{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CPNFA2RHS5J3HSLBVQXEIZZUO2","short_pith_number":"pith:CPNFA2RH","canonical_record":{"source":{"id":"1712.03971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-11T19:00:13Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"2cde26d5c5b41451dd9cae3096df89d92d98a22dba1ce9cb2a853e23200d1a2e","abstract_canon_sha256":"e4fd79b43a015d72d93bf4e62bd08cbb58457cc68a8369a242e370e299cc02ec"},"schema_version":"1.0"},"canonical_sha256":"13da506a279753b3c961ac2e446734768201941f0289e346508438aced9542aa","source":{"kind":"arxiv","id":"1712.03971","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03971","created_at":"2026-05-17T23:48:11Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03971v2","created_at":"2026-05-17T23:48:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03971","created_at":"2026-05-17T23:48:11Z"},{"alias_kind":"pith_short_12","alias_value":"CPNFA2RHS5J3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CPNFA2RHS5J3HSLB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CPNFA2RH","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CPNFA2RHS5J3HSLBVQXEIZZUO2","target":"record","payload":{"canonical_record":{"source":{"id":"1712.03971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-11T19:00:13Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"2cde26d5c5b41451dd9cae3096df89d92d98a22dba1ce9cb2a853e23200d1a2e","abstract_canon_sha256":"e4fd79b43a015d72d93bf4e62bd08cbb58457cc68a8369a242e370e299cc02ec"},"schema_version":"1.0"},"canonical_sha256":"13da506a279753b3c961ac2e446734768201941f0289e346508438aced9542aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:11.918332Z","signature_b64":"tR5PQ9tUWdMTum6QdUdOy5V5TN/UcYBc71PQqNyCfX0szVXLuLEhy0iGvcv6qsSlP6bYHO5yk/M9GVEnQqeNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13da506a279753b3c961ac2e446734768201941f0289e346508438aced9542aa","last_reissued_at":"2026-05-17T23:48:11.917576Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:11.917576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.03971","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":"2026-05-17T23:48:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feIrNWaAqo8tYevFbN8qk32YMdWclYxLLRfjAjVveAl/lRui0czOyZxSsTKRUZv3ptAlErjnX7BF2YMAdYG7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:08:33.627848Z"},"content_sha256":"c05e759abd7c41872dd99c82f92648201aec6177fb74ecd1ba2a50e7113275b1","schema_version":"1.0","event_id":"sha256:c05e759abd7c41872dd99c82f92648201aec6177fb74ecd1ba2a50e7113275b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CPNFA2RHS5J3HSLBVQXEIZZUO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Stephen O'Sullivan","submitted_at":"2017-12-11T19:00:13Z","abstract_excerpt":"In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in the imaginary direction as an increasing function of Gegenbauer parameter. Consequently, the polynomials are naturally suited to the construction of high order stabilized Runge-Kutta (SRK) explicit methods for systems of PDEs of mixed hyperbolic-parabolic type.\n  We present SRK methods composed of $L$ ordered forward Euler stages, with complex-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03971","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":"2026-05-17T23:48:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ei/VzqiCFJTPCmRVNaN3hLNfRUnG+3zsdSikVhEHRBWbRvBvv/iyUlIJu+rOKbJUwPdOuRK2JnLblJxCHnqSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:08:33.628188Z"},"content_sha256":"b39116f7e76b4d67cedfa342d3fe6df1db52e82330fe590458453e9ed1fb0b9e","schema_version":"1.0","event_id":"sha256:b39116f7e76b4d67cedfa342d3fe6df1db52e82330fe590458453e9ed1fb0b9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2/bundle.json","state_url":"https://pith.science/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2/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":"2026-06-09T01:08:33Z","links":{"resolver":"https://pith.science/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2","bundle":"https://pith.science/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2/bundle.json","state":"https://pith.science/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPNFA2RHS5J3HSLBVQXEIZZUO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CPNFA2RHS5J3HSLBVQXEIZZUO2","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":"e4fd79b43a015d72d93bf4e62bd08cbb58457cc68a8369a242e370e299cc02ec","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-11T19:00:13Z","title_canon_sha256":"2cde26d5c5b41451dd9cae3096df89d92d98a22dba1ce9cb2a853e23200d1a2e"},"schema_version":"1.0","source":{"id":"1712.03971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03971","created_at":"2026-05-17T23:48:11Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03971v2","created_at":"2026-05-17T23:48:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03971","created_at":"2026-05-17T23:48:11Z"},{"alias_kind":"pith_short_12","alias_value":"CPNFA2RHS5J3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CPNFA2RHS5J3HSLB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CPNFA2RH","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:b39116f7e76b4d67cedfa342d3fe6df1db52e82330fe590458453e9ed1fb0b9e","target":"graph","created_at":"2026-05-17T23:48:11Z","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, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in the imaginary direction as an increasing function of Gegenbauer parameter. Consequently, the polynomials are naturally suited to the construction of high order stabilized Runge-Kutta (SRK) explicit methods for systems of PDEs of mixed hyperbolic-parabolic type.\n  We present SRK methods composed of $L$ ordered forward Euler stages, with complex-","authors_text":"Stephen O'Sullivan","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-11T19:00:13Z","title":"Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03971","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:c05e759abd7c41872dd99c82f92648201aec6177fb74ecd1ba2a50e7113275b1","target":"record","created_at":"2026-05-17T23:48:11Z","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":"e4fd79b43a015d72d93bf4e62bd08cbb58457cc68a8369a242e370e299cc02ec","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-11T19:00:13Z","title_canon_sha256":"2cde26d5c5b41451dd9cae3096df89d92d98a22dba1ce9cb2a853e23200d1a2e"},"schema_version":"1.0","source":{"id":"1712.03971","kind":"arxiv","version":2}},"canonical_sha256":"13da506a279753b3c961ac2e446734768201941f0289e346508438aced9542aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13da506a279753b3c961ac2e446734768201941f0289e346508438aced9542aa","first_computed_at":"2026-05-17T23:48:11.917576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:11.917576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tR5PQ9tUWdMTum6QdUdOy5V5TN/UcYBc71PQqNyCfX0szVXLuLEhy0iGvcv6qsSlP6bYHO5yk/M9GVEnQqeNBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:11.918332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c05e759abd7c41872dd99c82f92648201aec6177fb74ecd1ba2a50e7113275b1","sha256:b39116f7e76b4d67cedfa342d3fe6df1db52e82330fe590458453e9ed1fb0b9e"],"state_sha256":"455ed7b71d59eb92c0b5e18be9d71be6650f1a68417612866f3d7faf31ef3d12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGerNOK364FaRZTzeSx3hluoOKZ/G/KT0f+HpV20vRdiwYG9Hra6ji0kXQ3qtMs8lsZvDCTFWQnlmU84yyUZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:08:33.630065Z","bundle_sha256":"b66f884787a1303b1871822e03552d916bd11fc2371b6fbd835bc2406000c9e4"}}