{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4WZ2BJUNIVF7GE35KEVXN5ZCD5","short_pith_number":"pith:4WZ2BJUN","canonical_record":{"source":{"id":"1701.06030","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T14:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"c0bb001d167350f52e71e3f02324404802bb806171ec449bc1afa787816bbfb7","abstract_canon_sha256":"b7fe9b382a8c908dc84f2eb1e4140445cd2f17800bb05cd532a6cb47deb7e901"},"schema_version":"1.0"},"canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","source":{"kind":"arxiv","id":"1701.06030","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06030","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06030v4","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06030","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"4WZ2BJUNIVF7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4WZ2BJUNIVF7GE35","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4WZ2BJUN","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4WZ2BJUNIVF7GE35KEVXN5ZCD5","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06030","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T14:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"c0bb001d167350f52e71e3f02324404802bb806171ec449bc1afa787816bbfb7","abstract_canon_sha256":"b7fe9b382a8c908dc84f2eb1e4140445cd2f17800bb05cd532a6cb47deb7e901"},"schema_version":"1.0"},"canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:21.820669Z","signature_b64":"dwu9Wrw7GLhqyspbViZsOUsKJFjzazSCQRNwfHyLAustdYvR0gCLwA2FSCxBmqA1wxVjW/c2UQ2z+rP3bhJXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","last_reissued_at":"2026-05-18T00:27:21.820036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:21.820036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06030","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5bOAxZ/FPHmqbDsJMrkz3t1ADpm2j+Rm0Ro8TN2PyMS13b/1T/3ZlJgBzJObdURqm89AAYncLN5T8JyfqilDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:25:56.318466Z"},"content_sha256":"3315a9a588b998080ef4313deb57c2428fb93d26b9814ba6ede0d9b4ab2df816","schema_version":"1.0","event_id":"sha256:3315a9a588b998080ef4313deb57c2428fb93d26b9814ba6ede0d9b4ab2df816"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4WZ2BJUNIVF7GE35KEVXN5ZCD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourth-order time-stepping for stiff PDEs on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hadrien Montanelli, Yuji Nakatsukasa","submitted_at":"2017-01-21T14:10:14Z","abstract_excerpt":"We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with multiplication matrices that differ from the usual ones, and implicit-explicit time-stepping schemes. Operating in coefficient space with these new matrices allows one to use a sparse direct solver, avoids the coordinate singularity and maintains smoothness at the poles, while implicit-explicit schemes circumvent severe restrictions on the time-steps due to stif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06030","kind":"arxiv","version":4},"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":"2026-05-18T00:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3V1Pe3Drzjo/2st1CbeULJnXErT5gXqeESSFKAjQhp1pF5SgoQmx32NJlVPxqIWK9kFSztxUIaDP3QN/VGONCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:25:56.318802Z"},"content_sha256":"54988b6017cf14099fe1ce048dc5c2f49e8130d6042b5c92c4412d64ac8416a2","schema_version":"1.0","event_id":"sha256:54988b6017cf14099fe1ce048dc5c2f49e8130d6042b5c92c4412d64ac8416a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/bundle.json","state_url":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/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":"2026-06-24T05:25:56Z","links":{"resolver":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5","bundle":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/bundle.json","state":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4WZ2BJUNIVF7GE35KEVXN5ZCD5","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":"b7fe9b382a8c908dc84f2eb1e4140445cd2f17800bb05cd532a6cb47deb7e901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T14:10:14Z","title_canon_sha256":"c0bb001d167350f52e71e3f02324404802bb806171ec449bc1afa787816bbfb7"},"schema_version":"1.0","source":{"id":"1701.06030","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06030","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06030v4","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06030","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"4WZ2BJUNIVF7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4WZ2BJUNIVF7GE35","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4WZ2BJUN","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:54988b6017cf14099fe1ce048dc5c2f49e8130d6042b5c92c4412d64ac8416a2","target":"graph","created_at":"2026-05-18T00:27:21Z","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":"We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with multiplication matrices that differ from the usual ones, and implicit-explicit time-stepping schemes. Operating in coefficient space with these new matrices allows one to use a sparse direct solver, avoids the coordinate singularity and maintains smoothness at the poles, while implicit-explicit schemes circumvent severe restrictions on the time-steps due to stif","authors_text":"Hadrien Montanelli, Yuji Nakatsukasa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T14:10:14Z","title":"Fourth-order time-stepping for stiff PDEs on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06030","kind":"arxiv","version":4},"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":"sha256:3315a9a588b998080ef4313deb57c2428fb93d26b9814ba6ede0d9b4ab2df816","target":"record","created_at":"2026-05-18T00:27:21Z","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":"b7fe9b382a8c908dc84f2eb1e4140445cd2f17800bb05cd532a6cb47deb7e901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T14:10:14Z","title_canon_sha256":"c0bb001d167350f52e71e3f02324404802bb806171ec449bc1afa787816bbfb7"},"schema_version":"1.0","source":{"id":"1701.06030","kind":"arxiv","version":4}},"canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","first_computed_at":"2026-05-18T00:27:21.820036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:21.820036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dwu9Wrw7GLhqyspbViZsOUsKJFjzazSCQRNwfHyLAustdYvR0gCLwA2FSCxBmqA1wxVjW/c2UQ2z+rP3bhJXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:21.820669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06030","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3315a9a588b998080ef4313deb57c2428fb93d26b9814ba6ede0d9b4ab2df816","sha256:54988b6017cf14099fe1ce048dc5c2f49e8130d6042b5c92c4412d64ac8416a2"],"state_sha256":"b9797ff56938b360db14782b62974d5e972bd4fdd55692a23c589c9eb1749372"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaRF129p6h2I2qgifVowgZK1LNV9W5yA2auYVMNXs2TzWFZ5eiyxRknnNndUBXfvfaxkkh+UhaF2Wb2R1RiOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:25:56.320763Z","bundle_sha256":"d926a46864fd0781568dca95af92d2c636d620218128d566d3984c1608a010f5"}}