{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SHHWM53YFDNXH4PEH5I77SF6VK","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":"9565e9d30bdb77dd5312894d8926a7850ca61159eb97c7661b2f6969f1f3c368","cross_cats_sorted":["cs.NA","math.AP"],"license":"","primary_cat":"math.NA","submitted_at":"2007-11-02T22:53:49Z","title_canon_sha256":"63af8fba07602a0b9513b3fd6b8fd1f5e7cf698ef7e78dd14321a91b16415e4a"},"schema_version":"1.0","source":{"id":"0711.0406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0406","created_at":"2026-06-03T22:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0406v1","created_at":"2026-06-03T22:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0406","created_at":"2026-06-03T22:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"SHHWM53YFDNX","created_at":"2026-06-03T22:06:03Z"},{"alias_kind":"pith_short_16","alias_value":"SHHWM53YFDNXH4PE","created_at":"2026-06-03T22:06:03Z"},{"alias_kind":"pith_short_8","alias_value":"SHHWM53Y","created_at":"2026-06-03T22:06:03Z"}],"graph_snapshots":[{"event_id":"sha256:9ac52bcdc0e18c48643ae0810e47d21e0a59ec4bf8e3927a0a71ea398891cb2b","target":"graph","created_at":"2026-06-03T22:06:03Z","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/0711.0406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, difference schemes, called generalized monotone schemes. Convergence toward the entropy solution is proven via a new technique of proof, assuming that the initial data has a finite number of extremum values only, and the flux-function is strictly c","authors_text":"Jian-Guo Liu, Philippe G. LeFloch","cross_cats":["cs.NA","math.AP"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2007-11-02T22:53:49Z","title":"Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0406","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:bced0d40607843b95ec3363cf3a9d9548fef255f7e1d006179237c99bbe31201","target":"record","created_at":"2026-06-03T22:06:03Z","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":"9565e9d30bdb77dd5312894d8926a7850ca61159eb97c7661b2f6969f1f3c368","cross_cats_sorted":["cs.NA","math.AP"],"license":"","primary_cat":"math.NA","submitted_at":"2007-11-02T22:53:49Z","title_canon_sha256":"63af8fba07602a0b9513b3fd6b8fd1f5e7cf698ef7e78dd14321a91b16415e4a"},"schema_version":"1.0","source":{"id":"0711.0406","kind":"arxiv","version":1}},"canonical_sha256":"91cf66777828db73f1e43f51ffc8beaab00f1416e8456238969526ac379d5435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91cf66777828db73f1e43f51ffc8beaab00f1416e8456238969526ac379d5435","first_computed_at":"2026-06-03T22:06:03.074844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:03.074844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qFn3YmeKVDWPUuY8Hj7HB+hXfGDrUONmDrPuju/vg+mN+9E9qIZpPMTx2QKCJfflmX2kV/XtABwKx7pALITmCw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:03.075269Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.0406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bced0d40607843b95ec3363cf3a9d9548fef255f7e1d006179237c99bbe31201","sha256:9ac52bcdc0e18c48643ae0810e47d21e0a59ec4bf8e3927a0a71ea398891cb2b"],"state_sha256":"c7d77b6f2f96edad3781ea10e5e4502f06e26ab55dddc8610f4e5303f41b8d77"}