{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TUPK4QFJI7JL7ULYK4ZJCG2ZKW","short_pith_number":"pith:TUPK4QFJ","canonical_record":{"source":{"id":"1601.00837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-05T14:29:55Z","cross_cats_sorted":[],"title_canon_sha256":"b76d888ba984ba0900e2c92188d6a0c00896a0a587eba03de4064a9656c49479","abstract_canon_sha256":"6fe602db31504bcbde5ffd79139d04e536f651d472234eee4fd63670a3ebe6e6"},"schema_version":"1.0"},"canonical_sha256":"9d1eae40a947d2bfd1785732911b595598295d48ca00031d26c1033ee5c91f5c","source":{"kind":"arxiv","id":"1601.00837","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00837","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00837v1","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00837","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"TUPK4QFJI7JL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TUPK4QFJI7JL7ULY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TUPK4QFJ","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TUPK4QFJI7JL7ULYK4ZJCG2ZKW","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-05T14:29:55Z","cross_cats_sorted":[],"title_canon_sha256":"b76d888ba984ba0900e2c92188d6a0c00896a0a587eba03de4064a9656c49479","abstract_canon_sha256":"6fe602db31504bcbde5ffd79139d04e536f651d472234eee4fd63670a3ebe6e6"},"schema_version":"1.0"},"canonical_sha256":"9d1eae40a947d2bfd1785732911b595598295d48ca00031d26c1033ee5c91f5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:21.547566Z","signature_b64":"k6zzvSQrxSfGhWkLDDOx64Q+SSYqAVtuW6iRQtlAS8bPiGxPKqDrFm5jqxtEMxl6sOudsFGdHeUOUb9oD2ewCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d1eae40a947d2bfd1785732911b595598295d48ca00031d26c1033ee5c91f5c","last_reissued_at":"2026-05-18T01:23:21.546869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:21.546869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00837","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":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S46lVc4N7b6tQjO1rW3iOi//tH/4kfhHVuAUKW8Snx+DcwsXS8POSU9cNqhNmG7dZbqwOnVFVvi9uIWClkHxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:31:35.131266Z"},"content_sha256":"3b4e365ae80295cef3fa1548f30354ae135e6067bf337a43a9198b6d90a2c277","schema_version":"1.0","event_id":"sha256:3b4e365ae80295cef3fa1548f30354ae135e6067bf337a43a9198b6d90a2c277"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TUPK4QFJI7JL7ULYK4ZJCG2ZKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical proof of stability of viscous shock profiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Blake Barker, Kevin Zumbrun","submitted_at":"2016-01-05T14:29:55Z","abstract_excerpt":"We carry out the first rigorous numerical proof based on Evans function computations of stability of viscous shock profiles, for the system of isentropic gas dynamics with monatomic equation of state. We treat a selection of shock strengths ranging from the lower stability boundary of Mach number $\\approx 1.86 $, below which profiles are known by energy estimates to be stable, to the upper stability boundary of $\\approx 1669$, above which profiles are expected to be provable by rigorous asymptotic analysis to be stable. These results open the possibilities of: (i) automatic rigorous verificati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00837","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":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2lrukwRBH2dHa3ftfjgU6FgDWMlT5BnT3Ac5dDRPgQTscuI+it/AGzyj0BkIwasOW9V07jl/2ClaTZm8H8qDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:31:35.131627Z"},"content_sha256":"ad01c5a75c0a69b94c1258c4a2d360a38a443b69b10966c6a58103b6e960a8f6","schema_version":"1.0","event_id":"sha256:ad01c5a75c0a69b94c1258c4a2d360a38a443b69b10966c6a58103b6e960a8f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW/bundle.json","state_url":"https://pith.science/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW/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":"2026-05-28T10:31:35Z","links":{"resolver":"https://pith.science/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW","bundle":"https://pith.science/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW/bundle.json","state":"https://pith.science/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUPK4QFJI7JL7ULYK4ZJCG2ZKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TUPK4QFJI7JL7ULYK4ZJCG2ZKW","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":"6fe602db31504bcbde5ffd79139d04e536f651d472234eee4fd63670a3ebe6e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-05T14:29:55Z","title_canon_sha256":"b76d888ba984ba0900e2c92188d6a0c00896a0a587eba03de4064a9656c49479"},"schema_version":"1.0","source":{"id":"1601.00837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00837","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00837v1","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00837","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"TUPK4QFJI7JL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TUPK4QFJI7JL7ULY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TUPK4QFJ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:ad01c5a75c0a69b94c1258c4a2d360a38a443b69b10966c6a58103b6e960a8f6","target":"graph","created_at":"2026-05-18T01:23:21Z","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 carry out the first rigorous numerical proof based on Evans function computations of stability of viscous shock profiles, for the system of isentropic gas dynamics with monatomic equation of state. We treat a selection of shock strengths ranging from the lower stability boundary of Mach number $\\approx 1.86 $, below which profiles are known by energy estimates to be stable, to the upper stability boundary of $\\approx 1669$, above which profiles are expected to be provable by rigorous asymptotic analysis to be stable. These results open the possibilities of: (i) automatic rigorous verificati","authors_text":"Blake Barker, Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-05T14:29:55Z","title":"Numerical proof of stability of viscous shock profiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00837","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":"sha256:3b4e365ae80295cef3fa1548f30354ae135e6067bf337a43a9198b6d90a2c277","target":"record","created_at":"2026-05-18T01:23:21Z","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":"6fe602db31504bcbde5ffd79139d04e536f651d472234eee4fd63670a3ebe6e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-05T14:29:55Z","title_canon_sha256":"b76d888ba984ba0900e2c92188d6a0c00896a0a587eba03de4064a9656c49479"},"schema_version":"1.0","source":{"id":"1601.00837","kind":"arxiv","version":1}},"canonical_sha256":"9d1eae40a947d2bfd1785732911b595598295d48ca00031d26c1033ee5c91f5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d1eae40a947d2bfd1785732911b595598295d48ca00031d26c1033ee5c91f5c","first_computed_at":"2026-05-18T01:23:21.546869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:21.546869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k6zzvSQrxSfGhWkLDDOx64Q+SSYqAVtuW6iRQtlAS8bPiGxPKqDrFm5jqxtEMxl6sOudsFGdHeUOUb9oD2ewCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:21.547566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b4e365ae80295cef3fa1548f30354ae135e6067bf337a43a9198b6d90a2c277","sha256:ad01c5a75c0a69b94c1258c4a2d360a38a443b69b10966c6a58103b6e960a8f6"],"state_sha256":"1c495d1d006ac4d8a0453877a9935f8096d58b8e577e9c06b109677ca2ae7d1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6PRKVUoO0DHztyWgoGOvtVOuQ1K7MGDvpKKBx1teKdqUKOZUX7z/yzLjPzW5O+vWKHat0bMDZoSsfM4pyC7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:31:35.133547Z","bundle_sha256":"a1a30cbf47be769b9f910378f857bf4db3eecea2e518151dcf661f5fc8b60f92"}}