{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WJ7QFCIOHDZ6BTENQA2YQLB4W4","short_pith_number":"pith:WJ7QFCIO","canonical_record":{"source":{"id":"1508.02045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-08-09T16:14:40Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.NA"],"title_canon_sha256":"8cd9693acedb91719c012c00eff406aa0a3f18384d8b9842c8742ceb30dd8c37","abstract_canon_sha256":"a83960e33f8d0ba1582107caa010a936f383fed2d9a36f2a60aaee8c5814a2b4"},"schema_version":"1.0"},"canonical_sha256":"b27f02890e38f3e0cc8d8035882c3cb7317648616be4f274fad1b5770f632e2f","source":{"kind":"arxiv","id":"1508.02045","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02045","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02045v2","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02045","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"WJ7QFCIOHDZ6","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJ7QFCIOHDZ6BTEN","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJ7QFCIO","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WJ7QFCIOHDZ6BTENQA2YQLB4W4","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-08-09T16:14:40Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.NA"],"title_canon_sha256":"8cd9693acedb91719c012c00eff406aa0a3f18384d8b9842c8742ceb30dd8c37","abstract_canon_sha256":"a83960e33f8d0ba1582107caa010a936f383fed2d9a36f2a60aaee8c5814a2b4"},"schema_version":"1.0"},"canonical_sha256":"b27f02890e38f3e0cc8d8035882c3cb7317648616be4f274fad1b5770f632e2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:04.994532Z","signature_b64":"cPqQTNj4eU5lVQbKSBnRC3h+/Fl7KRi4KFpe8AFIg+yssY6wdaNQ2FULV0fJjCg43wx49m/mDNncfDqpMCL0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27f02890e38f3e0cc8d8035882c3cb7317648616be4f274fad1b5770f632e2f","last_reissued_at":"2026-05-18T01:13:04.994121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:04.994121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02045","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":"2026-05-18T01:13:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d04PYWo6VUjSmGLuDV5zupqaGlavxmv5W6lwn3kbUl6sYFuwo2fsAMUbWSCysrQerT21za3M3va7mLVJ/E/sAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:47:56.013636Z"},"content_sha256":"81614a37c6190ffcaf4869d87277efe66bd5138b6d61b82d985ee7dd0505c1e3","schema_version":"1.0","event_id":"sha256:81614a37c6190ffcaf4869d87277efe66bd5138b6d61b82d985ee7dd0505c1e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WJ7QFCIOHDZ6BTENQA2YQLB4W4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Jan Zeman, Jaroslav Vond\\v{r}ejc, Nachiketa Mishra","submitted_at":"2015-08-09T16:14:40Z","abstract_excerpt":"In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is based on the Fourier-Galerkin method with exact and approximate integrations that has recently been shown to generalize the Lippmann-Schwinger setting of the original work by Moulinec and Suquet from 1994. It follows from this variational format that the ensuing system of linear equations can be solved by general-purpose iterative algorithms for symmetric posit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02045","kind":"arxiv","version":2},"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":"2026-05-18T01:13:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UxD51geFLK8W0nTtWsPgmUkeuRLPwrKDHs7OTJhNYdBBvuS9ktvUMhdowKKluw501P345Yrawc8q43awPqjpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:47:56.014340Z"},"content_sha256":"6814fae8cc81ef208b58a3ef0ae8ae970830e55e0b604da6df27378ef54dbc04","schema_version":"1.0","event_id":"sha256:6814fae8cc81ef208b58a3ef0ae8ae970830e55e0b604da6df27378ef54dbc04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4/bundle.json","state_url":"https://pith.science/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4/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":"2026-06-03T20:47:56Z","links":{"resolver":"https://pith.science/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4","bundle":"https://pith.science/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4/bundle.json","state":"https://pith.science/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJ7QFCIOHDZ6BTENQA2YQLB4W4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WJ7QFCIOHDZ6BTENQA2YQLB4W4","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":"a83960e33f8d0ba1582107caa010a936f383fed2d9a36f2a60aaee8c5814a2b4","cross_cats_sorted":["cond-mat.mtrl-sci","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-08-09T16:14:40Z","title_canon_sha256":"8cd9693acedb91719c012c00eff406aa0a3f18384d8b9842c8742ceb30dd8c37"},"schema_version":"1.0","source":{"id":"1508.02045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02045","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02045v2","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02045","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"WJ7QFCIOHDZ6","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJ7QFCIOHDZ6BTEN","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJ7QFCIO","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:6814fae8cc81ef208b58a3ef0ae8ae970830e55e0b604da6df27378ef54dbc04","target":"graph","created_at":"2026-05-18T01:13:04Z","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":"In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is based on the Fourier-Galerkin method with exact and approximate integrations that has recently been shown to generalize the Lippmann-Schwinger setting of the original work by Moulinec and Suquet from 1994. It follows from this variational format that the ensuing system of linear equations can be solved by general-purpose iterative algorithms for symmetric posit","authors_text":"Jan Zeman, Jaroslav Vond\\v{r}ejc, Nachiketa Mishra","cross_cats":["cond-mat.mtrl-sci","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-08-09T16:14:40Z","title":"A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02045","kind":"arxiv","version":2},"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":"sha256:81614a37c6190ffcaf4869d87277efe66bd5138b6d61b82d985ee7dd0505c1e3","target":"record","created_at":"2026-05-18T01:13:04Z","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":"a83960e33f8d0ba1582107caa010a936f383fed2d9a36f2a60aaee8c5814a2b4","cross_cats_sorted":["cond-mat.mtrl-sci","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-08-09T16:14:40Z","title_canon_sha256":"8cd9693acedb91719c012c00eff406aa0a3f18384d8b9842c8742ceb30dd8c37"},"schema_version":"1.0","source":{"id":"1508.02045","kind":"arxiv","version":2}},"canonical_sha256":"b27f02890e38f3e0cc8d8035882c3cb7317648616be4f274fad1b5770f632e2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b27f02890e38f3e0cc8d8035882c3cb7317648616be4f274fad1b5770f632e2f","first_computed_at":"2026-05-18T01:13:04.994121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:04.994121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPqQTNj4eU5lVQbKSBnRC3h+/Fl7KRi4KFpe8AFIg+yssY6wdaNQ2FULV0fJjCg43wx49m/mDNncfDqpMCL0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:04.994532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81614a37c6190ffcaf4869d87277efe66bd5138b6d61b82d985ee7dd0505c1e3","sha256:6814fae8cc81ef208b58a3ef0ae8ae970830e55e0b604da6df27378ef54dbc04"],"state_sha256":"45c9f5af72c715cb3ff2a517394165f8ea609eb8ef4d88490e7048c442da2ac6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ePv7src5/aCH2my1/VfkPizOPEBgqbykQGZ26qo3Zb0JdQyTAoLpz+Xvcj9pGVmXDSIl+A92vs7AxisRm964AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:47:56.016211Z","bundle_sha256":"edcab15b69298e5b0a1777f084ca3dd4903c1c6244549b6a1b334a2c6e2d27f3"}}