{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","short_pith_number":"pith:HTSDV7OL","canonical_record":{"source":{"id":"2608.00760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-01T16:45:23Z","cross_cats_sorted":["cs.NA","physics.med-ph","stat.CO"],"title_canon_sha256":"6cb33600dda2cc1e4843423bc219e2a26abd7cd84176823f59a33a9a2df3e1d5","abstract_canon_sha256":"19d3e71b082f0abd2a9c130cedabe5f8b06ef5b75920d8096f79aa350250b8d7"},"schema_version":"1.0"},"canonical_sha256":"3ce43afdcb0dc2883f63dd0627d9ce5e9b621f61eef34557436a7e91822e8519","source":{"kind":"arxiv","id":"2608.00760","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00760","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00760v1","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00760","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"HTSDV7OLBXBI","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"HTSDV7OLBXBIQP3D","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"HTSDV7OL","created_at":"2026-08-04T01:54:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-01T16:45:23Z","cross_cats_sorted":["cs.NA","physics.med-ph","stat.CO"],"title_canon_sha256":"6cb33600dda2cc1e4843423bc219e2a26abd7cd84176823f59a33a9a2df3e1d5","abstract_canon_sha256":"19d3e71b082f0abd2a9c130cedabe5f8b06ef5b75920d8096f79aa350250b8d7"},"schema_version":"1.0"},"canonical_sha256":"3ce43afdcb0dc2883f63dd0627d9ce5e9b621f61eef34557436a7e91822e8519","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T01:54:53.717973Z","signature_b64":"EIcoUDBRAm1CfJV1wnAbG4ImKbEdx4G4RF59y/xEyYQZQiWPu+4VG4qcOaEaSBpTUm9T2r4JbAB4icZ0jll8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ce43afdcb0dc2883f63dd0627d9ce5e9b621f61eef34557436a7e91822e8519","last_reissued_at":"2026-08-04T01:54:53.715939Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T01:54:53.715939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00760","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":"2026-08-04T01:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5RwkNfiATbRr3QbGCtJkK4B9+vZ2xQuo2gFhsb0REcdmLckZIoS++bkwRejJn0aefWBA3vQgSe+sl/P6TDApDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:47:11.398498Z"},"content_sha256":"23e99e792918ec5cc802c89a2fd0ca63815df050985c6013bbec441957e33de2","schema_version":"1.0","event_id":"sha256:23e99e792918ec5cc802c89a2fd0ca63815df050985c6013bbec441957e33de2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Inference Using a Differentiable Multigrid Linear Solver","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.med-ph","stat.CO"],"primary_cat":"math.NA","authors_text":"Andr\\'es Ram\\'irez, David F\\\"oger, Dominik J\\\"ustel, Hanieh Zandinejad, Laurin S\\\"oding, Philipp Frank, Philipp Gschwandtner, Philipp Haim, Philipp Mertsch, Ralf Kissmann, Torsten A. En{\\ss}lin, Vo Hong Minh Phan","submitted_at":"2026-08-01T16:45:23Z","abstract_excerpt":"Gradient-based Bayesian inference methods require efficient access to Jacobian and adjoint-Jacobian operators of high-dimensional forward models. While multigrid solvers provide near-optimal complexity for elliptic partial differential equations, they are rarely available in forms compatible with automatic differentiation (AD). We develop a differentiable multigrid solver for steady-state diffusion-absorption problems and derive its adjoint operations analytically through the full multigrid hierarchy. The resulting solver, DMGS, is implemented in C++ and interfaced with JAX to provide efficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00760","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/2608.00760/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":"2026-08-04T01:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HoaebDf7czIYqbsuV1vmey9tF5nKm4JjoOc91VX6NVC02ss7PckliCAzEx4T7b6SDmvljXBVid0b16BN1C7ICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:47:11.399029Z"},"content_sha256":"3668d947f96990925b3c3cc063ac3d6bb667c1536f6cfd9c60603e7624d34d79","schema_version":"1.0","event_id":"sha256:3668d947f96990925b3c3cc063ac3d6bb667c1536f6cfd9c60603e7624d34d79"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1051/0004-6361/202449933 