{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YKJUBLMHORP7XZIGA53TDILN5U","short_pith_number":"pith:YKJUBLMH","canonical_record":{"source":{"id":"2607.05437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2026-07-03T15:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"72b44930a221b40158ee95668b5f1e43690e90a50f6e3263b21f02fe1516c612","abstract_canon_sha256":"48b53789871e77746cae9c3da839679cbc4ac3f2cb607536c3810577a187e125"},"schema_version":"1.0"},"canonical_sha256":"c29340ad87745ffbe506077731a16ded0038d671728bb9da6ab6f3c302faac97","source":{"kind":"arxiv","id":"2607.05437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05437","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05437v1","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05437","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"YKJUBLMHORP7","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"pith_short_16","alias_value":"YKJUBLMHORP7XZIG","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"pith_short_8","alias_value":"YKJUBLMH","created_at":"2026-07-08T01:18:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YKJUBLMHORP7XZIGA53TDILN5U","target":"record","payload":{"canonical_record":{"source":{"id":"2607.05437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2026-07-03T15:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"72b44930a221b40158ee95668b5f1e43690e90a50f6e3263b21f02fe1516c612","abstract_canon_sha256":"48b53789871e77746cae9c3da839679cbc4ac3f2cb607536c3810577a187e125"},"schema_version":"1.0"},"canonical_sha256":"c29340ad87745ffbe506077731a16ded0038d671728bb9da6ab6f3c302faac97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:09.981725Z","signature_b64":"s3IQkAlUiJWJTJL0gX7ngJURUAJ5Ae1/6Fmp3Po6YVB1ZG2EjaUay0W3zJ1kxOiFeJ93sD+fXHypw2ddttDMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c29340ad87745ffbe506077731a16ded0038d671728bb9da6ab6f3c302faac97","last_reissued_at":"2026-07-08T01:18:09.981274Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:09.981274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.05437","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":"2026-07-08T01:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PH3PN3claCrdTyzj2M4f4Xi/804vjBqrFixOCLEPsJHYDSyQFyKtORW7UlN+Pni8Xn9rJ6cIJkiTbBrhJumWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:16:01.890112Z"},"content_sha256":"6fd326ac7de1f8a5d10f3acbad41a394449ce65db70619480017d5b6000479b7","schema_version":"1.0","event_id":"sha256:6fd326ac7de1f8a5d10f3acbad41a394449ce65db70619480017d5b6000479b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YKJUBLMHORP7XZIGA53TDILN5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The mmatrix toolbox: componentwise accurate algorithms for M-matrices with triplet representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.MS","authors_text":"Bruno Iannazzo, Federico Poloni, Mehdi Najafi Kalyani","submitted_at":"2026-07-03T15:02:49Z","abstract_excerpt":"We introduce the mmatrix toolbox, a Matlab software package for componentwise accurate computations with M-matrices described through left or right triplet representations. The core of the toolbox is a Fortran implementation, in the Lapack style, of the unblocked, recursive, and blocked versions of the GTH algorithm and its applications for the accurate computation of the solution of linear systems with M-matrix coefficient and nonnegative right-hand side, the LU factorization of an M-matrix and its inverse. These algorithms avoid subtractive cancellation; this property ensures high componentw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05437","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/2607.05437/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":"2026-07-08T01:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BeVg1R3DZf+Hmt+YhzuNIM4pvjI+cPp/47/5bG1a3jmuq5EIa4rZz7YLFzJh/winmpjzM5fSUAQsHxlaDdAFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:16:01.891034Z"},"content_sha256":"a38c4dcd99fdc16ad4081407125349de76e07961f776f91035b1f39edd75e05d","schema_version":"1.0","event_id":"sha256:a38c4dcd99fdc16ad4081407125349de76e07961f776f91035b1f39edd75e05d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKJUBLMHORP7XZIGA53TDILN5U/bundle.json","state_url":"https://pith.science/pith/YKJUBLMHORP7XZIGA53TDILN5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKJUBLMHORP7XZIGA53TDILN5U/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":"2026-08-17T00:16:01Z","links":{"resolver":"https://pith.science/pith/YKJUBLMHORP7XZIGA53TDILN5U","bundle":"https://pith.science/pith/YKJUBLMHORP7XZIGA53TDILN5U/bundle.json","state":"https://pith.science/pith/YKJUBLMHORP7XZIGA53TDILN5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKJUBLMHORP7XZIGA53TDILN5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YKJUBLMHORP7XZIGA53TDILN5U","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":"48b53789871e77746cae9c3da839679cbc4ac3f2cb607536c3810577a187e125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2026-07-03T15:02:49Z","title_canon_sha256":"72b44930a221b40158ee95668b5f1e43690e90a50f6e3263b21f02fe1516c612"},"schema_version":"1.0","source":{"id":"2607.05437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05437","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05437v1","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05437","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"YKJUBLMHORP7","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"pith_short_16","alias_value":"YKJUBLMHORP7XZIG","created_at":"2026-07-08T01:18:09Z"},{"alias_kind":"pith_short_8","alias_value":"YKJUBLMH","created_at":"2026-07-08T01:18:09Z"}],"graph_snapshots":[{"event_id":"sha256:a38c4dcd99fdc16ad4081407125349de76e07961f776f91035b1f39edd75e05d","target":"graph","created_at":"2026-07-08T01:18:09Z","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/2607.05437/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the mmatrix toolbox, a Matlab software package for componentwise accurate computations with M-matrices described through left or right triplet representations. The core of the toolbox is a Fortran implementation, in the Lapack style, of the unblocked, recursive, and blocked versions of the GTH algorithm and its applications for the accurate computation of the solution of linear systems with M-matrix coefficient and nonnegative right-hand side, the LU factorization of an M-matrix and its inverse. These algorithms avoid subtractive cancellation; this property ensures high componentw","authors_text":"Bruno Iannazzo, Federico Poloni, Mehdi Najafi Kalyani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2026-07-03T15:02:49Z","title":"The mmatrix toolbox: componentwise accurate algorithms for M-matrices with triplet representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05437","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":"sha256:6fd326ac7de1f8a5d10f3acbad41a394449ce65db70619480017d5b6000479b7","target":"record","created_at":"2026-07-08T01:18:09Z","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":"48b53789871e77746cae9c3da839679cbc4ac3f2cb607536c3810577a187e125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2026-07-03T15:02:49Z","title_canon_sha256":"72b44930a221b40158ee95668b5f1e43690e90a50f6e3263b21f02fe1516c612"},"schema_version":"1.0","source":{"id":"2607.05437","kind":"arxiv","version":1}},"canonical_sha256":"c29340ad87745ffbe506077731a16ded0038d671728bb9da6ab6f3c302faac97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c29340ad87745ffbe506077731a16ded0038d671728bb9da6ab6f3c302faac97","first_computed_at":"2026-07-08T01:18:09.981274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:09.981274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3IQkAlUiJWJTJL0gX7ngJURUAJ5Ae1/6Fmp3Po6YVB1ZG2EjaUay0W3zJ1kxOiFeJ93sD+fXHypw2ddttDMAg==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:09.981725Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fd326ac7de1f8a5d10f3acbad41a394449ce65db70619480017d5b6000479b7","sha256:a38c4dcd99fdc16ad4081407125349de76e07961f776f91035b1f39edd75e05d"],"state_sha256":"2aefd27ebeeb08647aab93319902857163c3f6b769b51cbcc2d1a878b30c1537"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N1JhDR/70TNSsBE2X2xz6P4JFyW393kTNVAxkEeUNxbEeS4k3OrjnxRgNboncghNmgEG9lFb2ZsRNn4fRzK0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T00:16:01.897428Z","bundle_sha256":"d27db90554914da75cca7b90f95a98ee0b258f9f9c2ad1c6f1a4fd24c60cb18a"}}