{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3M5BXHQ2V7KVSIYSMOZBNKVO6Z","short_pith_number":"pith:3M5BXHQ2","canonical_record":{"source":{"id":"2607.21265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T12:38:33Z","cross_cats_sorted":[],"title_canon_sha256":"6a535205bb40105c325709d39b8dc1a966be9bad55ddd772823228bd33661503","abstract_canon_sha256":"9b58e01cb399325afa6e16dbd98d23684c09d09001a5eadc7351066729e71ec0"},"schema_version":"1.0"},"canonical_sha256":"db3a1b9e1aafd559231263b216aaaef6678eb230d5c2032433b442357e4111c1","source":{"kind":"arxiv","id":"2607.21265","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21265","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21265v1","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21265","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"3M5BXHQ2V7KV","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"pith_short_16","alias_value":"3M5BXHQ2V7KVSIYS","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"pith_short_8","alias_value":"3M5BXHQ2","created_at":"2026-07-24T01:24:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3M5BXHQ2V7KVSIYSMOZBNKVO6Z","target":"record","payload":{"canonical_record":{"source":{"id":"2607.21265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T12:38:33Z","cross_cats_sorted":[],"title_canon_sha256":"6a535205bb40105c325709d39b8dc1a966be9bad55ddd772823228bd33661503","abstract_canon_sha256":"9b58e01cb399325afa6e16dbd98d23684c09d09001a5eadc7351066729e71ec0"},"schema_version":"1.0"},"canonical_sha256":"db3a1b9e1aafd559231263b216aaaef6678eb230d5c2032433b442357e4111c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T01:24:22.776304Z","signature_b64":"EfWeP4DmSMlRq4JZyZg6ndJe1x+R3ECWdVRE/dBALjBdPKCPdm65MB0EA9TMQjtkmcoE2aD8qM1gKiyl5Vu2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db3a1b9e1aafd559231263b216aaaef6678eb230d5c2032433b442357e4111c1","last_reissued_at":"2026-07-24T01:24:22.775213Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T01:24:22.775213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.21265","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":"2026-07-24T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Gjam+thVXyMb9mUh5i4cwknlkMiufam5qA4Ss8P2T9Gk/gZw+VKiXRzCnpbTNYsDvwF/oajTJnRx9E27TflBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:45:30.998521Z"},"content_sha256":"c62f0ad5158f8d1361e0d9dda550e8d72f37f7b97453f540641b79f4b8cd04a6","schema_version":"1.0","event_id":"sha256:c62f0ad5158f8d1361e0d9dda550e8d72f37f7b97453f540641b79f4b8cd04a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3M5BXHQ2V7KVSIYSMOZBNKVO6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neutral curves and traveling waves in plane Poiseuille flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Li, Yuxi Wang, Zhifei Zhang","submitted_at":"2026-07-23T12:38:33Z","abstract_excerpt":"We study the spectrum of the Orr--Sommerfeld operator associated with the incompressible plane Poiseuille flow in the high-Reynolds-number regime. In the Tollmien--Schlichting eigenvalue region, we prove the existence and uniqueness of the lower and upper branches of the neutral curve. For each sufficiently small fixed wavenumber $\\alpha$, the viscosities corresponding to the lower and upper neutral branches satisfy $\\nu\\sim |\\alpha|^7$ and $\\nu\\sim |\\alpha|^{11}$, respectively. Equivalently, for each sufficiently small viscosity $\\nu$, the corresponding lower and upper neutral wavenumbers sat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21265","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/2607.21265/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":"2026-07-24T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z6VG5V3uOPv4w5uyleee2ejYD1/V3q6kiUsSZEW0qiuvv3yDO8SiLhrusewjyV442DMg42tM4afKGFp92rFjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:45:30.999088Z"},"content_sha256":"8aad6eefccca86d3d207912be34919d038f52acae9521b17390f2dc8fc496970","schema_version":"1.0","event_id":"sha256:8aad6eefccca86d3d207912be34919d038f52acae9521b17390f2dc8fc496970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z