{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:J2W5DZTVVNNUUNXYZQ46ES3V6A","short_pith_number":"pith:J2W5DZTV","canonical_record":{"source":{"id":"2411.13094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-20T07:47:05Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"dbdec8a98fb340d03faca91914724cf7c55b83bf5067574e0e5dc18da7dfe348","abstract_canon_sha256":"33a028d6e9b1f4d5c5c3534b96b0846ec2b691986d6cff3cb4ea18235e14d956"},"schema_version":"1.0"},"canonical_sha256":"4eadd1e675ab5b4a36f8cc39e24b75f021b4f94ff4e940d9a8969fa959dcaf77","source":{"kind":"arxiv","id":"2411.13094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13094","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13094v1","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13094","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"J2W5DZTVVNNU","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_16","alias_value":"J2W5DZTVVNNUUNXY","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_8","alias_value":"J2W5DZTV","created_at":"2026-07-05T09:38:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:J2W5DZTVVNNUUNXYZQ46ES3V6A","target":"record","payload":{"canonical_record":{"source":{"id":"2411.13094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-20T07:47:05Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"dbdec8a98fb340d03faca91914724cf7c55b83bf5067574e0e5dc18da7dfe348","abstract_canon_sha256":"33a028d6e9b1f4d5c5c3534b96b0846ec2b691986d6cff3cb4ea18235e14d956"},"schema_version":"1.0"},"canonical_sha256":"4eadd1e675ab5b4a36f8cc39e24b75f021b4f94ff4e940d9a8969fa959dcaf77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:04.904852Z","signature_b64":"Q8CaBuSLHuriuSrDgVOV9hkHPOQHKjokiOLLnNG8fLwgOQ0jLLuY9FKmwd2n5MTelut7QkP/47WBQpay/taOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eadd1e675ab5b4a36f8cc39e24b75f021b4f94ff4e940d9a8969fa959dcaf77","last_reissued_at":"2026-07-05T09:38:04.903454Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:04.903454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.13094","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":"2026-07-05T09:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m/ZBpcHsn97muMiYSr8E/bYlXZsE3eLuda+wwSXy7KzAGC14fG4Cw71+9YXIqwWFdIAZqc3AaWSnA8EhOmyVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:53:33.616366Z"},"content_sha256":"c28d51d5ef8c7d30422019a3562fc638089ba974860a8960de2cc362dc620a9d","schema_version":"1.0","event_id":"sha256:c28d51d5ef8c7d30422019a3562fc638089ba974860a8960de2cc362dc620a9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:J2W5DZTVVNNUUNXYZQ46ES3V6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear orbital stability of stationary shock profiles for the Lax-Wendroff scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Gr\\'egory Faye (IMT), Jean-Fran\\c{c}ois Coulombel (IMT)","submitted_at":"2024-11-20T07:47:05Z","abstract_excerpt":"In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first clarify the spectral stability of such solutions depending on the convexity of the flux for the underlying conservation law. The main contribution of this article is a detailed study of the so-called Green's function for the linearized numerical scheme. As evidenced on numerical simulations, the Green's function exhibits a highly oscillating behavior ahead of the leading wave before this wave reaches the shock location"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13094","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13094/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6QxefvnbBxNfJs6abiRy3wMKsujb2H3lBnlGJHaZ0R1u8Zlb7NoRgz2ceVnsSXYN3Lpq5RfHq2n1w7FfKKmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:53:33.616879Z"},"content_sha256":"016756117f75d0d72e4cb6477f3a45ee40e37dae01116ada1ba617b8f38e238a","schema_version":"1.0","event_id":"sha256:016756117f75d0d72e4cb6477f3a45ee40e37dae01116ada1ba617b8f38e238a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A/bundle.json","state_url":"https://pith.science/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A/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":"2026-08-12T23:53:33Z","links":{"resolver":"https://pith.science/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A","bundle":"https://pith.science/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A/bundle.json","state":"https://pith.science/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J2W5DZTVVNNUUNXYZQ46ES3V6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:J2W5DZTVVNNUUNXYZQ46ES3V6A","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":"33a028d6e9b1f4d5c5c3534b96b0846ec2b691986d6cff3cb4ea18235e14d956","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-20T07:47:05Z","title_canon_sha256":"dbdec8a98fb340d03faca91914724cf7c55b83bf5067574e0e5dc18da7dfe348"},"schema_version":"1.0","source":{"id":"2411.13094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13094","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13094v1","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13094","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"J2W5DZTVVNNU","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_16","alias_value":"J2W5DZTVVNNUUNXY","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_8","alias_value":"J2W5DZTV","created_at":"2026-07-05T09:38:04Z"}],"graph_snapshots":[{"event_id":"sha256:016756117f75d0d72e4cb6477f3a45ee40e37dae01116ada1ba617b8f38e238a","target":"graph","created_at":"2026-07-05T09:38:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.13094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first clarify the spectral stability of such solutions depending on the convexity of the flux for the underlying conservation law. The main contribution of this article is a detailed study of the so-called Green's function for the linearized numerical scheme. As evidenced on numerical simulations, the Green's function exhibits a highly oscillating behavior ahead of the leading wave before this wave reaches the shock location","authors_text":"Gr\\'egory Faye (IMT), Jean-Fran\\c{c}ois Coulombel (IMT)","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-20T07:47:05Z","title":"Nonlinear orbital stability of stationary shock profiles for the Lax-Wendroff scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13094","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:c28d51d5ef8c7d30422019a3562fc638089ba974860a8960de2cc362dc620a9d","target":"record","created_at":"2026-07-05T09:38:04Z","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":"33a028d6e9b1f4d5c5c3534b96b0846ec2b691986d6cff3cb4ea18235e14d956","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-20T07:47:05Z","title_canon_sha256":"dbdec8a98fb340d03faca91914724cf7c55b83bf5067574e0e5dc18da7dfe348"},"schema_version":"1.0","source":{"id":"2411.13094","kind":"arxiv","version":1}},"canonical_sha256":"4eadd1e675ab5b4a36f8cc39e24b75f021b4f94ff4e940d9a8969fa959dcaf77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eadd1e675ab5b4a36f8cc39e24b75f021b4f94ff4e940d9a8969fa959dcaf77","first_computed_at":"2026-07-05T09:38:04.903454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:04.903454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q8CaBuSLHuriuSrDgVOV9hkHPOQHKjokiOLLnNG8fLwgOQ0jLLuY9FKmwd2n5MTelut7QkP/47WBQpay/taOBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:04.904852Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c28d51d5ef8c7d30422019a3562fc638089ba974860a8960de2cc362dc620a9d","sha256:016756117f75d0d72e4cb6477f3a45ee40e37dae01116ada1ba617b8f38e238a"],"state_sha256":"b59719a703d0a35c795d940ec06843d165315d89fe7aaf651aa29964cba1950b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8ascAgILE1+66gBSmDpWlBnEeCL03EDcLW7x/cE6sFYSjjW2ZuuuIa0YcQEOR3IXF649WECCgq9tDX11OumCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:53:33.625910Z","bundle_sha256":"a877cbd5f1ba017fcd4a294f5e2ee4bb85ca603ea80c213aa8c7664a8123b7d3"}}