{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WYTULFNKPO3VIR4PBD3JDSDRR5","short_pith_number":"pith:WYTULFNK","canonical_record":{"source":{"id":"2607.17468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T01:52:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bf01c8f2602672bb7681f70a4c196066eb47f4a6bd72c1701e33419fe4ac5489","abstract_canon_sha256":"30146282daeaa6dbf9c69c10c006fc7f25cb82d6d267a621e1f0e649b57d34ef"},"schema_version":"1.0"},"canonical_sha256":"b6274595aa7bb754478f08f691c8718f53b10269565d0b281cbac058be21f300","source":{"kind":"arxiv","id":"2607.17468","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.17468","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.17468v1","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.17468","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"pith_short_12","alias_value":"WYTULFNKPO3V","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"pith_short_16","alias_value":"WYTULFNKPO3VIR4P","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"pith_short_8","alias_value":"WYTULFNK","created_at":"2026-07-21T01:21:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WYTULFNKPO3VIR4PBD3JDSDRR5","target":"record","payload":{"canonical_record":{"source":{"id":"2607.17468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T01:52:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bf01c8f2602672bb7681f70a4c196066eb47f4a6bd72c1701e33419fe4ac5489","abstract_canon_sha256":"30146282daeaa6dbf9c69c10c006fc7f25cb82d6d267a621e1f0e649b57d34ef"},"schema_version":"1.0"},"canonical_sha256":"b6274595aa7bb754478f08f691c8718f53b10269565d0b281cbac058be21f300","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:21:47.047918Z","signature_b64":"9OXExbCMKnmu7/xNZ8V3MdCmMmzWch92WqzU+NemdwxjITxQuqU5e06Mo4gCwJbf7RA9AsBYano2wBq7dBSsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6274595aa7bb754478f08f691c8718f53b10269565d0b281cbac058be21f300","last_reissued_at":"2026-07-21T01:21:47.047006Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:21:47.047006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.17468","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":"2026-07-21T01:21:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZ0R/S9CF/lUaF4KjhQmk1BeFiKSEdFnuCp+lfrpDegaLYRSDJ5XStp22Ps5xbIqrT2FlnwYuiFbtW5sUxtFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:53:31.489069Z"},"content_sha256":"8085fc555d4dd3876ce9fe912ff1d50c98cb90e5da7870b42351cc3026fdc134","schema_version":"1.0","event_id":"sha256:8085fc555d4dd3876ce9fe912ff1d50c98cb90e5da7870b42351cc3026fdc134"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WYTULFNKPO3VIR4PBD3JDSDRR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Couette Flow with Robin Boundary Condition (I): the viscosity-independent friction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Binqian Niu, Siming He, Weiren Zhao","submitted_at":"2026-07-20T01:52:20Z","abstract_excerpt":"This article is the first paper in the series. In this series of articles, we will examine the influence of the friction factor $\\alpha$ at the solid--fluid boundary on the stability of Couette flow. Specifically, we consider the stability of Couette flow in a bounded periodic channel $\\mathbb{T} \\times [-1,1]$ under Robin-type boundary conditions ($u^2|_{y=\\pm 1} = 0$, $[\\alpha \\partial_n u^1 + u^1]|_{y=\\pm1} = f $), where $\\alpha$ is the friction factor and $n$ is the unit outer normal vector. In this article, we prove that for a given friction factor $\\alpha$, as long as the fluid