graph","created_at":"2026-07-05T08:54:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.05677/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions (infinite-dimensional vectors) from a reproducing kernel Hilbert space (RKHS). We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition. An advantage of CP-HiFi is that it can enforce smoothness ","authors_text":"Alex H. Williams, Anru R. Zhang, Brett W. Larsen, Tamara G. Kolda","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-11T02:58:28Z","title":"Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05677","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":"sha256:8fffefa61c2f21c46a048b4ffff21e9e330049c1a0fd00f94c899919cde2e76f","target":"record","created_at":"2026-07-05T08:54:23Z","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":"faa034f2167259f7095cd6cd0aed7737e90c88fcd4c3fa72d3b6f7fc900ab760","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-11T02:58:28Z","title_canon_sha256":"71efeea36f1495d72dc1a89e5afeb23994ef8c042630e86e7a5893db8661b765"},"schema_version":"1.0","source":{"id":"2408.05677","kind":"arxiv","version":1}},"canonical_sha256":"8d8690ce6d0c3f6aa2267257a1daa895388bd734bd597efafe3487bed1a40f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d8690ce6d0c3f6aa2267257a1daa895388bd734bd597efafe3487bed1a40f72","first_computed_at":"2026-07-05T08:54:23.494293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:54:23.494293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fG8Sm0K3eyFyAtC0ir5MBpjvViajDfNCm3p3LFPeSYbxfsuCd6z558R0a/iOLHYgsZn0ttedhUf/T6hOU29UCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:54:23.494709Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.05677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fffefa61c2f21c46a048b4ffff21e9e330049c1a0fd00f94c899919cde2e76f","sha256:edd29d75e7c15f5070c642d4842df9ce1c57e7b5f84d289a8cfa59505df4c94a"],"state_sha256":"856ee0ce876bd7a1bcbc864a089057eb5fe9466e01d10081133e9590e5b52d06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cw0XEFUYvg1e/s7F64kSBU8V1xhg0OQLLxeWCxnwZ2u3Y1TcZMn2+84uh//9dT1CtqRVh5zdyIRFxpscrOVTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-15T21:39:44.184681Z","bundle_sha256":"ce8e00b382126fb5b7f3e59db6ef901bedae7080838349d2f55494840b4b9e09"}}