{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DHANUQBKYKN6LEOAYJTT7B3KS4","short_pith_number":"pith:DHANUQBK","canonical_record":{"source":{"id":"2409.09471","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-09-14T15:44:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fa9ffe6168cbd9d3c4b6cfec5931320be1acc29667e6284891483842e1397d49","abstract_canon_sha256":"cd95f8a138a8e4f553098976c2600a97321ea4e19e263d268f52082c358556f2"},"schema_version":"1.0"},"canonical_sha256":"19c0da402ac29be591c0c2673f876a97244de27acc17a7cb00d101d737f629f1","source":{"kind":"arxiv","id":"2409.09471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.09471","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"arxiv_version","alias_value":"2409.09471v1","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09471","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"pith_short_12","alias_value":"DHANUQBKYKN6","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHANUQBKYKN6LEOA","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHANUQBK","created_at":"2026-07-05T09:07:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DHANUQBKYKN6LEOAYJTT7B3KS4","target":"record","payload":{"canonical_record":{"source":{"id":"2409.09471","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-09-14T15:44:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fa9ffe6168cbd9d3c4b6cfec5931320be1acc29667e6284891483842e1397d49","abstract_canon_sha256":"cd95f8a138a8e4f553098976c2600a97321ea4e19e263d268f52082c358556f2"},"schema_version":"1.0"},"canonical_sha256":"19c0da402ac29be591c0c2673f876a97244de27acc17a7cb00d101d737f629f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:07:10.212423Z","signature_b64":"go/oVEAD5sETEzWMhdVpiEKN1qCw414yEvmGMyhoq8avPo+rlXe9tpbmjEO7pS7UnM1W1ksIl+D/nwKIkZacBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19c0da402ac29be591c0c2673f876a97244de27acc17a7cb00d101d737f629f1","last_reissued_at":"2026-07-05T09:07:10.212061Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:07:10.212061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.09471","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":"2026-07-05T09:07:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bQSVHXZK/TyIGacDNferb8VjNNbRkwkXS6ys8ePy/PLYvIQhCJuYhReWahOvoqOo0Ns6rLUUer+re1TisILyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:13:46.508102Z"},"content_sha256":"5543f88506216de9ac52a345256972ab06caa7208e19b81667b10e2f94ad2fb5","schema_version":"1.0","event_id":"sha256:5543f88506216de9ac52a345256972ab06caa7208e19b81667b10e2f94ad2fb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DHANUQBKYKN6LEOAYJTT7B3KS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized sketched TT-GMRES for linear systems with tensor structure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alberto Bucci, Davide Palitta, Leonardo Robol","submitted_at":"2024-09-14T15:44:21Z","abstract_excerpt":"In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well as reducing the storage demand for its allocation, the solution of linear tensor equations is a less explored venue. Even if many of the routines available in the literature are based on alternating minimization schemes (ALS), we pursue a different path and utilize Krylov methods instead. The use of Krylov methods in the tensor realm is not new. However, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09471","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/2409.09471/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":"2026-07-05T09:07:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1M+uoFP3bSd/Kb/7oLpJFINQqqw1pAe6IRyUJjgYTOPtlhArMN8eMf6+DLVJH3DX08ylZERmEUudBo6anXp6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:13:46.508685Z"},"content_sha256":"4cfc4a8f9b20d2a1bfbbda16a6b7c86a31350edea20e0d7c84520a90f4f69953","schema_version":"1.0","event_id":"sha256:4cfc4a8f9b20d2a1bfbbda16a6b7c86a31350edea20e0d7c84520a90f4f69953"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHANUQBKYKN6LEOAYJTT7B3KS4/bundle.json","state_url":"https://pith.science/pith/DHANUQBKYKN6LEOAYJTT7B3KS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHANUQBKYKN6LEOAYJTT7B3KS4/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":"2026-08-23T16:13:46Z","links":{"resolver":"https://pith.science/pith/DHANUQBKYKN6LEOAYJTT7B3KS4","bundle":"https://pith.science/pith/DHANUQBKYKN6LEOAYJTT7B3KS4/bundle.json","state":"https://pith.science/pith/DHANUQBKYKN6LEOAYJTT7B3KS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHANUQBKYKN6LEOAYJTT7B3KS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DHANUQBKYKN6LEOAYJTT7B3KS4","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":"cd95f8a138a8e4f553098976c2600a97321ea4e19e263d268f52082c358556f2","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-09-14T15:44:21Z","title_canon_sha256":"fa9ffe6168cbd9d3c4b6cfec5931320be1acc29667e6284891483842e1397d49"},"schema_version":"1.0","source":{"id":"2409.09471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.09471","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"arxiv_version","alias_value":"2409.09471v1","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09471","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"pith_short_12","alias_value":"DHANUQBKYKN6","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHANUQBKYKN6LEOA","created_at":"2026-07-05T09:07:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHANUQBK","created_at":"2026-07-05T09:07:10Z"}],"graph_snapshots":[{"event_id":"sha256:4cfc4a8f9b20d2a1bfbbda16a6b7c86a31350edea20e0d7c84520a90f4f69953","target":"graph","created_at":"2026-07-05T09:07:10Z","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/2409.09471/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well as reducing the storage demand for its allocation, the solution of linear tensor equations is a less explored venue. Even if many of the routines available in the literature are based on alternating minimization schemes (ALS), we pursue a different path and utilize Krylov methods instead. The use of Krylov methods in the tensor realm is not new. However, the","authors_text":"Alberto Bucci, Davide Palitta, Leonardo Robol","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-09-14T15:44:21Z","title":"Randomized sketched TT-GMRES for linear systems with tensor structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09471","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":"sha256:5543f88506216de9ac52a345256972ab06caa7208e19b81667b10e2f94ad2fb5","target":"record","created_at":"2026-07-05T09:07:10Z","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":"cd95f8a138a8e4f553098976c2600a97321ea4e19e263d268f52082c358556f2","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-09-14T15:44:21Z","title_canon_sha256":"fa9ffe6168cbd9d3c4b6cfec5931320be1acc29667e6284891483842e1397d49"},"schema_version":"1.0","source":{"id":"2409.09471","kind":"arxiv","version":1}},"canonical_sha256":"19c0da402ac29be591c0c2673f876a97244de27acc17a7cb00d101d737f629f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19c0da402ac29be591c0c2673f876a97244de27acc17a7cb00d101d737f629f1","first_computed_at":"2026-07-05T09:07:10.212061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:07:10.212061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"go/oVEAD5sETEzWMhdVpiEKN1qCw414yEvmGMyhoq8avPo+rlXe9tpbmjEO7pS7UnM1W1ksIl+D/nwKIkZacBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:07:10.212423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.09471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5543f88506216de9ac52a345256972ab06caa7208e19b81667b10e2f94ad2fb5","sha256:4cfc4a8f9b20d2a1bfbbda16a6b7c86a31350edea20e0d7c84520a90f4f69953"],"state_sha256":"fb3fa42e10eb7fb3baf6aede0a47ac5c1708f601ef50609e782477cedb25339d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ij0DLi35nqdlvAGFNyAPqMbl0JLHXmscJIP/5pka/l5mLRPQzlLGmh8Ff4A0XM28D8XlQu4wRhaw3/PN/44QCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T16:13:46.513915Z","bundle_sha256":"674531e0d252bb396e57cc419074c17a5fd616f7fa072ba70c0595ba9e3511d0"}}