{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AXJ2DQ24NAKBPHFCMDQTDDANRA","short_pith_number":"pith:AXJ2DQ24","canonical_record":{"source":{"id":"2501.19183","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T14:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"b0057ea873be0335879cc3e1ae5c012a6b41cb68f28224f062a4128c41cfa421","abstract_canon_sha256":"41381fc0e8dbb1cc16f83eeb26d118a50fa4d553dc2c7d3fd87e3aa55cffd974"},"schema_version":"1.0"},"canonical_sha256":"05d3a1c35c6814179ca260e1318c0d8811c39a54d999aa46cd9c5c8ed6f80f74","source":{"kind":"arxiv","id":"2501.19183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.19183","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"2501.19183v1","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.19183","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"AXJ2DQ24NAKB","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"pith_short_16","alias_value":"AXJ2DQ24NAKBPHFC","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"pith_short_8","alias_value":"AXJ2DQ24","created_at":"2026-07-05T10:07:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AXJ2DQ24NAKBPHFCMDQTDDANRA","target":"record","payload":{"canonical_record":{"source":{"id":"2501.19183","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T14:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"b0057ea873be0335879cc3e1ae5c012a6b41cb68f28224f062a4128c41cfa421","abstract_canon_sha256":"41381fc0e8dbb1cc16f83eeb26d118a50fa4d553dc2c7d3fd87e3aa55cffd974"},"schema_version":"1.0"},"canonical_sha256":"05d3a1c35c6814179ca260e1318c0d8811c39a54d999aa46cd9c5c8ed6f80f74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:57.366484Z","signature_b64":"Zfolbf88vhwDwpZccmEyRsSjtPE1e9h+evAFo4N57AoPogqUwImKDEE1PGZtsmUiDxwbw7io9yD70TgwSnd8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05d3a1c35c6814179ca260e1318c0d8811c39a54d999aa46cd9c5c8ed6f80f74","last_reissued_at":"2026-07-05T10:07:57.365998Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:57.365998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.19183","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":"2026-07-05T10:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKAqdOrfbNSuKVQVif63iw7rkWEYJ41691TgWNL+5NQo+uS3hkovz70PFKz2TD6sgvD+pXSd4lTh/00v6SA1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:28:08.311155Z"},"content_sha256":"e618047718d542d1749b06fdb6fae99831cb2fcf57057d4c2b1cea0fab208633","schema_version":"1.0","event_id":"sha256:e618047718d542d1749b06fdb6fae99831cb2fcf57057d4c2b1cea0fab208633"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AXJ2DQ24NAKBPHFCMDQTDDANRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Position: Curvature Matrices Should Be Democratized via Linear Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Agustinus Kristiadi, Andres Fernandez, Felix Dangel, Lukas Tatzel, Runa Eschenhagen, Weronika Ormaniec","submitted_at":"2025-01-31T14:46:30Z","abstract_excerpt":"Structured large matrices are prevalent in machine learning. A particularly important class is curvature matrices like the Hessian, which are central to understanding the loss landscape of neural nets (NNs), and enable second-order optimization, uncertainty quantification, model pruning, data attribution, and more. However, curvature computations can be challenging due to the complexity of automatic differentiation, and the variety and structural assumptions of curvature proxies, like sparsity and Kronecker factorization. In this position paper, we argue that linear operators -- an interface f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19183","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/2501.19183/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":"2026-07-05T10:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/lnQ5S6fdtgsap4a0/h7J90+qBhKgnGi6qXVxFBIP8ikHgYu1kfL33Z4hcls4v8p/KCOVkPJimiiJK5A0HAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:28:08.312296Z"},"content_sha256":"34d5e76841272e80cf8ffb4c964cfbe1d91b36e829c8457cb03272aa3bb3a5d2","schema_version":"1.0","event_id":"sha256:34d5e76841272e80cf8ffb4c964cfbe1d91b36e829c8457cb03272aa3bb3a5d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA/bundle.json","state_url":"https://