resolves to 'Nonparametric Bayesian reconstruction of Galactic magnetic fields using information field theory'. A reader following the printed text alone cannot reach it.","snippet":"Tsouros, Alexandros, Bendre, Abhijit B., Edenhofer, Gordian, Enßlin, Torsten, Frank, Philipp, Mastorakis, Michalis, Pavlidou, Vasiliki: Nonparametric bayesian reconstruction of galactic magnetic fields using information field theory - the i","arxiv_id":"2608.00760","detector":"doi_compliance","evidence":{"ref_index":40,"verdict_class":"incontrovertible","resolved_title":"Nonparametric Bayesian reconstruction of Galactic magnetic fields using information field theory","printed_excerpt":"10.1051/0004-6361/20","reconstructed_doi":"10.1051/0004-6361/202449933"},"severity":"advisory","ref_index":40,"audited_at":"2026-08-05T00:29:42.301539Z","event_type":"pith.integrity.v1","detected_doi":"10.1051/0004-6361/202449933","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"b99601149cef8136f536ee3ee5f67a77d60a02839459b56de05a0df5c6cccb1b","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Nonparametric Bayesian reconstruction of Galactic magnetic fields using information field theory","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17985,"payload_sha256":"12ef694fdd071532cc55a4b837afa6d4c952d608c1a906dc13625b409f2ecd9b","signature_b64":"4pYbfVDXUY1NAXxEHeGpbdkT8WJ5EmKouTsQs8MA4iMeI8ijTq1detGtvDKNnv7KFS7jctHrmg6J3H/tfYLJDA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T00:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qtV9x4hdABvvqgepXs28YmoNebd/2mGDVkfRcLzaF1rHzS4diktFsRq6WVigS0YxUNO4fnP6zDBMS7DQY82xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:47:11.402034Z"},"content_sha256":"ca8561d9ed25141809e3470e1a3b477befa1f132ce461fa851b263ed7a20c10d","schema_version":"1.0","event_id":"sha256:ca8561d9ed25141809e3470e1a3b477befa1f132ce461fa851b263ed7a20c10d"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1002/andp.201800290 resolves to 'NIFT<scp>y</scp> 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC C'. A reader following the printed text alone cannot reach it.","snippet":"Steininger, T., Dixit, J., Frank, P., Greiner, M., Hutschenreuter, S., Knollm ¨uller, J., Leike, R., Porqueres, N., Pumpe, D., Reinecke, M., Sraml, M., Varady, C., Enßlin, T.: NIFTy 3 - Numerical Information Field Theory: A Python Framework","arxiv_id":"2608.00760","detector":"doi_compliance","evidence":{"ref_index":35,"verdict_class":"incontrovertible","resolved_title":"NIFT<scp>y</scp> 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters","printed_excerpt":"10.1002/andp.20180","reconstructed_doi":"10.1002/andp.201800290"},"severity":"advisory","ref_index":35,"audited_at":"2026-08-05T00:29:42.301539Z","event_type":"pith.integrity.v1","detected_doi":"10.1002/andp.201800290","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"7024d3854aaf8a4b9a630e8b6eda8e92fb52a5d776f07db910f50555fd94dd0f","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"NIFT<scp>y</scp> 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17984,"payload_sha256":"fb10cc486752d7bb705ee387834a9401dd03e90ac40707ddc05d2034d6495e8e","signature_b64":"73o5IYLnIjqnMa3DOSr25CqZ1mh/VTErZQHjUqStYzaWJw0d1VE/vLEN0uIO5YY2ZTc/LsLUYmvKhfe0IrxgBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T00:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdj3CvunHz37BCJx4b2RtrC16Y5ALlt8xNdx31GeCzP/adrR1lSLkPNxHyZKl09Gh72hdCT5Z9jYzfbA9w9vBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:47:11.402436Z"},"content_sha256":"4d4b35da25f9b2482a625660bbfb444b6a497723ba366b29e63a6e323202c301","schema_version":"1.0","event_id":"sha256:4d4b35da25f9b2482a625660bbfb444b6a497723ba366b29e63a6e323202c301"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1051/0004-6361/202451361 resolves to 'Spatially coherent 3D distributions of HI and CO in the Milky Way'. A reader following the printed text alone cannot reach it.","snippet":"S ¨oding, L., Edenhofer, G., Enßlin, T.A., Frank, P., Kissmann, R., Phan, V .H.M., Ram ´ırez, A., Zandinejad, H., Mertsch, P.: Spatially coherent 3D distributions