{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:J54T5VNBGNQZHBYGHRWQAUVIO7","short_pith_number":"pith:J54T5VNB","canonical_record":{"source":{"id":"1011.3366","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T12:51:25Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"3b0e05d91fe51413418e8656b40da2891b479d7eb8ffed8ceac546648cd0021a","abstract_canon_sha256":"7489c6777915a6860699d1be9e03483002bdf231c0862a18026a2bbdb15531d1"},"schema_version":"1.0"},"canonical_sha256":"4f793ed5a133619387063c6d0052a877cdbf1daf42b860379a0185f3b9d955ce","source":{"kind":"arxiv","id":"1011.3366","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3366","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3366v3","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3366","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"J54T5VNBGNQZ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J54T5VNBGNQZHBYG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J54T5VNB","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:J54T5VNBGNQZHBYGHRWQAUVIO7","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3366","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T12:51:25Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"3b0e05d91fe51413418e8656b40da2891b479d7eb8ffed8ceac546648cd0021a","abstract_canon_sha256":"7489c6777915a6860699d1be9e03483002bdf231c0862a18026a2bbdb15531d1"},"schema_version":"1.0"},"canonical_sha256":"4f793ed5a133619387063c6d0052a877cdbf1daf42b860379a0185f3b9d955ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:54.919553Z","signature_b64":"/pX32lzoFbOhdR/mJn79F77u7Sqx38nzgDy8KS53rMHkI0msgXTm4rJ5L9NLx2TmFXN7Rg58LVwEtuRfsIdKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f793ed5a133619387063c6d0052a877cdbf1daf42b860379a0185f3b9d955ce","last_reissued_at":"2026-05-18T04:12:54.919106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:54.919106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3366","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goXIQuWzIHgLW56D6E4OZbfFk9S2QdH86OG1A3yPKn2V22/crA1jlLPZsPqNXEshyAfxYYDwJ8u8Bvr1ZC19AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:21:35.423421Z"},"content_sha256":"26d5447a92c14990ae9c0a416bf4ce6254ce2f42a03ae72cecc64aff00f07f6a","schema_version":"1.0","event_id":"sha256:26d5447a92c14990ae9c0a416bf4ce6254ce2f42a03ae72cecc64aff00f07f6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:J54T5VNBGNQZHBYGHRWQAUVIO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Late-time/stiff relaxation asymptotic-preserving approximations of hyperbolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Christophe Berthon, Philippe G. LeFloch, Rodolphe Turpault","submitted_at":"2010-11-15T12:51:25Z","abstract_excerpt":"We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective system of equations describing the late-time/stiff relaxation singular limit. The structure of this new system is discussed and the role of a mathematical entropy is emphasized. Second, we propose a new finite volume discretization which, in late-time asymptotics, allows us to recover a discrete version of the same effective asymptotic system. This is achieved "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3366","kind":"arxiv","version":3},"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":"2026-05-18T04:12:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlazzzJa7CUwrQrV98r4AJQtEgOsvt0MUEPTg1DWFFqMr+vsq+uTYjRN0sLNhTOMIb038wLRA2b0OnpJeXPzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:21:35.424031Z"},"content_sha256":"98149d1d71a3f63494fc41e35bcf715566fb5029ccdba2c6f0c415c3ebdc7936","schema_version":"1.0","event_id":"sha256:98149d1d71a3f63494fc41e35bcf715566fb5029ccdba2c6f0c415c3ebdc7936"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J54T5VNBGNQZHBYGHRWQAUVIO7/bundle.json","state_url":"https://pith.science/pith/J54T5VNBGNQZHBYGHRWQAUVIO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J54T5VNBGNQZHBYGHRWQAUVIO7/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":"2026-06-11T20:21:35Z","links":{"resolver":"https://pith.science/pith/J54T5VNBGNQZHBYGHRWQAUVIO7","bundle":"https://pith.science/pith/J54T5VNBGNQZHBYGHRWQAUVIO7/bundle.json","state":"https://pith.science/pith/J54T5VNBGNQZHBYGHRWQAUVIO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J54T5VNBGNQZHBYGHRWQAUVIO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J54T5VNBGNQZHBYGHRWQAUVIO7","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":"7489c6777915a6860699d1be9e03483002bdf231c0862a18026a2bbdb15531d1","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T12:51:25Z","title_canon_sha256":"3b0e05d91fe51413418e8656b40da2891b479d7eb8ffed8ceac546648cd0021a"},"schema_version":"1.0","source":{"id":"1011.3366","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3366","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3366v3","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3366","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"J54T5VNBGNQZ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J54T5VNBGNQZHBYG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J54T5VNB","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:98149d1d71a3f63494fc41e35bcf715566fb5029ccdba2c6f0c415c3ebdc7936","target":"graph","created_at":"2026-05-18T04:12:54Z","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 investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective system of equations describing the late-time/stiff relaxation singular limit. The structure of this new system is discussed and the role of a mathematical entropy is emphasized. Second, we propose a new finite volume discretization which, in late-time asymptotics, allows us to recover a discrete version of the same effective asymptotic system. This is achieved ","authors_text":"Christophe Berthon, Philippe G. LeFloch, Rodolphe Turpault","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T12:51:25Z","title":"Late-time/stiff relaxation asymptotic-preserving approximations of hyperbolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3366","kind":"arxiv","version":3},"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":"sha256:26d5447a92c14990ae9c0a416bf4ce6254ce2f42a03ae72cecc64aff00f07f6a","target":"record","created_at":"2026-05-18T04:12:54Z","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":"7489c6777915a6860699d1be9e03483002bdf231c0862a18026a2bbdb15531d1","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-15T12:51:25Z","title_canon_sha256":"3b0e05d91fe51413418e8656b40da2891b479d7eb8ffed8ceac546648cd0021a"},"schema_version":"1.0","source":{"id":"1011.3366","kind":"arxiv","version":3}},"canonical_sha256":"4f793ed5a133619387063c6d0052a877cdbf1daf42b860379a0185f3b9d955ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f793ed5a133619387063c6d0052a877cdbf1daf42b860379a0185f3b9d955ce","first_computed_at":"2026-05-18T04:12:54.919106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:54.919106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/pX32lzoFbOhdR/mJn79F77u7Sqx38nzgDy8KS53rMHkI0msgXTm4rJ5L9NLx2TmFXN7Rg58LVwEtuRfsIdKCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:54.919553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3366","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26d5447a92c14990ae9c0a416bf4ce6254ce2f42a03ae72cecc64aff00f07f6a","sha256:98149d1d71a3f63494fc41e35bcf715566fb5029ccdba2c6f0c415c3ebdc7936"],"state_sha256":"86a7f1f55447b514d94f70ba28d2afd955391ea574a5b5b3f2f8858738a171e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZhSbqbFhhiEASHCdLPT9JdCqsnnhNLddH5RYynoFkB3/RfbVmE2AGDjkYbj/U7MDp8y/K2b1Fzt4UK+frT7wBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:21:35.427900Z","bundle_sha256":"605efee5c47f36ba55b5e235d69c04626f907223753721de3ba3e246d26cef7c"}}