{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LGC3QFACNCIKUQLZECB5XCSURR","short_pith_number":"pith:LGC3QFAC","canonical_record":{"source":{"id":"1507.04396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-15T21:19:25Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"b797706fbc4d79ab00cfb01b56dfc489aa9ecc95f4f1e9a02d67099dd8e30897","abstract_canon_sha256":"be5fe9facdc5f14f63a68052d6e6a65bcde18d934e26a3b1fe94f637c21fc59d"},"schema_version":"1.0"},"canonical_sha256":"5985b814026890aa41792083db8a548c40122d7d9dc7abd5e3e59152ccf9f2de","source":{"kind":"arxiv","id":"1507.04396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04396","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04396v1","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04396","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"LGC3QFACNCIK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGC3QFACNCIKUQLZ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGC3QFAC","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LGC3QFACNCIKUQLZECB5XCSURR","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-15T21:19:25Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"b797706fbc4d79ab00cfb01b56dfc489aa9ecc95f4f1e9a02d67099dd8e30897","abstract_canon_sha256":"be5fe9facdc5f14f63a68052d6e6a65bcde18d934e26a3b1fe94f637c21fc59d"},"schema_version":"1.0"},"canonical_sha256":"5985b814026890aa41792083db8a548c40122d7d9dc7abd5e3e59152ccf9f2de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:47.530277Z","signature_b64":"SV5/DwSvzCsUXbVoNUxTMjYB/fyqHm/d5kqrcpCmGE6GePYFt+jkZr06r0H2zFJhvwdMZof6mSvtbk7jm4nNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5985b814026890aa41792083db8a548c40122d7d9dc7abd5e3e59152ccf9f2de","last_reissued_at":"2026-05-18T01:36:47.529632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:47.529632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04396","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":"2026-05-18T01:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWCxqj+YI6PkVTSJyLFfaG/iC6aKvXm99wmpRqznQuGzpi4bwuoWPG5YMk9xZrwODFeD7Rt5EI3ps1jcu8UXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:01:13.428112Z"},"content_sha256":"b925f0c49fdca469276e1a13de1778c7fed3f982ed23cf369233a2826535864d","schema_version":"1.0","event_id":"sha256:b925f0c49fdca469276e1a13de1778c7fed3f982ed23cf369233a2826535864d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LGC3QFACNCIKUQLZECB5XCSURR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel MMF: a Multiresolution Approach to Matrix Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.NA","authors_text":"Nedelina Teneva, Pramod K. Mudrakarta, Risi Kondor","submitted_at":"2015-07-15T21:19:25Z","abstract_excerpt":"Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for sparse matrices. We argue that this makes pMMF a valuable new computational primitive in its own right, and present experiments on using pMMF for two distinct purposes: compressing matrices and preconditioning large sparse linear systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04396","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":"2026-05-18T01:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1m0YRHIj/zOMCLCI1rz+wxRD58PbpolvbQLGLDmf0LRNJU5q0ZBkBubIT3eZjBtaCcBRp84Idg9rZTxRDZvTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:01:13.428498Z"},"content_sha256":"f767ba472c0a6ec4c16ebff8ecc07e014120c3230167db06bcabb5b1f749427b","schema_version":"1.0","event_id":"sha256:f767ba472c0a6ec4c16ebff8ecc07e014120c3230167db06bcabb5b1f749427b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGC3QFACNCIKUQLZECB5XCSURR/bundle.json","state_url":"https://pith.science/pith/LGC3QFACNCIKUQLZECB5XCSURR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGC3QFACNCIKUQLZECB5XCSURR/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":"2026-05-31T23:01:13Z","links":{"resolver":"https://pith.science/pith/LGC3QFACNCIKUQLZECB5XCSURR","bundle":"https://pith.science/pith/LGC3QFACNCIKUQLZECB5XCSURR/bundle.json","state":"https://pith.science/pith/LGC3QFACNCIKUQLZECB5XCSURR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGC3QFACNCIKUQLZECB5XCSURR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LGC3QFACNCIKUQLZECB5XCSURR","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":"be5fe9facdc5f14f63a68052d6e6a65bcde18d934e26a3b1fe94f637c21fc59d","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-15T21:19:25Z","title_canon_sha256":"b797706fbc4d79ab00cfb01b56dfc489aa9ecc95f4f1e9a02d67099dd8e30897"},"schema_version":"1.0","source":{"id":"1507.04396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04396","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04396v1","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04396","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"LGC3QFACNCIK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGC3QFACNCIKUQLZ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGC3QFAC","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:f767ba472c0a6ec4c16ebff8ecc07e014120c3230167db06bcabb5b1f749427b","target":"graph","created_at":"2026-05-18T01:36:47Z","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":"Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for sparse matrices. We argue that this makes pMMF a valuable new computational primitive in its own right, and present experiments on using pMMF for two distinct purposes: compressing matrices and preconditioning large sparse linear systems.","authors_text":"Nedelina Teneva, Pramod K. Mudrakarta, Risi Kondor","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-15T21:19:25Z","title":"Parallel MMF: a Multiresolution Approach to Matrix Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04396","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:b925f0c49fdca469276e1a13de1778c7fed3f982ed23cf369233a2826535864d","target":"record","created_at":"2026-05-18T01:36:47Z","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":"be5fe9facdc5f14f63a68052d6e6a65bcde18d934e26a3b1fe94f637c21fc59d","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-07-15T21:19:25Z","title_canon_sha256":"b797706fbc4d79ab00cfb01b56dfc489aa9ecc95f4f1e9a02d67099dd8e30897"},"schema_version":"1.0","source":{"id":"1507.04396","kind":"arxiv","version":1}},"canonical_sha256":"5985b814026890aa41792083db8a548c40122d7d9dc7abd5e3e59152ccf9f2de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5985b814026890aa41792083db8a548c40122d7d9dc7abd5e3e59152ccf9f2de","first_computed_at":"2026-05-18T01:36:47.529632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:47.529632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SV5/DwSvzCsUXbVoNUxTMjYB/fyqHm/d5kqrcpCmGE6GePYFt+jkZr06r0H2zFJhvwdMZof6mSvtbk7jm4nNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:47.530277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b925f0c49fdca469276e1a13de1778c7fed3f982ed23cf369233a2826535864d","sha256:f767ba472c0a6ec4c16ebff8ecc07e014120c3230167db06bcabb5b1f749427b"],"state_sha256":"d56d9e18bdbf2ad9ea085246d0eadb0e15d2c390052fa47b9d3a7e48edad7cbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHgVbZw/Q/1uSSjHinHctxSB8gfIaij4P34nfkxWh6iiB40zn/KLvBQ3u23Zayke96ksUL54RBmRFTM2U2kmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:01:13.430936Z","bundle_sha256":"4460c46d1f7913639439c164df74cd32a5a33f81fe732d5603465860638ee53d"}}