{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HIL4DVOC6BXVPRZRIJTHQ5DD2X","short_pith_number":"pith:HIL4DVOC","canonical_record":{"source":{"id":"1402.2095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2014-02-10T10:47:00Z","cross_cats_sorted":["cond-mat.stat-mech","physics.data-an"],"title_canon_sha256":"02e538b74d84b51ae31e33fc801a28ee4af89ba47b7874416346d224e1f42ff3","abstract_canon_sha256":"2ec4f6b3eac554efde85de2bfcff35a0c0e3998e1bafddd7d5aa98a729967e33"},"schema_version":"1.0"},"canonical_sha256":"3a17c1d5c2f06f57c7314266787463d5d3d447add95488cbe463ec9069571c88","source":{"kind":"arxiv","id":"1402.2095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2095","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2095v1","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2095","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"HIL4DVOC6BXV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HIL4DVOC6BXVPRZR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HIL4DVOC","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HIL4DVOC6BXVPRZRIJTHQ5DD2X","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2014-02-10T10:47:00Z","cross_cats_sorted":["cond-mat.stat-mech","physics.data-an"],"title_canon_sha256":"02e538b74d84b51ae31e33fc801a28ee4af89ba47b7874416346d224e1f42ff3","abstract_canon_sha256":"2ec4f6b3eac554efde85de2bfcff35a0c0e3998e1bafddd7d5aa98a729967e33"},"schema_version":"1.0"},"canonical_sha256":"3a17c1d5c2f06f57c7314266787463d5d3d447add95488cbe463ec9069571c88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:25.958777Z","signature_b64":"CF7oTrZQxiGcgQXYiMjQ1DeN+92HgbQRvQeDuKjxehwDpsW+gjdDvB/UXP4KpVyOfQ+n1evCGaduyQ89NHZCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a17c1d5c2f06f57c7314266787463d5d3d447add95488cbe463ec9069571c88","last_reissued_at":"2026-05-18T02:48:25.958276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:25.958276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2095","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":"2026-05-18T02:48:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44tqsGzZ2ymw1YPuEXqd924iBHB7C/A4a3XcVRbK9HSQbJnu08mEz+idpL3IJWARAemALe11kQBY+3LrhjfQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:39:48.841613Z"},"content_sha256":"3ef6b5a078958efb77fa175ead817d5e78a03524e82b4ed2fed2dd6fb152345c","schema_version":"1.0","event_id":"sha256:3ef6b5a078958efb77fa175ead817d5e78a03524e82b4ed2fed2dd6fb152345c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HIL4DVOC6BXVPRZRIJTHQ5DD2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluating functions of positive-definite matrices using colored noise thermostats","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.data-an"],"primary_cat":"physics.comp-ph","authors_text":"Chaim Dryzun, Marco Nava, Michele Ceriotti, Michele Parrinello","submitted_at":"2014-02-10T10:47:00Z","abstract_excerpt":"Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential cou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2095","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":"2026-05-18T02:48:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJj3GuX0aTKcVQ5ZAPBy2LGdE65/Kus/8MUIXCx5qCRNrFb7ee4XB+v1JD8v00BnABCjkO3C90i67sv7dhNlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:39:48.841967Z"},"content_sha256":"c5863a0c2325e9239c68d37ef9689354f4ee5e206a33ad272b97f49e545b436c","schema_version":"1.0","event_id":"sha256:c5863a0c2325e9239c68d37ef9689354f4ee5e206a33ad272b97f49e545b436c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X/bundle.json","state_url":"https://pith.science/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X/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":"2026-06-02T21:39:48Z","links":{"resolver":"https://pith.science/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X","bundle":"https://pith.science/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X/bundle.json","state":"https://pith.science/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIL4DVOC6BXVPRZRIJTHQ5DD2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HIL4DVOC6BXVPRZRIJTHQ5DD2X","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":"2ec4f6b3eac554efde85de2bfcff35a0c0e3998e1bafddd7d5aa98a729967e33","cross_cats_sorted":["cond-mat.stat-mech","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2014-02-10T10:47:00Z","title_canon_sha256":"02e538b74d84b51ae31e33fc801a28ee4af89ba47b7874416346d224e1f42ff3"},"schema_version":"1.0","source":{"id":"1402.2095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2095","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2095v1","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2095","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"HIL4DVOC6BXV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HIL4DVOC6BXVPRZR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HIL4DVOC","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:c5863a0c2325e9239c68d37ef9689354f4ee5e206a33ad272b97f49e545b436c","target":"graph","created_at":"2026-05-18T02:48:25Z","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":"Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential cou","authors_text":"Chaim Dryzun, Marco Nava, Michele Ceriotti, Michele Parrinello","cross_cats":["cond-mat.stat-mech","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2014-02-10T10:47:00Z","title":"Evaluating functions of positive-definite matrices using colored noise thermostats"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2095","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":"sha256:3ef6b5a078958efb77fa175ead817d5e78a03524e82b4ed2fed2dd6fb152345c","target":"record","created_at":"2026-05-18T02:48:25Z","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":"2ec4f6b3eac554efde85de2bfcff35a0c0e3998e1bafddd7d5aa98a729967e33","cross_cats_sorted":["cond-mat.stat-mech","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2014-02-10T10:47:00Z","title_canon_sha256":"02e538b74d84b51ae31e33fc801a28ee4af89ba47b7874416346d224e1f42ff3"},"schema_version":"1.0","source":{"id":"1402.2095","kind":"arxiv","version":1}},"canonical_sha256":"3a17c1d5c2f06f57c7314266787463d5d3d447add95488cbe463ec9069571c88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a17c1d5c2f06f57c7314266787463d5d3d447add95488cbe463ec9069571c88","first_computed_at":"2026-05-18T02:48:25.958276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:25.958276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CF7oTrZQxiGcgQXYiMjQ1DeN+92HgbQRvQeDuKjxehwDpsW+gjdDvB/UXP4KpVyOfQ+n1evCGaduyQ89NHZCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:25.958777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ef6b5a078958efb77fa175ead817d5e78a03524e82b4ed2fed2dd6fb152345c","sha256:c5863a0c2325e9239c68d37ef9689354f4ee5e206a33ad272b97f49e545b436c"],"state_sha256":"04abf9bfa91e34c825337c2034f353f4a5940cb6cc83bb146dd6bc66ff9ae468"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ynr5xn7z5IkkhsZyK6TgpukjUuSTMRddZ3T+OfBRphxMDqV+iJNYNYbXbQQhy4mFoFclzoC3HK0SZp51yptsDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:39:48.844307Z","bundle_sha256":"785c1be6baf8e82a8d6971ae12edaad2e64499c236ad9f750351c4cc419d46c2"}}