{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7FT3R4XQLCTVWR523CFX6J7PK6","short_pith_number":"pith:7FT3R4XQ","canonical_record":{"source":{"id":"2605.13343","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-13T11:02:27Z","cross_cats_sorted":["cs.DC","cs.LG","cs.NA","math.NA"],"title_canon_sha256":"b84f5f8f42baeca84db57e33ff3c38b3c6033eba735ed50b67230699d01c378f","abstract_canon_sha256":"7be0647020a3e2f740d0c52257ebe1424a07ad4192c39bca638bfe6a4f08e8eb"},"schema_version":"1.0"},"canonical_sha256":"f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033","source":{"kind":"arxiv","id":"2605.13343","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13343","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13343v2","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13343","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"7FT3R4XQLCTV","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"7FT3R4XQLCTVWR52","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"7FT3R4XQ","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7FT3R4XQLCTVWR523CFX6J7PK6","target":"record","payload":{"canonical_record":{"source":{"id":"2605.13343","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-13T11:02:27Z","cross_cats_sorted":["cs.DC","cs.LG","cs.NA","math.NA"],"title_canon_sha256":"b84f5f8f42baeca84db57e33ff3c38b3c6033eba735ed50b67230699d01c378f","abstract_canon_sha256":"7be0647020a3e2f740d0c52257ebe1424a07ad4192c39bca638bfe6a4f08e8eb"},"schema_version":"1.0"},"canonical_sha256":"f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:48.367061Z","signature_b64":"TNJ/qaQgT2rcaJ15seElSEybLNYlsdW++DNp64325ssMM8AZff/tWnVk9ZIz9QCP2GsFmMxFj1BG3ar6nZGxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033","last_reissued_at":"2026-05-18T02:44:48.366686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:48.366686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.13343","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QHuC/vEOW5l5AQSecw26lpbC8HpGZZaNPdba5xj2j/cWwudJdu4w0iMWMofu+vwbi3ELqX1+87ApcIJj02UcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:20:23.993531Z"},"content_sha256":"375c2fc5fafa4bf8e5365f70107fff39e4e3e9cb9bd29a9ebaa6fdba4268e796","schema_version":"1.0","event_id":"sha256:375c2fc5fafa4bf8e5365f70107fff39e4e3e9cb9bd29a9ebaa6fdba4268e796"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7FT3R4XQLCTVWR523CFX6J7PK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hierarchical Transformer Preconditioning for Interactive Physics Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization.","cross_cats":["cs.DC","cs.LG","cs.NA","math.NA"],"primary_cat":"cs.GR","authors_text":"Carl Osborne, Crystal Owens, Minghao Guo, Wojciech Matusik","submitted_at":"2026-05-13T11:02:27Z","abstract_excerpt":"Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We introduce the Hierarchical Transformer Preconditioner, a neural preconditioner anchored to a weak-admissibility H-matrix partition. The partition provides a multiscale structural prior (dense diagonal leaves plus coarsening off-diagonal tiles) that enables full-graph approximate-inverse computation with O(N) scaling at fixed block sizes. The network models the"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On stiff multiphase Poisson systems (up to 100:1 density contrast, N = 1,024-16,384), the solver runs from ~143 to ~21 fps. At N = 8,192, it reaches 17.9 ms/frame, with 2.2x speedup over GPU Jacobi, ~28x over GPU IC/DILU (AMGX multicolor_dilu), and 2.7x over neural SPAI retrained per scale on the same benchmark.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The weak-admissibility H-matrix partition plus highway connections in the transformer are assumed to capture long-range couplings sufficiently for the cosine-Hutchinson objective to produce a preconditioner that improves PCG convergence on irregular spectra without post-hoc tuning.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A hierarchical transformer preconditioner with H-matrix structure and cosine-Hutchinson training delivers up to 2.7x speedup over prior neural methods on stiff multiphase Poisson systems up to N=16384.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5d4cd04566f98bede90cf530938c2db68986170d94e5536a8f180fbf033cd4b5"},"source":{"id":"2605.13343","kind":"arxiv","version":2},"verdict":{"id":"11fc26fb-a73e-4ed9-8d93-e541e8b6a280","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:39:58.435457Z","strongest_claim":"On stiff multiphase Poisson systems (up to 100:1 density contrast, N = 1,024-16,384), the solver runs from ~143 to ~21 fps. At N = 8,192, it reaches 17.9 ms/frame, with 2.2x speedup over GPU Jacobi, ~28x over GPU IC/DILU (AMGX multicolor_dilu), and 2.7x over neural SPAI retrained per scale on the same benchmark.","one_line_summary":"A hierarchical transformer preconditioner with H-matrix structure and cosine-Hutchinson training delivers up to 2.7x speedup over prior neural methods on stiff multiphase Poisson systems up to N=16384.