pith.science/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA/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":"2026-08-07T10:28:08Z","links":{"resolver":"https://pith.science/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA","bundle":"https://pith.science/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA/bundle.json","state":"https://pith.science/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXJ2DQ24NAKBPHFCMDQTDDANRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AXJ2DQ24NAKBPHFCMDQTDDANRA","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":"41381fc0e8dbb1cc16f83eeb26d118a50fa4d553dc2c7d3fd87e3aa55cffd974","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T14:46:30Z","title_canon_sha256":"b0057ea873be0335879cc3e1ae5c012a6b41cb68f28224f062a4128c41cfa421"},"schema_version":"1.0","source":{"id":"2501.19183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.19183","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"2501.19183v1","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.19183","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"AXJ2DQ24NAKB","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"pith_short_16","alias_value":"AXJ2DQ24NAKBPHFC","created_at":"2026-07-05T10:07:57Z"},{"alias_kind":"pith_short_8","alias_value":"AXJ2DQ24","created_at":"2026-07-05T10:07:57Z"}],"graph_snapshots":[{"event_id":"sha256:34d5e76841272e80cf8ffb4c964cfbe1d91b36e829c8457cb03272aa3bb3a5d2","target":"graph","created_at":"2026-07-05T10:07:57Z","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/2501.19183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Structured large matrices are prevalent in machine learning. A particularly important class is curvature matrices like the Hessian, which are central to understanding the loss landscape of neural nets (NNs), and enable second-order optimization, uncertainty quantification, model pruning, data attribution, and more. However, curvature computations can be challenging due to the complexity of automatic differentiation, and the variety and structural assumptions of curvature proxies, like sparsity and Kronecker factorization. In this position paper, we argue that linear operators -- an interface f","authors_text":"Agustinus Kristiadi, Andres Fernandez, Felix Dangel, Lukas Tatzel, Runa Eschenhagen, Weronika Ormaniec","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T14:46:30Z","title":"Position: Curvature Matrices Should Be Democratized via Linear Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19183","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:e618047718d542d1749b06fdb6fae99831cb2fcf57057d4c2b1cea0fab208633","target":"record","created_at":"2026-07-05T10:07:57Z","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":"41381fc0e8dbb1cc16f83eeb26d118a50fa4d553dc2c7d3fd87e3aa55cffd974","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T14:46:30Z","title_canon_sha256":"b0057ea873be0335879cc3e1ae5c012a6b41cb68f28224f062a4128c41cfa421"},"schema_version":"1.0","source":{"id":"2501.19183","kind":"arxiv","version":1}},"canonical_sha256":"05d3a1c35c6814179ca260e1318c0d8811c39a54d999aa46cd9c5c8ed6f80f74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05d3a1c35c6814179ca260e1318c0d8811c39a54d999aa46cd9c5c8ed6f80f74","first_computed_at":"2026-07-05T10:07:57.365998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:57.365998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zfolbf88vhwDwpZccmEyRsSjtPE1e9h+evAFo4N57AoPogqUwImKDEE1PGZtsmUiDxwbw7io9yD70TgwSnd8Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:57.366484Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.19183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e618047718d542d1749b06fdb6fae99831cb2fcf57057d4c2b1cea0fab208633","sha256:34d5e76841272e80cf8ffb4c964cfbe1d91b36e829c8457cb03272aa3bb3a5d2"],"state_sha256":"94f3dd77a710d620262aa47dd7600dd819228683d99cb6322850d50843042350"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hxcl0TT5p1dKZxreOxzB2gFrL1d39EOi29Y6uqtk33W2BISrfQHMYwOG9dLn7FXw0fMdKv7GNbXy7mai1z7JAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T10:28:08.320654Z","bundle_sha256":"6536037eab610fcc8e9eb5d750dfe5f192be528de6199ab0eb9d211f29f64ef9"}}