{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3SIAOER5NH73VJFTPT2PJMGUTD","short_pith_number":"pith:3SIAOER5","canonical_record":{"source":{"id":"1609.01436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-06T08:44:24Z","cross_cats_sorted":[],"title_canon_sha256":"670f0351d3a662aac82392a7c14e9ac781937c17be7b2cd5173965b9cc1d4f6f","abstract_canon_sha256":"067ecc4d00c1b08ab025544a5b54b0600101e692060af86f6d666cf8801c7ef7"},"schema_version":"1.0"},"canonical_sha256":"dc9007123d69ffbaa4b37cf4f4b0d498cf34f1db2c0126012cd1d333a654a212","source":{"kind":"arxiv","id":"1609.01436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01436","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01436v1","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01436","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"3SIAOER5NH73","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3SIAOER5NH73VJFT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3SIAOER5","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3SIAOER5NH73VJFTPT2PJMGUTD","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-06T08:44:24Z","cross_cats_sorted":[],"title_canon_sha256":"670f0351d3a662aac82392a7c14e9ac781937c17be7b2cd5173965b9cc1d4f6f","abstract_canon_sha256":"067ecc4d00c1b08ab025544a5b54b0600101e692060af86f6d666cf8801c7ef7"},"schema_version":"1.0"},"canonical_sha256":"dc9007123d69ffbaa4b37cf4f4b0d498cf34f1db2c0126012cd1d333a654a212","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:39.601662Z","signature_b64":"jUtxVEqKscqiQYMYqhpNMhTY+b38GDW+TYtC8zZNBIymG+DNYCJawxAHMA7u8mUaYfQX2NHuqYJpbY/D5/+NCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc9007123d69ffbaa4b37cf4f4b0d498cf34f1db2c0126012cd1d333a654a212","last_reissued_at":"2026-05-18T01:05:39.601180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:39.601180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01436","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":"2026-05-18T01:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3q21rqK2TLOXBdOlCof+zXPUCQpgKqbPwAe0CjRB0W5+Vh+w6k7zC+WTxWppkjlsP9y2Y1yKEE8hdwy0fhMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:50:40.423833Z"},"content_sha256":"39deba71f744fcc4c376cd4010c76f974f2a08a75514aedfb2331981402a6226","schema_version":"1.0","event_id":"sha256:39deba71f744fcc4c376cd4010c76f974f2a08a75514aedfb2331981402a6226"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3SIAOER5NH73VJFTPT2PJMGUTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christophe Berthon (LMJL), H\\'el\\`ene Mathis (LMJL), Marianne Bessemoulin-Chatard (LMJL)","submitted_at":"2016-09-06T08:44:24Z","abstract_excerpt":"This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate of classical solutions of the p-system with damping towards the smooth solutions of the porous media equation using a relative entropy method. Adopting a semi-discrete scheme, we establish that the convergence rate is preserved by the approximated solutions. Several numerical experiments illustrate the relevance of this result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01436","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":"2026-05-18T01:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bAMvmiNO89uUYxMY1Og8oThqn5fXq4Hl1bRuXT+e/wwHcTEGFSuESlqilM/yyacDeLlaK1Mu0uSc4HdpzvKjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:50:40.424502Z"},"content_sha256":"d5c4c0d2cc6d3ac8aea7b16107a098df771ae7cbd59ee7d20ffa42a685b6bb71","schema_version":"1.0","event_id":"sha256:d5c4c0d2cc6d3ac8aea7b16107a098df771ae7cbd59ee7d20ffa42a685b6bb71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SIAOER5NH73VJFTPT2PJMGUTD/bundle.json","state_url":"https://pith.science/pith/3SIAOER5NH73VJFTPT2PJMGUTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SIAOER5NH73VJFTPT2PJMGUTD/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":"2026-06-06T12:50:40Z","links":{"resolver":"https://pith.science/pith/3SIAOER5NH73VJFTPT2PJMGUTD","bundle":"https://pith.science/pith/3SIAOER5NH73VJFTPT2PJMGUTD/bundle.json","state":"https://pith.science/pith/3SIAOER5NH73VJFTPT2PJMGUTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SIAOER5NH73VJFTPT2PJMGUTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3SIAOER5NH73VJFTPT2PJMGUTD","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":"067ecc4d00c1b08ab025544a5b54b0600101e692060af86f6d666cf8801c7ef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-06T08:44:24Z","title_canon_sha256":"670f0351d3a662aac82392a7c14e9ac781937c17be7b2cd5173965b9cc1d4f6f"},"schema_version":"1.0","source":{"id":"1609.01436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01436","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01436v1","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01436","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"3SIAOER5NH73","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3SIAOER5NH73VJFT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3SIAOER5","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:d5c4c0d2cc6d3ac8aea7b16107a098df771ae7cbd59ee7d20ffa42a685b6bb71","target":"graph","created_at":"2026-05-18T01:05:39Z","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":"This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate of classical solutions of the p-system with damping towards the smooth solutions of the porous media equation using a relative entropy method. Adopting a semi-discrete scheme, we establish that the convergence rate is preserved by the approximated solutions. Several numerical experiments illustrate the relevance of this result.","authors_text":"Christophe Berthon (LMJL), H\\'el\\`ene Mathis (LMJL), Marianne Bessemoulin-Chatard (LMJL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-06T08:44:24Z","title":"Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01436","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":"sha256:39deba71f744fcc4c376cd4010c76f974f2a08a75514aedfb2331981402a6226","target":"record","created_at":"2026-05-18T01:05:39Z","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":"067ecc4d00c1b08ab025544a5b54b0600101e692060af86f6d666cf8801c7ef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-06T08:44:24Z","title_canon_sha256":"670f0351d3a662aac82392a7c14e9ac781937c17be7b2cd5173965b9cc1d4f6f"},"schema_version":"1.0","source":{"id":"1609.01436","kind":"arxiv","version":1}},"canonical_sha256":"dc9007123d69ffbaa4b37cf4f4b0d498cf34f1db2c0126012cd1d333a654a212","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc9007123d69ffbaa4b37cf4f4b0d498cf34f1db2c0126012cd1d333a654a212","first_computed_at":"2026-05-18T01:05:39.601180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:39.601180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jUtxVEqKscqiQYMYqhpNMhTY+b38GDW+TYtC8zZNBIymG+DNYCJawxAHMA7u8mUaYfQX2NHuqYJpbY/D5/+NCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:39.601662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39deba71f744fcc4c376cd4010c76f974f2a08a75514aedfb2331981402a6226","sha256:d5c4c0d2cc6d3ac8aea7b16107a098df771ae7cbd59ee7d20ffa42a685b6bb71"],"state_sha256":"1a443280a065da844f70a2f5a51884b2c037c78342284e249d5c2f17d6de7189"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZEb9RiCEHjc7U8q7YPm7PokCAAsuqybPB88IA/OKjlgCVW/5il0Y7zc5vMXk2Nd8Rt7YSbTlVJUc7rWDnBQfBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:50:40.428542Z","bundle_sha256":"cf69a82bd8d5362ecd48f1978a1957d6e45d65cd8c06b01ea1e66145c461c507"}}