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The weak-admissibility H-matrix partition plus highway connections in the transformer are assumed to capture long-range couplings sufficiently for the cosine-Hutchinson objective to produce a preconditioner that improves PCG convergence on irregular spectra without post-hoc tuning.","pith_extraction_headline":"A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization."},"references":{"count":3,"sample":[{"doi":"","year":2021,"title":"Swin Transformer: Hierarchical Vision Transformer using Shifted Windows","work_id":"d6d2cf36-1b48-40c9-86e8-1d5666324ae1","ref_index":1,"cited_arxiv_id":"2103.14030","is_internal_anchor":true},{"doi":"","year":2017,"title":"In Advances in Neural Information Processing Systems 30 (NIPS 2017)","work_id":"3f79b81f-78b7-4f3a-bb04-c8f238996bb8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"https://arxiv.org/abs/2510.27517 5","work_id":"49a43e61-b266-4b12-9f83-41d8024d2a5b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":3,"snapshot_sha256":"f864819d64965bfa3de9eb0f1129a814a9d946b11a04f8ff5973a1e944973b57","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2f05c689ad2a35c2b7371a74ecf6f193f0a15c9165ffdf79bd7dcc902a8f492b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"11fc26fb-a73e-4ed9-8d93-e541e8b6a280"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p/6pU9X1PNqYrV9H9i1lSFNWAmipRfDR/LMgGuSi8RM0Z5f88GMOS8CMIKheUXBYTascI6ZxCWKw5B9pnAvVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:20:23.994294Z"},"content_sha256":"49e28f45945c2138dd0df666bbea2233e0e76991e589d3370a49a36cba1485e8","schema_version":"1.0","event_id":"sha256:49e28f45945c2138dd0df666bbea2233e0e76991e589d3370a49a36cba1485e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FT3R4XQLCTVWR523CFX6J7PK6/bundle.json","state_url":"https://pith.science/pith/7FT3R4XQLCTVWR523CFX6J7PK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FT3R4XQLCTVWR523CFX6J7PK6/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":"2026-05-31T10:20:23Z","links":{"resolver":"https://pith.science/pith/7FT3R4XQLCTVWR523CFX6J7PK6","bundle":"https://pith.science/pith/7FT3R4XQLCTVWR523CFX6J7PK6/bundle.json","state":"https://pith.science/pith/7FT3R4XQLCTVWR523CFX6J7PK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FT3R4XQLCTVWR523CFX6J7PK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7FT3R4XQLCTVWR523CFX6J7PK6","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":"7be0647020a3e2f740d0c52257ebe1424a07ad4192c39bca638bfe6a4f08e8eb","cross_cats_sorted":["cs.DC","cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-13T11:02:27Z","title_canon_sha256":"b84f5f8f42baeca84db57e33ff3c38b3c6033eba735ed50b67230699d01c378f"},"schema_version":"1.0","source":{"id":"2605.13343","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13343","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13343v2","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13343","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"7FT3R4XQLCTV","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"7FT3R4XQLCTVWR52","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"7FT3R4XQ","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:49e28f45945c2138dd0df666bbea2233e0e76991e589d3370a49a36cba1485e8","target":"graph","created_at":"2026-05-18T02:44:48Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"On stiff multiphase Poisson systems (up to 100:1 density contrast, N = 1,024-16,384), the solver runs from ~143 to ~21 fps. At N = 8,192, it reaches 17.9 ms/frame, with 2.2x speedup over GPU Jacobi, ~28x over GPU IC/DILU (AMGX multicolor_dilu), and 2.7x over neural SPAI retrained per scale on the same benchmark."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The weak-admissibility H-matrix partition plus highway connections in the transformer are assumed to capture long-range couplings sufficiently for the cosine-Hutchinson objective to produce a preconditioner that improves PCG convergence on irregular spectra without post-hoc tuning."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A hierarchical transformer preconditioner with H-matrix structure and cosine-Hutchinson training delivers up to 2.7x speedup over prior neural methods on stiff multiphase Poisson systems up to N=16384."