{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LS6TW4LDSL5ISQFIKQRU7BSK7Q","short_pith_number":"pith:LS6TW4LD","canonical_record":{"source":{"id":"2405.04853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-08T07:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"c017fe30399bc328b48cc9de3c80f968f290d75a18f4ad82f7efe22b21c5f85a","abstract_canon_sha256":"13d8baad35fc2cbb80953816f24859ad59697e3265ebe2cb27f4c2c99fe1fe04"},"schema_version":"1.0"},"canonical_sha256":"5cbd3b716392fa8940a854234f864afc26cb77bcac3dc9bbd62fd9a011928c9c","source":{"kind":"arxiv","id":"2405.04853","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.04853","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"2405.04853v1","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04853","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"LS6TW4LDSL5I","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"pith_short_16","alias_value":"LS6TW4LDSL5ISQFI","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"pith_short_8","alias_value":"LS6TW4LD","created_at":"2026-07-05T08:16:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LS6TW4LDSL5ISQFIKQRU7BSK7Q","target":"record","payload":{"canonical_record":{"source":{"id":"2405.04853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-08T07:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"c017fe30399bc328b48cc9de3c80f968f290d75a18f4ad82f7efe22b21c5f85a","abstract_canon_sha256":"13d8baad35fc2cbb80953816f24859ad59697e3265ebe2cb27f4c2c99fe1fe04"},"schema_version":"1.0"},"canonical_sha256":"5cbd3b716392fa8940a854234f864afc26cb77bcac3dc9bbd62fd9a011928c9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:16:55.115763Z","signature_b64":"0kzc4BSWBu+Jim5rcGy6HpUvVCHfofa/ebtvxmLPc8/qNbjEF/XF4Dg1vIrhStesNPWXA0ZuxLcyAqqWTGGaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cbd3b716392fa8940a854234f864afc26cb77bcac3dc9bbd62fd9a011928c9c","last_reissued_at":"2026-07-05T08:16:55.115125Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:16:55.115125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.04853","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":"2026-07-05T08:16:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McVifvTCzG5zNcxnN/tcoX3cHsbzf2QC+iMJgwdMrP31MlJruOXxveyO9DAxaC/2BTqQ6ruyofB8RemTZHWyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:17:24.163468Z"},"content_sha256":"f7ad3d3ed2ad8974df773ec5377274f4c94f0684c994125e1a37bea9eff92cc8","schema_version":"1.0","event_id":"sha256:f7ad3d3ed2ad8974df773ec5377274f4c94f0684c994125e1a37bea9eff92cc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LS6TW4LDSL5ISQFIKQRU7BSK7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mack modes in supersonic boundary layer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Di Wu, Nader Masmoudi, Yuxi Wang, Zhifei Zhang","submitted_at":"2024-05-08T07:00:52Z","abstract_excerpt":"Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04853","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04853/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:16:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8UKtahDJvs/g73bdm8l5oGTrJOel2TdcgmimyN9V3UFXYH8lPeqe0v/bOcJPKHk2J4dinNvasNuPOkYB4RfsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:17:24.164106Z"},"content_sha256":"8eef6b3801d6d21fb7687b91af7415c90491c38fd40d9aed8aa99522ce36aeb6","schema_version":"1.0","event_id":"sha256:8eef6b3801d6d21fb7687b91af7415c90491c38fd40d9aed8aa99522ce36aeb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q/bundle.json","state_url":"https://pith.science/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q/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":"2026-08-12T16:17:24Z","links":{"resolver":"https://pith.science/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q","bundle":"https://pith.science/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q/bundle.json","state":"https://pith.science/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LS6TW4LDSL5ISQFIKQRU7BSK7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LS6TW4LDSL5ISQFIKQRU7BSK7Q","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":"13d8baad35fc2cbb80953816f24859ad59697e3265ebe2cb27f4c2c99fe1fe04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-08T07:00:52Z","title_canon_sha256":"c017fe30399bc328b48cc9de3c80f968f290d75a18f4ad82f7efe22b21c5f85a"},"schema_version":"1.0","source":{"id":"2405.04853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.04853","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"2405.04853v1","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04853","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"LS6TW4LDSL5I","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"pith_short_16","alias_value":"LS6TW4LDSL5ISQFI","created_at":"2026-07-05T08:16:55Z"},{"alias_kind":"pith_short_8","alias_value":"LS6TW4LD","created_at":"2026-07-05T08:16:55Z"}],"graph_snapshots":[{"event_id":"sha256:8eef6b3801d6d21fb7687b91af7415c90491c38fd40d9aed8aa99522ce36aeb6","target":"graph","created_at":"2026-07-05T08:16:55Z","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/2405.04853/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system.","authors_text":"Di Wu, Nader Masmoudi, Yuxi Wang, Zhifei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-08T07:00:52Z","title":"Mack modes in supersonic boundary layer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04853","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:f7ad3d3ed2ad8974df773ec5377274f4c94f0684c994125e1a37bea9eff92cc8","target":"record","created_at":"2026-07-05T08:16:55Z","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":"13d8baad35fc2cbb80953816f24859ad59697e3265ebe2cb27f4c2c99fe1fe04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-08T07:00:52Z","title_canon_sha256":"c017fe30399bc328b48cc9de3c80f968f290d75a18f4ad82f7efe22b21c5f85a"},"schema_version":"1.0","source":{"id":"2405.04853","kind":"arxiv","version":1}},"canonical_sha256":"5cbd3b716392fa8940a854234f864afc26cb77bcac3dc9bbd62fd9a011928c9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cbd3b716392fa8940a854234f864afc26cb77bcac3dc9bbd62fd9a011928c9c","first_computed_at":"2026-07-05T08:16:55.115125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:16:55.115125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kzc4BSWBu+Jim5rcGy6HpUvVCHfofa/ebtvxmLPc8/qNbjEF/XF4Dg1vIrhStesNPWXA0ZuxLcyAqqWTGGaDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:16:55.115763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.04853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ad3d3ed2ad8974df773ec5377274f4c94f0684c994125e1a37bea9eff92cc8","sha256:8eef6b3801d6d21fb7687b91af7415c90491c38fd40d9aed8aa99522ce36aeb6"],"state_sha256":"e1f3b031f812e98ba7c7950d379b5a113b36dcdda970f27c0231016e53d31cf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sccccRw4v4D6ScSF6CRFSfkoaqP9ZZ4L0BgiX2FiSw1z+hJjodwtMhVGIzA/3TDC6pVUa+AfpfEMSOEFk5rbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:17:24.170771Z","bundle_sha256":"13c7b18733c3b3b774c7d0adbf9d2cc56b4afa3903e10d7ac0f192a91a788d0e"}}