{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JJZW7YD26DXDCOKKWLWUZXTOBO","short_pith_number":"pith:JJZW7YD2","canonical_record":{"source":{"id":"1409.8583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T15:11:37Z","cross_cats_sorted":[],"title_canon_sha256":"7c8ab7d67796081f6a6793a68f711a7cd8ea601612435ef9ca309f3b5c152d62","abstract_canon_sha256":"c2eb49b260d552204e534cef70112573a19932f32cf38b6034ed4030ac63b011"},"schema_version":"1.0"},"canonical_sha256":"4a736fe07af0ee31394ab2ed4cde6e0b9a008527ace8e051d8e9348726683ed7","source":{"kind":"arxiv","id":"1409.8583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8583","created_at":"2026-05-18T02:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8583v1","created_at":"2026-05-18T02:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8583","created_at":"2026-05-18T02:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"JJZW7YD26DXD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JJZW7YD26DXDCOKK","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JJZW7YD2","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JJZW7YD26DXDCOKKWLWUZXTOBO","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T15:11:37Z","cross_cats_sorted":[],"title_canon_sha256":"7c8ab7d67796081f6a6793a68f711a7cd8ea601612435ef9ca309f3b5c152d62","abstract_canon_sha256":"c2eb49b260d552204e534cef70112573a19932f32cf38b6034ed4030ac63b011"},"schema_version":"1.0"},"canonical_sha256":"4a736fe07af0ee31394ab2ed4cde6e0b9a008527ace8e051d8e9348726683ed7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:24.178642Z","signature_b64":"5eCP1r9zLiXHJvSh/w7l3/HO4ilJyB6NoAoIuG0s2zSI5SkKrCXy/PqDgwOhcSS6DV14gS355a/N6ZDfbtk9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a736fe07af0ee31394ab2ed4cde6e0b9a008527ace8e051d8e9348726683ed7","last_reissued_at":"2026-05-18T02:41:24.178147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:24.178147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8583","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":"2026-05-18T02:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJ2H61UKbhX/lgnKILHGaS9oTJhOqcZDLHZPwN0zOEvMmiOm1lJdJJQC/TnRPWowusKCFDjYzTZIk/ljXoQwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:24:32.307967Z"},"content_sha256":"c4c6aa3e9e80ee977009aa5d3c7eaa614434b5f645bcd362b993e44da5028aaa","schema_version":"1.0","event_id":"sha256:c4c6aa3e9e80ee977009aa5d3c7eaa614434b5f645bcd362b993e44da5028aaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JJZW7YD26DXDCOKKWLWUZXTOBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal second order diagonally implicit SSP Runge--Kutta methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Adri\\'an N\\'emeth, Tiham\\'er A. Kocsis","submitted_at":"2014-09-30T15:11:37Z","abstract_excerpt":"Optimal Strong Stability Preserving (SSP) Runge--Kutta methods has been widely investegated in the last decade and many open conjectures have been formulated. The iterated implicit midpoint rule has been observed numerically optimal in large classes of second order methods, and was proven to be optimal for some small cases, but no general proof was known so far to show its optimality. In this paper we show a new approach to analytically investigate this problem and determine the unique optimal methods in the class of second order diagonally implicit Runge--Kutta methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8583","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":"2026-05-18T02:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjKG8ccEj9YNeII7rryB6Udnw1hIbqF0OE3X/0Gfdm0OtyX0whiKoi4i+R0nRl6oPGhGDJy2ZKkM1s66Fu7/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:24:32.308343Z"},"content_sha256":"5e181966c854d12cd0cf85fa451920c08ecb295978acc0fd0b12418221ab57c6","schema_version":"1.0","event_id":"sha256:5e181966c854d12cd0cf85fa451920c08ecb295978acc0fd0b12418221ab57c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJZW7YD26DXDCOKKWLWUZXTOBO/bundle.json","state_url":"https://pith.science/pith/JJZW7YD26DXDCOKKWLWUZXTOBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJZW7YD26DXDCOKKWLWUZXTOBO/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":"2026-05-31T12:24:32Z","links":{"resolver":"https://pith.science/pith/JJZW7YD26DXDCOKKWLWUZXTOBO","bundle":"https://pith.science/pith/JJZW7YD26DXDCOKKWLWUZXTOBO/bundle.json","state":"https://pith.science/pith/JJZW7YD26DXDCOKKWLWUZXTOBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJZW7YD26DXDCOKKWLWUZXTOBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JJZW7YD26DXDCOKKWLWUZXTOBO","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":"c2eb49b260d552204e534cef70112573a19932f32cf38b6034ed4030ac63b011","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T15:11:37Z","title_canon_sha256":"7c8ab7d67796081f6a6793a68f711a7cd8ea601612435ef9ca309f3b5c152d62"},"schema_version":"1.0","source":{"id":"1409.8583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8583","created_at":"2026-05-18T02:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8583v1","created_at":"2026-05-18T02:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8583","created_at":"2026-05-18T02:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"JJZW7YD26DXD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JJZW7YD26DXDCOKK","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JJZW7YD2","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:5e181966c854d12cd0cf85fa451920c08ecb295978acc0fd0b12418221ab57c6","target":"graph","created_at":"2026-05-18T02:41:24Z","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":"Optimal Strong Stability Preserving (SSP) Runge--Kutta methods has been widely investegated in the last decade and many open conjectures have been formulated. The iterated implicit midpoint rule has been observed numerically optimal in large classes of second order methods, and was proven to be optimal for some small cases, but no general proof was known so far to show its optimality. In this paper we show a new approach to analytically investigate this problem and determine the unique optimal methods in the class of second order diagonally implicit Runge--Kutta methods.","authors_text":"Adri\\'an N\\'emeth, Tiham\\'er A. Kocsis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T15:11:37Z","title":"Optimal second order diagonally implicit SSP Runge--Kutta methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8583","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:c4c6aa3e9e80ee977009aa5d3c7eaa614434b5f645bcd362b993e44da5028aaa","target":"record","created_at":"2026-05-18T02:41:24Z","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":"c2eb49b260d552204e534cef70112573a19932f32cf38b6034ed4030ac63b011","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T15:11:37Z","title_canon_sha256":"7c8ab7d67796081f6a6793a68f711a7cd8ea601612435ef9ca309f3b5c152d62"},"schema_version":"1.0","source":{"id":"1409.8583","kind":"arxiv","version":1}},"canonical_sha256":"4a736fe07af0ee31394ab2ed4cde6e0b9a008527ace8e051d8e9348726683ed7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a736fe07af0ee31394ab2ed4cde6e0b9a008527ace8e051d8e9348726683ed7","first_computed_at":"2026-05-18T02:41:24.178147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:24.178147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5eCP1r9zLiXHJvSh/w7l3/HO4ilJyB6NoAoIuG0s2zSI5SkKrCXy/PqDgwOhcSS6DV14gS355a/N6ZDfbtk9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:24.178642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4c6aa3e9e80ee977009aa5d3c7eaa614434b5f645bcd362b993e44da5028aaa","sha256:5e181966c854d12cd0cf85fa451920c08ecb295978acc0fd0b12418221ab57c6"],"state_sha256":"6d83a7a25e53453a29a7ecfda9c0cc65616459861c19908c0b0383aeffdbacff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PcpGk6eVlK2uyVIExIwekcy5XtZH3oUf5G6TgTo6UznxB2rNy4nMYHNrOiVMmThqQQ5nmb16jqGd2q4h18rlAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:24:32.310787Z","bundle_sha256":"439bbcdabf90e32164e58f33feb529cb4cd0a812de853c42cf58639ae3ccca7a"}}