/bundle.json","state_url":"https://pith.science/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z/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":"2026-08-14T15:45:31Z","links":{"resolver":"https://pith.science/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z","bundle":"https://pith.science/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z/bundle.json","state":"https://pith.science/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3M5BXHQ2V7KVSIYSMOZBNKVO6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3M5BXHQ2V7KVSIYSMOZBNKVO6Z","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":"9b58e01cb399325afa6e16dbd98d23684c09d09001a5eadc7351066729e71ec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T12:38:33Z","title_canon_sha256":"6a535205bb40105c325709d39b8dc1a966be9bad55ddd772823228bd33661503"},"schema_version":"1.0","source":{"id":"2607.21265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21265","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21265v1","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21265","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"3M5BXHQ2V7KV","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"pith_short_16","alias_value":"3M5BXHQ2V7KVSIYS","created_at":"2026-07-24T01:24:22Z"},{"alias_kind":"pith_short_8","alias_value":"3M5BXHQ2","created_at":"2026-07-24T01:24:22Z"}],"graph_snapshots":[{"event_id":"sha256:8aad6eefccca86d3d207912be34919d038f52acae9521b17390f2dc8fc496970","target":"graph","created_at":"2026-07-24T01:24:22Z","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/2607.21265/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the spectrum of the Orr--Sommerfeld operator associated with the incompressible plane Poiseuille flow in the high-Reynolds-number regime. In the Tollmien--Schlichting eigenvalue region, we prove the existence and uniqueness of the lower and upper branches of the neutral curve. For each sufficiently small fixed wavenumber $\\alpha$, the viscosities corresponding to the lower and upper neutral branches satisfy $\\nu\\sim |\\alpha|^7$ and $\\nu\\sim |\\alpha|^{11}$, respectively. Equivalently, for each sufficiently small viscosity $\\nu$, the corresponding lower and upper neutral wavenumbers sat","authors_text":"Hui Li, Yuxi Wang, Zhifei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T12:38:33Z","title":"Neutral curves and traveling waves in plane Poiseuille flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21265","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:c62f0ad5158f8d1361e0d9dda550e8d72f37f7b97453f540641b79f4b8cd04a6","target":"record","created_at":"2026-07-24T01:24:22Z","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":"9b58e01cb399325afa6e16dbd98d23684c09d09001a5eadc7351066729e71ec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T12:38:33Z","title_canon_sha256":"6a535205bb40105c325709d39b8dc1a966be9bad55ddd772823228bd33661503"},"schema_version":"1.0","source":{"id":"2607.21265","kind":"arxiv","version":1}},"canonical_sha256":"db3a1b9e1aafd559231263b216aaaef6678eb230d5c2032433b442357e4111c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db3a1b9e1aafd559231263b216aaaef6678eb230d5c2032433b442357e4111c1","first_computed_at":"2026-07-24T01:24:22.775213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-24T01:24:22.775213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EfWeP4DmSMlRq4JZyZg6ndJe1x+R3ECWdVRE/dBALjBdPKCPdm65MB0EA9TMQjtkmcoE2aD8qM1gKiyl5Vu2DQ==","signature_status":"signed_v1","signed_at":"2026-07-24T01:24:22.776304Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c62f0ad5158f8d1361e0d9dda550e8d72f37f7b97453f540641b79f4b8cd04a6","sha256:8aad6eefccca86d3d207912be34919d038f52acae9521b17390f2dc8fc496970"],"state_sha256":"9bb1326dc1312f9b0c5af6d903b61dfe4f51317730a29359650c6747b48e2e9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ek1hHw0cMSI/kwlYxPseL3UrxT1SgzrAvR2x5FaSsrH/99/BXtXmNmPz+YqhbfHx0Tsijda5KUYKXcb2ROqmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:45:31.003293Z","bundle_sha256":"c5bad0be98a55f9e282468d066770bcf195a1583f983f035c33db83485d9750f"}}