of HI and CO in the Milky Way. A&A693, A139 (2025). DOI 10.1051/0004-6361/202","arxiv_id":"2608.00760","detector":"doi_compliance","evidence":{"ref_index":34,"verdict_class":"incontrovertible","resolved_title":"Spatially coherent 3D distributions of HI and CO in the Milky Way","printed_excerpt":"10.1051/0004-6361/2024","reconstructed_doi":"10.1051/0004-6361/202451361"},"severity":"advisory","ref_index":34,"audited_at":"2026-08-05T00:29:42.301539Z","event_type":"pith.integrity.v1","detected_doi":"10.1051/0004-6361/202451361","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"70cd4c8cdb9883eab4192faa73b48f949917a8303269a828cd20dd504293d439","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Spatially coherent 3D distributions of HI and CO in the Milky Way","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17983,"payload_sha256":"acae340cc389c89fe8542d33dc8586cd298dc2075b740c11e9ab3bfa4afbaf4f","signature_b64":"E/tgp7uNDlHrAnvPeFOoyNV0HiSo9zKjWhshBlll8dxDEn1LrefMKrV9q88FftvzWnCJKcH8Z5hH1g9S6CxBDg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T00:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tqL/hzUFpMLUf1z9xTbv3vAEendalu+6dpJ8k1Wz5bEj/W4WYVut0rAbBe7tyGx39VvPp9Be1vyAGQGjoeWxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:47:11.402808Z"},"content_sha256":"2820707f0e4048a0d9d76f6dfe5968b22ff5247ffe92a41fbc67e2478fe790f1","schema_version":"1.0","event_id":"sha256:2820707f0e4048a0d9d76f6dfe5968b22ff5247ffe92a41fbc67e2478fe790f1"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1051/0004-6361/202347628 resolves to 'A parsec-scale Galactic 3D dust map out to 1.25 kpc from the Sun'. A reader following the printed text alone cannot reach it.","snippet":"Edenhofer, Gordian, Zucker, Catherine, Frank, Philipp, Saydjari, Andrew K., Speagle, Joshua S., Finkbeiner, Douglas, Enßlin, Torsten A.: A parsec-scale galactic 3d dust map out to 1.25 kpc from the sun. A&A685, A82 (2024). DOI 10.1051/0004-","arxiv_id":"2608.00760","detector":"doi_compliance","evidence":{"ref_index":12,"verdict_class":"incontrovertible","resolved_title":"A parsec-scale Galactic 3D dust map out to 1.25 kpc from the Sun","printed_excerpt":"10.1051/0004-6","reconstructed_doi":"10.1051/0004-6361/202347628"},"severity":"advisory","ref_index":12,"audited_at":"2026-08-05T00:29:42.301539Z","event_type":"pith.integrity.v1","detected_doi":"10.1051/0004-6361/202347628","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"29fd3897111d5e0a8635c1e41ff670bc806819e116ba6492683eb2f04e6d9c8b","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"A parsec-scale Galactic 3D dust map out to 1.25 kpc from the Sun","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17982,"payload_sha256":"cc92e193118eb8fa068d595074b0da98e5e4a8999a18f78c09d8de8b6cfb9979","signature_b64":"iweuYgL+UHOBEr/UV/c3nRkKpJUZsh/aictE8jc76lqOEXCuPuj5zEHpPywrQIsm+1JGTRO6uG9F30+Yq0tEBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T00:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/rkWfwFcTqmjY9eyX2A+3p39qWXU1Y2kNgJ+I4oLXnxdsk+ztCZrD9OkWlJ9/M7SqbzfIMSkfq3/rUyx584CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:47:11.403176Z"},"content_sha256":"2986fa6ae6a7b4e09f92cefc3f40a7a4de55299c0fad197d70f06103ba22a422","schema_version":"1.0","event_id":"sha256:2986fa6ae6a7b4e09f92cefc3f40a7a4de55299c0fad197d70f06103ba22a422"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2/bundle.json","state_url":"https://pith.science/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2/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":"2026-08-05T14:47:11Z","links":{"resolver":"https://pith.science/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2","bundle":"https://pith.science/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2/bundle.json","state":"https://pith.science/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTSDV7OLBXBIQP3D3UDCPWOOL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HTSDV7OLBXBIQP3D3UDCPWOOL2","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"19d3e71b082f0abd2a9c130cedabe5f8b06ef5b75920d8096f79aa350250b8d7","cross_cats_sorted":["cs.NA","physics.med-ph