{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TXBXGJUDEEUZSUMG7U44XL3MCZ","short_pith_number":"pith:TXBXGJUD","canonical_record":{"source":{"id":"2506.08444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-10T04:38:26Z","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"title_canon_sha256":"23fa899e6f4d2991806f3e1e4a9b896af8d2e6d11023a414a0a8b18430b4640c","abstract_canon_sha256":"265fa1e44ec02a0375222b81415980adad1b4f9672504bea7eead64bd96a7a3c"},"schema_version":"1.0"},"canonical_sha256":"9dc37326832129995186fd39cbaf6c1662b48b8b41c684ee09f5bd2d65fd538a","source":{"kind":"arxiv","id":"2506.08444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08444","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08444v1","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08444","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"TXBXGJUDEEUZ","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"TXBXGJUDEEUZSUMG","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"TXBXGJUD","created_at":"2026-07-05T11:18:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TXBXGJUDEEUZSUMG7U44XL3MCZ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.08444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-10T04:38:26Z","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"title_canon_sha256":"23fa899e6f4d2991806f3e1e4a9b896af8d2e6d11023a414a0a8b18430b4640c","abstract_canon_sha256":"265fa1e44ec02a0375222b81415980adad1b4f9672504bea7eead64bd96a7a3c"},"schema_version":"1.0"},"canonical_sha256":"9dc37326832129995186fd39cbaf6c1662b48b8b41c684ee09f5bd2d65fd538a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:49.589836Z","signature_b64":"myg/eXpecWGfFmOvBWmkchS2Kwc9lGhlkMbZJ5iTmFGb+36hbl95rKcPiLYaF/bD1UxO3ClilVE9XVNtLJFIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dc37326832129995186fd39cbaf6c1662b48b8b41c684ee09f5bd2d65fd538a","last_reissued_at":"2026-07-05T11:18:49.589435Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:49.589435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.08444","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":"2026-07-05T11:18:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"br6hxUZ4J1+feyvXoXKHxzQidG3av620bRpsDu0qvnLh2E0jm7/FZ6EXvvaniQJ7ucP2/9br23TxHyAP0n5LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T21:30:38.186929Z"},"content_sha256":"d5b52d66569bcfca69648beca1a104420a1ed3686627da159c9febc48b47a2b8","schema_version":"1.0","event_id":"sha256:d5b52d66569bcfca69648beca1a104420a1ed3686627da159c9febc48b47a2b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TXBXGJUDEEUZSUMG7U44XL3MCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"2N-storage Runge-Kutta methods: c-reflection symmetry and factorization of the Butcher tableau","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","hep-lat","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Alexei Bazavov","submitted_at":"2025-06-10T04:38:26Z","abstract_excerpt":"Low-storage Runge-Kutta schemes of Williamson's type, so-called 2N-storage schemes, are further examined as a follow-up to the recent work. It is found that the augmented Butcher tableau factorizes into a product of matrices with special properties. Those properties reveal that the 2N-storage methods of the order of global accuracy less than five possess a symmetry, called c-reflection symmetry, i.e. most methods exist in pairs. A transformation that relates the Butcher tableaux of the pairs is found and the fact that the c-reflected method satisfies the same order conditions as the original o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08444","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/2506.08444/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":"2026-07-05T11:18:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQUGS+eXu7xThGks/adeJ6Xt0ckqpdSrCSNMBYEL9CBM2rAO+hrFu4Tt84JrBOGgVFJK9VlUhn1JhobMgVoBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T21:30:38.187828Z"},"content_sha256":"2900a7da468c68c2863581c3126b2b41cf3874dcc3f80372dcd7520546cd1b35","schema_version":"1.0","event_id":"sha256:2900a7da468c68c2863581c3126b2b41cf3874dcc3f80372dcd7520546cd1b35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ/bundle.json","state_url":"https://pith.science/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ/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":"2026-08-07T21:30:38Z","links":{"resolver":"https://pith.science/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ","bundle":"https://pith.science/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ/bundle.json","state":"https://pith.science/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXBXGJUDEEUZSUMG7U44XL3MCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TXBXGJUDEEUZSUMG7U44XL3MCZ","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":"265fa1e44ec02a0375222b81415980adad1b4f9672504bea7eead64bd96a7a3c","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-10T04:38:26Z","title_canon_sha256":"23fa899e6f4d2991806f3e1e4a9b896af8d2e6d11023a414a0a8b18430b4640c"},"schema_version":"1.0","source":{"id":"2506.08444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08444","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08444v1","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08444","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"TXBXGJUDEEUZ","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"TXBXGJUDEEUZSUMG","created_at":"2026-07-05T11:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"TXBXGJUD","created_at":"2026-07-05T11:18:49Z"}],"graph_snapshots":[{"event_id":"sha256:2900a7da468c68c2863581c3126b2b41cf3874dcc3f80372dcd7520546cd1b35","target":"graph","created_at":"2026-07-05T11:18:49Z","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/2506.08444/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-storage Runge-Kutta schemes of Williamson's type, so-called 2N-storage schemes, are further examined as a follow-up to the recent work. It is found that the augmented Butcher tableau factorizes into a product of matrices with special properties. Those properties reveal that the 2N-storage methods of the order of global accuracy less than five possess a symmetry, called c-reflection symmetry, i.e. most methods exist in pairs. A transformation that relates the Butcher tableaux of the pairs is found and the fact that the c-reflected method satisfies the same order conditions as the original o","authors_text":"Alexei Bazavov","cross_cats":["cs.NA","hep-lat","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-10T04:38:26Z","title":"2N-storage Runge-Kutta methods: c-reflection symmetry and factorization of the Butcher tableau"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08444","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:d5b52d66569bcfca69648beca1a104420a1ed3686627da159c9febc48b47a2b8","target":"record","created_at":"2026-07-05T11:18:49Z","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":"265fa1e44ec02a0375222b81415980adad1b4f9672504bea7eead64bd96a7a3c","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-10T04:38:26Z","title_canon_sha256":"23fa899e6f4d2991806f3e1e4a9b896af8d2e6d11023a414a0a8b18430b4640c"},"schema_version":"1.0","source":{"id":"2506.08444","kind":"arxiv","version":1}},"canonical_sha256":"9dc37326832129995186fd39cbaf6c1662b48b8b41c684ee09f5bd2d65fd538a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dc37326832129995186fd39cbaf6c1662b48b8b41c684ee09f5bd2d65fd538a","first_computed_at":"2026-07-05T11:18:49.589435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:49.589435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"myg/eXpecWGfFmOvBWmkchS2Kwc9lGhlkMbZJ5iTmFGb+36hbl95rKcPiLYaF/bD1UxO3ClilVE9XVNtLJFIAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:49.589836Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5b52d66569bcfca69648beca1a104420a1ed3686627da159c9febc48b47a2b8","sha256:2900a7da468c68c2863581c3126b2b41cf3874dcc3f80372dcd7520546cd1b35"],"state_sha256":"e135d717c5d0f9f03ca4cab17ab9096cbf497b4f367514c1da709a5ef6c2a1ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"249jtkAJd8R0G8NVMA1og63mZGajiwpBj0xO1ZTHmx/kAR/MnhORE07DEM7zpNJl3E3EA1L7M11QbCn03pYEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T21:30:38.193690Z","bundle_sha256":"5c5a81966ab74bc34b8cf8467fa159cd5e5b12b86c7db1374b8cda09992cb610"}}