{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YTVC2UFQSEFZH2QBVL5EKOS52J","short_pith_number":"pith:YTVC2UFQ","canonical_record":{"source":{"id":"1603.03955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-12T18:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"f75d357eca09c770a0a93251712337081e56f6443a88cc6b1b0ee66fe07be826","abstract_canon_sha256":"a5c0ff0a5754c47e3b3a1121ce8145ff019e80257cd40f225ff02b24b8a9e13f"},"schema_version":"1.0"},"canonical_sha256":"c4ea2d50b0910b93ea01aafa453a5dd25539631dffde7722b8d23a94a97619ad","source":{"kind":"arxiv","id":"1603.03955","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03955","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03955v1","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03955","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"YTVC2UFQSEFZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YTVC2UFQSEFZH2QB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YTVC2UFQ","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YTVC2UFQSEFZH2QBVL5EKOS52J","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-12T18:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"f75d357eca09c770a0a93251712337081e56f6443a88cc6b1b0ee66fe07be826","abstract_canon_sha256":"a5c0ff0a5754c47e3b3a1121ce8145ff019e80257cd40f225ff02b24b8a9e13f"},"schema_version":"1.0"},"canonical_sha256":"c4ea2d50b0910b93ea01aafa453a5dd25539631dffde7722b8d23a94a97619ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:03.041306Z","signature_b64":"D/tKAf1JOAwO/AUtjiBysJwj/j24bMp0aGy6zbaRiuO/b4vzLPD/42c7mb7DZUQ9WEBajTmKZpTjPLsatEvzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4ea2d50b0910b93ea01aafa453a5dd25539631dffde7722b8d23a94a97619ad","last_reissued_at":"2026-05-18T00:39:03.040731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:03.040731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03955","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":"2026-05-18T00:39:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/DyUQsILlPtSncSRyiDkHfChB7jXer1NzQN6zfwK5szP9gnMZH4Ayx1gS4rTxDpRJap4iLsjo3K4BCTBZ72bAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:32:31.207387Z"},"content_sha256":"a21286defdacf20e47273b68b2837a888c93ea8289b087d6906051b797c35718","schema_version":"1.0","event_id":"sha256:a21286defdacf20e47273b68b2837a888c93ea8289b087d6906051b797c35718"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YTVC2UFQSEFZH2QBVL5EKOS52J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidimensional stability of large-amplitude Navier-Stokes shocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gregory Lyng, Jeffrey Humpherys, Kevin Zumbrun","submitted_at":"2016-03-12T18:32:10Z","abstract_excerpt":"Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier--Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients $\\mu$, $\\mu +\\eta$, and $\\nu=\\kappa/c_v$ in the physical ratios predicted by statistical mechanics, with Mach number $M>1.035$. Our results indicate unconditional stability with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03955","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":"2026-05-18T00:39:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oZpiQ0a+28w2WtcKYhBCcJDd6ceRvVWaZ6D2RsMpZAj+2GP9ujOqz8Npgyn7E4JiqGMiLAtyVT4ExPWsERj8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:32:31.207978Z"},"content_sha256":"7e0f1a0f38e2e9b1412bf25d2b264d6907e9873ca1ec27fe67cfee5f4d3be4f6","schema_version":"1.0","event_id":"sha256:7e0f1a0f38e2e9b1412bf25d2b264d6907e9873ca1ec27fe67cfee5f4d3be4f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTVC2UFQSEFZH2QBVL5EKOS52J/bundle.json","state_url":"https://pith.science/pith/YTVC2UFQSEFZH2QBVL5EKOS52J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTVC2UFQSEFZH2QBVL5EKOS52J/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":"2026-05-28T04:32:31Z","links":{"resolver":"https://pith.science/pith/YTVC2UFQSEFZH2QBVL5EKOS52J","bundle":"https://pith.science/pith/YTVC2UFQSEFZH2QBVL5EKOS52J/bundle.json","state":"https://pith.science/pith/YTVC2UFQSEFZH2QBVL5EKOS52J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTVC2UFQSEFZH2QBVL5EKOS52J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YTVC2UFQSEFZH2QBVL5EKOS52J","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":"a5c0ff0a5754c47e3b3a1121ce8145ff019e80257cd40f225ff02b24b8a9e13f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-12T18:32:10Z","title_canon_sha256":"f75d357eca09c770a0a93251712337081e56f6443a88cc6b1b0ee66fe07be826"},"schema_version":"1.0","source":{"id":"1603.03955","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03955","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03955v1","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03955","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"YTVC2UFQSEFZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YTVC2UFQSEFZH2QB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YTVC2UFQ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:7e0f1a0f38e2e9b1412bf25d2b264d6907e9873ca1ec27fe67cfee5f4d3be4f6","target":"graph","created_at":"2026-05-18T00:39:03Z","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"},"paper":{"abstract_excerpt":"Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier--Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients $\\mu$, $\\mu +\\eta$, and $\\nu=\\kappa/c_v$ in the physical ratios predicted by statistical mechanics, with Mach number $M>1.035$. Our results indicate unconditional stability with","authors_text":"Gregory Lyng, Jeffrey Humpherys, Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-12T18:32:10Z","title":"Multidimensional stability of large-amplitude Navier-Stokes shocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03955","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:a21286defdacf20e47273b68b2837a888c93ea8289b087d6906051b797c35718","target":"record","created_at":"2026-05-18T00:39:03Z","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":"a5c0ff0a5754c47e3b3a1121ce8145ff019e80257cd40f225ff02b24b8a9e13f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-12T18:32:10Z","title_canon_sha256":"f75d357eca09c770a0a93251712337081e56f6443a88cc6b1b0ee66fe07be826"},"schema_version":"1.0","source":{"id":"1603.03955","kind":"arxiv","version":1}},"canonical_sha256":"c4ea2d50b0910b93ea01aafa453a5dd25539631dffde7722b8d23a94a97619ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4ea2d50b0910b93ea01aafa453a5dd25539631dffde7722b8d23a94a97619ad","first_computed_at":"2026-05-18T00:39:03.040731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:03.040731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D/tKAf1JOAwO/AUtjiBysJwj/j24bMp0aGy6zbaRiuO/b4vzLPD/42c7mb7DZUQ9WEBajTmKZpTjPLsatEvzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:03.041306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03955","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a21286defdacf20e47273b68b2837a888c93ea8289b087d6906051b797c35718","sha256:7e0f1a0f38e2e9b1412bf25d2b264d6907e9873ca1ec27fe67cfee5f4d3be4f6"],"state_sha256":"de85d4916a1298bac0f5c55cf27d84cc926f95a1f7d88dcb41d89845ad8a2ae3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BbueDb2P7DMmwhD3UfuVpTmd/JzMvfKtHk9ctGAOY/VSU96ZE4zBDV2Jll4GT2DRtDzLt0XcpHkNC1b62dAsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:32:31.210718Z","bundle_sha256":"29e3acd9abc1b2f740d055328e3edb7c564b35cc2993583de44e2ddfd6ec800e"}}