{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BX7HZA3REJZ4C7HFNAO56S7PSX","short_pith_number":"pith:BX7HZA3R","canonical_record":{"source":{"id":"1810.04221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T19:17:32Z","cross_cats_sorted":[],"title_canon_sha256":"9dafd6d846222e31f36ba19a230f9fa90a9b327aca8df53066218a7033940fe8","abstract_canon_sha256":"5c53538ad97dfee5bcb2d54ee438e2c0b4b3e8fbfca47a85df939b12fbde7d18"},"schema_version":"1.0"},"canonical_sha256":"0dfe7c83712273c17ce5681ddf4bef95ff2bcc50f6b3082b2eb289514df4c563","source":{"kind":"arxiv","id":"1810.04221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04221","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04221v1","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04221","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"BX7HZA3REJZ4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BX7HZA3REJZ4C7HF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BX7HZA3R","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BX7HZA3REJZ4C7HFNAO56S7PSX","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04221","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T19:17:32Z","cross_cats_sorted":[],"title_canon_sha256":"9dafd6d846222e31f36ba19a230f9fa90a9b327aca8df53066218a7033940fe8","abstract_canon_sha256":"5c53538ad97dfee5bcb2d54ee438e2c0b4b3e8fbfca47a85df939b12fbde7d18"},"schema_version":"1.0"},"canonical_sha256":"0dfe7c83712273c17ce5681ddf4bef95ff2bcc50f6b3082b2eb289514df4c563","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:40.780767Z","signature_b64":"suqaPLTTrdm4D3vrlGZ2zHADYYgqRzrgMm4E0VVsIabbBZoRNcwXxh8PQ18YcWC4cQ2M5EYmghVdmvYigY/mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dfe7c83712273c17ce5681ddf4bef95ff2bcc50f6b3082b2eb289514df4c563","last_reissued_at":"2026-05-18T00:03:40.780171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:40.780171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04221","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":"2026-05-18T00:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wBvcHJcViu97j3AJcfYfV0c/ib1yz8xTDkh1X8+TootEikmMu5hr/YHtw+Dawx9GTZL7cOmRULVkL0a2SKuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:28:54.220203Z"},"content_sha256":"1917b9a67a0b10f5200dd10af3892730cf6b5d084362bf6d581af0798a4efcf5","schema_version":"1.0","event_id":"sha256:1917b9a67a0b10f5200dd10af3892730cf6b5d084362bf6d581af0798a4efcf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BX7HZA3REJZ4C7HFNAO56S7PSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"AMG based on compatible weighted matching for GPUs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dario Pasquini, Massimo Bernaschi, Pasqua D'Ambra","submitted_at":"2018-10-09T19:17:32Z","abstract_excerpt":"We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the authors and already available in the open-source package BootCMatch: Bootstrap algebraic multigrid based on Compatible weighted Matching for standard CPU. The AMG method relies on a new approach for coarsening sparse symmetric positive definite (spd) matrices, named \"coarsening based on compatible weighted matching\". It exploits maximum weight matching in the adja"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04221","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":"2026-05-18T00:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLCktQax6+ERnOfMLtDlvZ/zEahbB8Vnr+o6h+Vgd6Spw9h1urrq5D4Gjfy/gNBPoqU16HDuAZknABikRJ3DAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:28:54.220560Z"},"content_sha256":"c83abaefc2b087ef13fa1badc9fb8e751ec27bced13f1e3567b904e4314f7ec9","schema_version":"1.0","event_id":"sha256:c83abaefc2b087ef13fa1badc9fb8e751ec27bced13f1e3567b904e4314f7ec9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BX7HZA3REJZ4C7HFNAO56S7PSX/bundle.json","state_url":"https://pith.science/pith/BX7HZA3REJZ4C7HFNAO56S7PSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BX7HZA3REJZ4C7HFNAO56S7PSX/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":"2026-06-23T06:28:54Z","links":{"resolver":"https://pith.science/pith/BX7HZA3REJZ4C7HFNAO56S7PSX","bundle":"https://pith.science/pith/BX7HZA3REJZ4C7HFNAO56S7PSX/bundle.json","state":"https://pith.science/pith/BX7HZA3REJZ4C7HFNAO56S7PSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BX7HZA3REJZ4C7HFNAO56S7PSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BX7HZA3REJZ4C7HFNAO56S7PSX","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":"5c53538ad97dfee5bcb2d54ee438e2c0b4b3e8fbfca47a85df939b12fbde7d18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T19:17:32Z","title_canon_sha256":"9dafd6d846222e31f36ba19a230f9fa90a9b327aca8df53066218a7033940fe8"},"schema_version":"1.0","source":{"id":"1810.04221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04221","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04221v1","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04221","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"BX7HZA3REJZ4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BX7HZA3REJZ4C7HF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BX7HZA3R","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:c83abaefc2b087ef13fa1badc9fb8e751ec27bced13f1e3567b904e4314f7ec9","target":"graph","created_at":"2026-05-18T00:03:40Z","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":"We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the authors and already available in the open-source package BootCMatch: Bootstrap algebraic multigrid based on Compatible weighted Matching for standard CPU. The AMG method relies on a new approach for coarsening sparse symmetric positive definite (spd) matrices, named \"coarsening based on compatible weighted matching\". It exploits maximum weight matching in the adja","authors_text":"Dario Pasquini, Massimo Bernaschi, Pasqua D'Ambra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T19:17:32Z","title":"AMG based on compatible weighted matching for GPUs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04221","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":"sha256:1917b9a67a0b10f5200dd10af3892730cf6b5d084362bf6d581af0798a4efcf5","target":"record","created_at":"2026-05-18T00:03:40Z","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":"5c53538ad97dfee5bcb2d54ee438e2c0b4b3e8fbfca47a85df939b12fbde7d18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T19:17:32Z","title_canon_sha256":"9dafd6d846222e31f36ba19a230f9fa90a9b327aca8df53066218a7033940fe8"},"schema_version":"1.0","source":{"id":"1810.04221","kind":"arxiv","version":1}},"canonical_sha256":"0dfe7c83712273c17ce5681ddf4bef95ff2bcc50f6b3082b2eb289514df4c563","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dfe7c83712273c17ce5681ddf4bef95ff2bcc50f6b3082b2eb289514df4c563","first_computed_at":"2026-05-18T00:03:40.780171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:40.780171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"suqaPLTTrdm4D3vrlGZ2zHADYYgqRzrgMm4E0VVsIabbBZoRNcwXxh8PQ18YcWC4cQ2M5EYmghVdmvYigY/mCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:40.780767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1917b9a67a0b10f5200dd10af3892730cf6b5d084362bf6d581af0798a4efcf5","sha256:c83abaefc2b087ef13fa1badc9fb8e751ec27bced13f1e3567b904e4314f7ec9"],"state_sha256":"7426d1a38baf7e03eafafb9c9fabd42fdca46cabfe137d2ab8cef8f614024161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eTlyR/iYzJgdj+FD+qV4uwTjfNIwLFdJv+XrF0vMV08U13vH0/PHtq8doIO8LYgSg/m38clioocSBKNherjtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:28:54.222781Z","bundle_sha256":"1af36729e7dbb1f006a1f13dd4301f905126714d75a71dd9f6219a79d2350660"}}