{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PM5OA36KTBHX7GH4QTWOF7Z3AA","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":"41a5bc45892f927ad3c346f5d34c6a1aef9218eda167eba406a7fc3306075443","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T18:52:17Z","title_canon_sha256":"6523417acdc75f42ff01a6546e57376fdadb4a589f9ce62f9b3f89d870d0f60e"},"schema_version":"1.0","source":{"id":"2607.24994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24994","created_at":"2026-07-29T00:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24994v1","created_at":"2026-07-29T00:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24994","created_at":"2026-07-29T00:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"PM5OA36KTBHX","created_at":"2026-07-29T00:24:56Z"},{"alias_kind":"pith_short_16","alias_value":"PM5OA36KTBHX7GH4","created_at":"2026-07-29T00:24:56Z"},{"alias_kind":"pith_short_8","alias_value":"PM5OA36K","created_at":"2026-07-29T00:24:56Z"}],"graph_snapshots":[{"event_id":"sha256:be6bf93a37e6e5de62d13f4788607b394af4e9cdeb0ff5b4313da886d25aa6bf","target":"graph","created_at":"2026-07-29T00:24:56Z","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/2607.24994/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a viscous one-dimensional conservation law, coupled to a fast ordinary differential equation. For a vanishing viscosity, the system has an infinite-dimensional family of time-periodic solutions, corresponding to relaxation oscillations. We show that for symmetric initial conditions, a small positive viscosity selects a unique periodic solution, which we prove to be linearly stable. The proof exploits the slow-fast structure through an averaging strategy, as well as spectral-theoretic methods. The results are illustrated by numerical simulations.","authors_text":"Hiroshi Horii, Julien Barr\\'e, Nils Berglund","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T18:52:17Z","title":"Diffusion stabilises time-periodic solutions in conservation laws coupled to a relaxation oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24994","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":"sha256:377e14ab5c81624abef082b86a3643030374a6309ed0cbb4401ce2c910611a16","target":"record","created_at":"2026-07-29T00:24:56Z","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":"41a5bc45892f927ad3c346f5d34c6a1aef9218eda167eba406a7fc3306075443","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T18:52:17Z","title_canon_sha256":"6523417acdc75f42ff01a6546e57376fdadb4a589f9ce62f9b3f89d870d0f60e"},"schema_version":"1.0","source":{"id":"2607.24994","kind":"arxiv","version":1}},"canonical_sha256":"7b3ae06fca984f7f98fc84ece2ff3b000071ff8f4920b96ec33f6f3c5d77206c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b3ae06fca984f7f98fc84ece2ff3b000071ff8f4920b96ec33f6f3c5d77206c","first_computed_at":"2026-07-29T00:24:56.893842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T00:24:56.893842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OLYo6RgTWFAyuP5g7fzW7kBG/cAmcpEpLzsKjXGbEErMU0GZuaf1zxEV0dvubTTiY+p3ylAkN5FcwL55gEumCw==","signature_status":"signed_v1","signed_at":"2026-07-29T00:24:56.894679Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:377e14ab5c81624abef082b86a3643030374a6309ed0cbb4401ce2c910611a16","sha256:be6bf93a37e6e5de62d13f4788607b394af4e9cdeb0ff5b4313da886d25aa6bf"],"state_sha256":"c8538e29900c65672cde0efb6c5b04605a96d293dceb6036a291a28bfd7fd8e3"}