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization."}],"snapshot_sha256":"5d4cd04566f98bede90cf530938c2db68986170d94e5536a8f180fbf033cd4b5"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2f05c689ad2a35c2b7371a74ecf6f193f0a15c9165ffdf79bd7dcc902a8f492b"},"paper":{"abstract_excerpt":"Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We introduce the Hierarchical Transformer Preconditioner, a neural preconditioner anchored to a weak-admissibility H-matrix partition. The partition provides a multiscale structural prior (dense diagonal leaves plus coarsening off-diagonal tiles) that enables full-graph approximate-inverse computation with O(N) scaling at fixed block sizes. The network models the","authors_text":"Carl Osborne, Crystal Owens, Minghao Guo, Wojciech Matusik","cross_cats":["cs.DC","cs.LG","cs.NA","math.NA"],"headline":"A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-13T11:02:27Z","title":"Hierarchical Transformer Preconditioning for Interactive Physics Simulation"},"references":{"count":3,"internal_anchors":1,"resolved_work":3,"sample":[{"cited_arxiv_id":"2103.14030","doi":"","is_internal_anchor":true,"ref_index":1,"title":"Swin Transformer: Hierarchical Vision Transformer using Shifted Windows","work_id":"d6d2cf36-1b48-40c9-86e8-1d5666324ae1","year":2021},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"In Advances in Neural Information Processing Systems 30 (NIPS 2017)","work_id":"3f79b81f-78b7-4f3a-bb04-c8f238996bb8","year":2017},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"https://arxiv.org/abs/2510.27517 5","work_id":"49a43e61-b266-4b12-9f83-41d8024d2a5b","year":2025}],"snapshot_sha256":"f864819d64965bfa3de9eb0f1129a814a9d946b11a04f8ff5973a1e944973b57"},"source":{"id":"2605.13343","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-15T02:39:58.435457Z","id":"11fc26fb-a73e-4ed9-8d93-e541e8b6a280","model_set":{"reader":"grok-4.3"},"one_line_summary":"A hierarchical transformer preconditioner with H-matrix structure and cosine-Hutchinson training delivers up to 2.7x speedup over prior neural methods on stiff multiphase Poisson systems up to N=16384.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A hierarchical transformer preconditioner solves stiff multiphase Poisson systems up to 28 times faster than standard GPU incomplete factorization.","strongest_claim":"On stiff multiphase Poisson systems (up to 100:1 density contrast, N = 1,024-16,384), the solver runs from ~143 to ~21 fps. At N = 8,192, it reaches 17.9 ms/frame, with 2.2x speedup over GPU Jacobi, ~28x over GPU IC/DILU (AMGX multicolor_dilu), and 2.7x over neural SPAI retrained per scale on the same benchmark.","weakest_assumption":"The weak-admissibility H-matrix partition plus highway connections in the transformer are assumed to capture long-range couplings sufficiently for the cosine-Hutchinson objective to produce a preconditioner that improves PCG convergence on irregular spectra without post-hoc tuning."}},"verdict_id":"11fc26fb-a73e-4ed9-8d93-e541e8b6a280"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:375c2fc5fafa4bf8e5365f70107fff39e4e3e9cb9bd29a9ebaa6fdba4268e796","target":"record","created_at":"2026-05-18T02:44:48Z","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":"7be0647020a3e2f740d0c52257ebe1424a07ad4192c39bca638bfe6a4f08e8eb","cross_cats_sorted":["cs.DC","cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2026-05-13T11:02:27Z","title_canon_sha256":"b84f5f8f42baeca84db57e33ff3c38b3c6033eba735ed50b67230699d01c378f"},"schema_version":"1.0","source":{"id":"2605.13343","kind":"arxiv","version":2}},"canonical_sha256":"f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f967b8f2f058a75b47bad88b7f27ef579e869232b8c275fa670ebf8bd73fa033","first_computed_at":"2026-05-18T02:44:48.366686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.366686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TNJ/qaQgT2rcaJ15seElSEybLNYlsdW++DNp64325ssMM8AZff/tWnVk9ZIz9QCP2GsFmMxFj1BG3ar6nZGxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.367061Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13343","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:375c2fc5fafa4bf8e5365f70107fff39e4e3e9cb9bd29a9ebaa6fdba4268e796","sha256:49e28f45945c2138dd0df666bbea2233e0e76991e589d3370a49a36cba1485e8"],"state_sha256":"273fe766eac117661d89604eb8b6f03b0c24a4e75355ce4c36108d8a8b1f69b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jCiWpbTR3/GBKFcHXiUYmDA9MlG8XnosvHFasdmuegVJnRAKwCiBWYRHbN0LSWLeJK/4k8meJvqkUbBNPiD9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:20:23.997745Z","bundle_sha256":"5f0b6457757c6efdb7e6ffdaf5e165c6f105c6b092a0501b1f6b1c4a35a24008"}}