","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-01T16:45:23Z","title_canon_sha256":"6cb33600dda2cc1e4843423bc219e2a26abd7cd84176823f59a33a9a2df3e1d5"},"schema_version":"1.0","source":{"id":"2608.00760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00760","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00760v1","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00760","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"HTSDV7OLBXBI","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"HTSDV7OLBXBIQP3D","created_at":"2026-08-04T01:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"HTSDV7OL","created_at":"2026-08-04T01:54:53Z"}],"graph_snapshots":[{"event_id":"sha256:3668d947f96990925b3c3cc063ac3d6bb667c1536f6cfd9c60603e7624d34d79","target":"graph","created_at":"2026-08-04T01:54:53Z","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/2608.00760/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient-based Bayesian inference methods require efficient access to Jacobian and adjoint-Jacobian operators of high-dimensional forward models. While multigrid solvers provide near-optimal complexity for elliptic partial differential equations, they are rarely available in forms compatible with automatic differentiation (AD). We develop a differentiable multigrid solver for steady-state diffusion-absorption problems and derive its adjoint operations analytically through the full multigrid hierarchy. The resulting solver, DMGS, is implemented in C++ and interfaced with JAX to provide efficien","authors_text":"Andr\\'es Ram\\'irez, David F\\\"oger, Dominik J\\\"ustel, Hanieh Zandinejad, Laurin S\\\"oding, Philipp Frank, Philipp Gschwandtner, Philipp Haim, Philipp Mertsch, Ralf Kissmann, Torsten A. En{\\ss}lin, Vo Hong Minh Phan","cross_cats":["cs.NA","physics.med-ph","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-01T16:45:23Z","title":"Variational Inference Using a Differentiable Multigrid Linear Solver"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00760","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":"sha256:23e99e792918ec5cc802c89a2fd0ca63815df050985c6013bbec441957e33de2","target":"record","created_at":"2026-08-04T01:54:53Z","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":"19d3e71b082f0abd2a9c130cedabe5f8b06ef5b75920d8096f79aa350250b8d7","cross_cats_sorted":["cs.NA","physics.med-ph","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-08-01T16:45:23Z","title_canon_sha256":"6cb33600dda2cc1e4843423bc219e2a26abd7cd84176823f59a33a9a2df3e1d5"},"schema_version":"1.0","source":{"id":"2608.00760","kind":"arxiv","version":1}},"canonical_sha256":"3ce43afdcb0dc2883f63dd0627d9ce5e9b621f61eef34557436a7e91822e8519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ce43afdcb0dc2883f63dd0627d9ce5e9b621f61eef34557436a7e91822e8519","first_computed_at":"2026-08-04T01:54:53.715939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T01:54:53.715939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EIcoUDBRAm1CfJV1wnAbG4ImKbEdx4G4RF59y/xEyYQZQiWPu+4VG4qcOaEaSBpTUm9T2r4JbAB4icZ0jll8Cw==","signature_status":"signed_v1","signed_at":"2026-08-04T01:54:53.717973Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00760","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:2820707f0e4048a0d9d76f6dfe5968b22ff5247ffe92a41fbc67e2478fe790f1","sha256:2986fa6ae6a7b4e09f92cefc3f40a7a4de55299c0fad197d70f06103ba22a422","sha256:4d4b35da25f9b2482a625660bbfb444b6a497723ba366b29e63a6e323202c301","sha256:ca8561d9ed25141809e3470e1a3b477befa1f132ce461fa851b263ed7a20c10d"]}],"invalid_events":[],"applied_event_ids":["sha256:23e99e792918ec5cc802c89a2fd0ca63815df050985c6013bbec441957e33de2","sha256:3668d947f96990925b3c3cc063ac3d6bb667c1536f6cfd9c60603e7624d34d79"],"state_sha256":"94cd0a675276031b8b3f8bf50aa912b1316941e107b31168d00fdfa2d593c397"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tw+lcGP+yXIWqLD5/uuTgQHz3R5qzn1yquvRoW6v7J2L8QOXDjIohhIP+aOZkmoLjDeNQc8+bypN5uiYql3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:47:11.406502Z","bundle_sha256":"68c485e6caa238d42e8fef312fc19abaef1e04cc8d5809d309333be8f0e52b6b"}}