{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JYIM3J2HJTJGMS4VQUV4K2J5PI","short_pith_number":"pith:JYIM3J2H","canonical_record":{"source":{"id":"1309.1617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T12:25:44Z","cross_cats_sorted":[],"title_canon_sha256":"dbfff59507e9f1a9facd0ccd71b2c8d8c811f674d1ce814356c758104b4d98ed","abstract_canon_sha256":"2e9d07df4d5f9fb96089fbdf0218575991f3706e7d43424b49e4eb9d89450118"},"schema_version":"1.0"},"canonical_sha256":"4e10cda7474cd2664b95852bc5693d7a31b7115a9ac576f6a1d64a696483067a","source":{"kind":"arxiv","id":"1309.1617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1617","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1617v1","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1617","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"JYIM3J2HJTJG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JYIM3J2HJTJGMS4V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JYIM3J2H","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JYIM3J2HJTJGMS4VQUV4K2J5PI","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T12:25:44Z","cross_cats_sorted":[],"title_canon_sha256":"dbfff59507e9f1a9facd0ccd71b2c8d8c811f674d1ce814356c758104b4d98ed","abstract_canon_sha256":"2e9d07df4d5f9fb96089fbdf0218575991f3706e7d43424b49e4eb9d89450118"},"schema_version":"1.0"},"canonical_sha256":"4e10cda7474cd2664b95852bc5693d7a31b7115a9ac576f6a1d64a696483067a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:46.369223Z","signature_b64":"a8ksYtzBJ7XIgym7tLrvgyVwAkgC3UIuh46qPvLR0ywhgKCCsgDIhAM3E51GZ4PUglHUI3v2kni2edELhE9TCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e10cda7474cd2664b95852bc5693d7a31b7115a9ac576f6a1d64a696483067a","last_reissued_at":"2026-05-18T00:44:46.368823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:46.368823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1617","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":"2026-05-18T00:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KLUpEEx0ICRLpoX3QOzGrxegw/34b6u4H59DOnUPa/bXovsKoMl40yEOORFMWb2njmVTFQ0FGoLqTF0uh6iXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:45:07.561024Z"},"content_sha256":"1933cacdf4b8ab446410f5754285f963dceda43b8c91d81ce0a838fe32bd5ad1","schema_version":"1.0","event_id":"sha256:1933cacdf4b8ab446410f5754285f963dceda43b8c91d81ce0a838fe32bd5ad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JYIM3J2HJTJGMS4VQUV4K2J5PI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"To be or not to be intrusive? The solution of parametric and stochastic equations - the \"plain vanilla\" Galerkin case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Litvinenko, Anthony Nouy, Dishi Liu, Hermann G. Matthies, Lo\\\"ic Giraldi","submitted_at":"2013-09-06T12:25:44Z","abstract_excerpt":"In parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters. Interpolation in the parameters is an obvious possibility, in this context often labeled as a collocation method. In the frequent situation where one has a \"solver\" for the equation for a given parameter value - this may be a software component or a program - it is evident that this can independently solve for the parameter values to be interpolated. Such uncoupled methods which allow the use of the original solver are c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1617","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":"2026-05-18T00:44:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TU6JQoIwEuBozWuO0ahMHJYbWjAcliqeLXBRuKCas5kATP20qhkTrJEjYv7/AzMJq6ncf1LPtjVR/jR6GKjHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:45:07.561392Z"},"content_sha256":"549c1182feaa56c0cce07d30cbedd04fc85a3cd335e653656bfeb383526a6884","schema_version":"1.0","event_id":"sha256:549c1182feaa56c0cce07d30cbedd04fc85a3cd335e653656bfeb383526a6884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI/bundle.json","state_url":"https://pith.science/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI/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":"2026-06-24T02:45:07Z","links":{"resolver":"https://pith.science/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI","bundle":"https://pith.science/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI/bundle.json","state":"https://pith.science/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYIM3J2HJTJGMS4VQUV4K2J5PI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JYIM3J2HJTJGMS4VQUV4K2J5PI","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":"2e9d07df4d5f9fb96089fbdf0218575991f3706e7d43424b49e4eb9d89450118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T12:25:44Z","title_canon_sha256":"dbfff59507e9f1a9facd0ccd71b2c8d8c811f674d1ce814356c758104b4d98ed"},"schema_version":"1.0","source":{"id":"1309.1617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1617","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1617v1","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1617","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"JYIM3J2HJTJG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JYIM3J2HJTJGMS4V","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JYIM3J2H","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:549c1182feaa56c0cce07d30cbedd04fc85a3cd335e653656bfeb383526a6884","target":"graph","created_at":"2026-05-18T00:44:46Z","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 parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters. Interpolation in the parameters is an obvious possibility, in this context often labeled as a collocation method. In the frequent situation where one has a \"solver\" for the equation for a given parameter value - this may be a software component or a program - it is evident that this can independently solve for the parameter values to be interpolated. Such uncoupled methods which allow the use of the original solver are c","authors_text":"Alexander Litvinenko, Anthony Nouy, Dishi Liu, Hermann G. Matthies, Lo\\\"ic Giraldi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T12:25:44Z","title":"To be or not to be intrusive? The solution of parametric and stochastic equations - the \"plain vanilla\" Galerkin case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1617","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":"sha256:1933cacdf4b8ab446410f5754285f963dceda43b8c91d81ce0a838fe32bd5ad1","target":"record","created_at":"2026-05-18T00:44:46Z","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":"2e9d07df4d5f9fb96089fbdf0218575991f3706e7d43424b49e4eb9d89450118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-06T12:25:44Z","title_canon_sha256":"dbfff59507e9f1a9facd0ccd71b2c8d8c811f674d1ce814356c758104b4d98ed"},"schema_version":"1.0","source":{"id":"1309.1617","kind":"arxiv","version":1}},"canonical_sha256":"4e10cda7474cd2664b95852bc5693d7a31b7115a9ac576f6a1d64a696483067a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e10cda7474cd2664b95852bc5693d7a31b7115a9ac576f6a1d64a696483067a","first_computed_at":"2026-05-18T00:44:46.368823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:46.368823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a8ksYtzBJ7XIgym7tLrvgyVwAkgC3UIuh46qPvLR0ywhgKCCsgDIhAM3E51GZ4PUglHUI3v2kni2edELhE9TCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:46.369223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1933cacdf4b8ab446410f5754285f963dceda43b8c91d81ce0a838fe32bd5ad1","sha256:549c1182feaa56c0cce07d30cbedd04fc85a3cd335e653656bfeb383526a6884"],"state_sha256":"0ad0c08630a0ef75223a344cfa042151d45d616c0ad79b473e19940a81310eef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3W7skHX1ylc6CAWazJCgKMTXr8S+Ac6N2rzMfkusAIymrrjt5DNNQGYSBOqjvvGu2F1dxjzChfPQniP98+iTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:45:07.563478Z","bundle_sha256":"edafa45c3302cd38223f7d869453684e418360f0708247f39070b738ca6f5aef"}}