{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:AICNZ4RHSXFYQD23MTRF7DY5MU","short_pith_number":"pith:AICNZ4RH","canonical_record":{"source":{"id":"0812.3582","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-12-18T16:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"bd6022cdf87eed29b10a792336050e1fcd81fcdad1521371656dd610b237d00c","abstract_canon_sha256":"1b88d2a58112c14059248c02781366cbcc98ad55940d37fe7c28d32a8d366d83"},"schema_version":"1.0"},"canonical_sha256":"0204dcf22795cb880f5b64e25f8f1d65009818e863b9e7fe445f4cc9cbebe442","source":{"kind":"arxiv","id":"0812.3582","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3582","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3582v3","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3582","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"AICNZ4RHSXFY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AICNZ4RHSXFYQD23","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AICNZ4RH","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:AICNZ4RHSXFYQD23MTRF7DY5MU","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3582","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-12-18T16:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"bd6022cdf87eed29b10a792336050e1fcd81fcdad1521371656dd610b237d00c","abstract_canon_sha256":"1b88d2a58112c14059248c02781366cbcc98ad55940d37fe7c28d32a8d366d83"},"schema_version":"1.0"},"canonical_sha256":"0204dcf22795cb880f5b64e25f8f1d65009818e863b9e7fe445f4cc9cbebe442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:56.670362Z","signature_b64":"i7fJnJv1mKGd4W0wMaOGUZz097KF+Il1Os/SYMJ5truYBOR/stkk4+tRpFeqTLA8Nmc/9YazRye4/YuyecZiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0204dcf22795cb880f5b64e25f8f1d65009818e863b9e7fe445f4cc9cbebe442","last_reissued_at":"2026-05-18T02:24:56.669691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:56.669691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3582","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQxq6gjCZQ6+b9ThDnSlbe/HlXdjj2o5bRG59OUkh6sABm9/LjVUZWjUnpvAc77Ak6KRf5MkSZ1vTmznpcRjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:50:55.146512Z"},"content_sha256":"d35ca8592c7ead888019a1bcec6cb3d4ab21da1177f397c1cc41fb1b1f4d6ce0","schema_version":"1.0","event_id":"sha256:d35ca8592c7ead888019a1bcec6cb3d4ab21da1177f397c1cc41fb1b1f4d6ce0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:AICNZ4RHSXFYQD23MTRF7DY5MU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Texier, Kevin Zumbrun","submitted_at":"2008-12-18T16:37:37Z","abstract_excerpt":"We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier--Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic \"galloping\", or \"pulsating\", solutions, in agreement with physical and numerical observation. In the process, we determine readily numerically verifiable stability and bifurcation conditions in terms of an associated Evans function, and obtain the first complete nonlinear stability result for strong detonations of the reacting Navier--Stokes equations, in the limit as amplitude (hence also he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3582","kind":"arxiv","version":3},"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":"2026-05-18T02:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tAUi0hDdutMyBXuN24ZUdq+9QCgCoZQuN82kuCN5+Flk148DOqkKOHI+M8zMnq2KgwAMPWly1a6x6j4f0tlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:50:55.147149Z"},"content_sha256":"1cdc55ef23392716fb7dc17a5c343f9e1d244b80be2e274c6a8b4b844d95d979","schema_version":"1.0","event_id":"sha256:1cdc55ef23392716fb7dc17a5c343f9e1d244b80be2e274c6a8b4b844d95d979"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AICNZ4RHSXFYQD23MTRF7DY5MU/bundle.json","state_url":"https://pith.science/pith/AICNZ4RHSXFYQD23MTRF7DY5MU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AICNZ4RHSXFYQD23MTRF7DY5MU/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":"2026-05-30T21:50:55Z","links":{"resolver":"https://pith.science/pith/AICNZ4RHSXFYQD23MTRF7DY5MU","bundle":"https://pith.science/pith/AICNZ4RHSXFYQD23MTRF7DY5MU/bundle.json","state":"https://pith.science/pith/AICNZ4RHSXFYQD23MTRF7DY5MU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AICNZ4RHSXFYQD23MTRF7DY5MU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AICNZ4RHSXFYQD23MTRF7DY5MU","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":"1b88d2a58112c14059248c02781366cbcc98ad55940d37fe7c28d32a8d366d83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-12-18T16:37:37Z","title_canon_sha256":"bd6022cdf87eed29b10a792336050e1fcd81fcdad1521371656dd610b237d00c"},"schema_version":"1.0","source":{"id":"0812.3582","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3582","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3582v3","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3582","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"AICNZ4RHSXFY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AICNZ4RHSXFYQD23","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AICNZ4RH","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1cdc55ef23392716fb7dc17a5c343f9e1d244b80be2e274c6a8b4b844d95d979","target":"graph","created_at":"2026-05-18T02:24:56Z","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"},"paper":{"abstract_excerpt":"We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier--Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic \"galloping\", or \"pulsating\", solutions, in agreement with physical and numerical observation. In the process, we determine readily numerically verifiable stability and bifurcation conditions in terms of an associated Evans function, and obtain the first complete nonlinear stability result for strong detonations of the reacting Navier--Stokes equations, in the limit as amplitude (hence also he","authors_text":"Benjamin Texier, Kevin Zumbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-12-18T16:37:37Z","title":"Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3582","kind":"arxiv","version":3},"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:d35ca8592c7ead888019a1bcec6cb3d4ab21da1177f397c1cc41fb1b1f4d6ce0","target":"record","created_at":"2026-05-18T02:24:56Z","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":"1b88d2a58112c14059248c02781366cbcc98ad55940d37fe7c28d32a8d366d83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-12-18T16:37:37Z","title_canon_sha256":"bd6022cdf87eed29b10a792336050e1fcd81fcdad1521371656dd610b237d00c"},"schema_version":"1.0","source":{"id":"0812.3582","kind":"arxiv","version":3}},"canonical_sha256":"0204dcf22795cb880f5b64e25f8f1d65009818e863b9e7fe445f4cc9cbebe442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0204dcf22795cb880f5b64e25f8f1d65009818e863b9e7fe445f4cc9cbebe442","first_computed_at":"2026-05-18T02:24:56.669691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:56.669691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7fJnJv1mKGd4W0wMaOGUZz097KF+Il1Os/SYMJ5truYBOR/stkk4+tRpFeqTLA8Nmc/9YazRye4/YuyecZiAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:56.670362Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3582","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d35ca8592c7ead888019a1bcec6cb3d4ab21da1177f397c1cc41fb1b1f4d6ce0","sha256:1cdc55ef23392716fb7dc17a5c343f9e1d244b80be2e274c6a8b4b844d95d979"],"state_sha256":"6deb978670ac60e73a252849bda4a19ebe2067ef712ec54b4881e0051eeaf440"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1GGGYZRe5vuwZIOwjIVqaLrdwGGrNrj7UZq7XzUiyvvO8iASU23+Y1rMARWFm5QSlmDPO3OylJ11Wa7+VVqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:50:55.149712Z","bundle_sha256":"02e3edbb73d4068c78444f6a477c42d0a0b95d69dd50dac4353edf0076dfb31e"}}