viscosity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17468","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/2607.17468/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":"2026-07-21T01:21:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gOuMlCCS9I8VODZK1g1V30VFpxIUUkxP0PZu5diDTChBRLHBqGBcC261ZBXb3FvZ/49p5LXCrSUlcQ8ywlKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:53:31.489574Z"},"content_sha256":"380df8f050c2d69a6825d0d6c136916015e2674ad88cba23a8fac0add3cdc14f","schema_version":"1.0","event_id":"sha256:380df8f050c2d69a6825d0d6c136916015e2674ad88cba23a8fac0add3cdc14f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYTULFNKPO3VIR4PBD3JDSDRR5/bundle.json","state_url":"https://pith.science/pith/WYTULFNKPO3VIR4PBD3JDSDRR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYTULFNKPO3VIR4PBD3JDSDRR5/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":"2026-08-08T13:53:31Z","links":{"resolver":"https://pith.science/pith/WYTULFNKPO3VIR4PBD3JDSDRR5","bundle":"https://pith.science/pith/WYTULFNKPO3VIR4PBD3JDSDRR5/bundle.json","state":"https://pith.science/pith/WYTULFNKPO3VIR4PBD3JDSDRR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYTULFNKPO3VIR4PBD3JDSDRR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WYTULFNKPO3VIR4PBD3JDSDRR5","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":"30146282daeaa6dbf9c69c10c006fc7f25cb82d6d267a621e1f0e649b57d34ef","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T01:52:20Z","title_canon_sha256":"bf01c8f2602672bb7681f70a4c196066eb47f4a6bd72c1701e33419fe4ac5489"},"schema_version":"1.0","source":{"id":"2607.17468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.17468","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.17468v1","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.17468","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"pith_short_12","alias_value":"WYTULFNKPO3V","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"pith_short_16","alias_value":"WYTULFNKPO3VIR4P","created_at":"2026-07-21T01:21:47Z"},{"alias_kind":"pith_short_8","alias_value":"WYTULFNK","created_at":"2026-07-21T01:21:47Z"}],"graph_snapshots":[{"event_id":"sha256:380df8f050c2d69a6825d0d6c136916015e2674ad88cba23a8fac0add3cdc14f","target":"graph","created_at":"2026-07-21T01:21:47Z","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/2607.17468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article is the first paper in the series. In this series of articles, we will examine the influence of the friction factor $\\alpha$ at the solid--fluid boundary on the stability of Couette flow. Specifically, we consider the stability of Couette flow in a bounded periodic channel $\\mathbb{T} \\times [-1,1]$ under Robin-type boundary conditions ($u^2|_{y=\\pm 1} = 0$, $[\\alpha \\partial_n u^1 + u^1]|_{y=\\pm1} = f $), where $\\alpha$ is the friction factor and $n$ is the unit outer normal vector. In this article, we prove that for a given friction factor $\\alpha$, as long as the fluid viscosity","authors_text":"Binqian Niu, Siming He, Weiren Zhao","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T01:52:20Z","title":"Couette Flow with Robin Boundary Condition (I): the viscosity-independent friction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17468","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":"sha256:8085fc555d4dd3876ce9fe912ff1d50c98cb90e5da7870b42351cc3026fdc134","target":"record","created_at":"2026-07-21T01:21:47Z","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":"30146282daeaa6dbf9c69c10c006fc7f25cb82d6d267a621e1f0e649b57d34ef","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T01:52:20Z","title_canon_sha256":"bf01c8f2602672bb7681f70a4c196066eb47f4a6bd72c1701e33419fe4ac5489"},"schema_version":"1.0","source":{"id":"2607.17468","kind":"arxiv","version":1}},"canonical_sha256":"b6274595aa7bb754478f08f691c8718f53b10269565d0b281cbac058be21f300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6274595aa7bb754478f08f691c8718f53b10269565d0b281cbac058be21f300","first_computed_at":"2026-07-21T01:21:47.047006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:21:47.047006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9OXExbCMKnmu7/xNZ8V3MdCmMmzWch92WqzU+NemdwxjITxQuqU5e06Mo4gCwJbf7RA9AsBYano2wBq7dBSsDw==","signature_status":"signed_v1","signed_at":"2026-07-21T01:21:47.047918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.17468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8085fc555d4dd3876ce9fe912ff1d50c98cb90e5da7870b42351cc3026fdc134","sha256:380df8f050c2d69a6825d0d6c136916015e2674ad88cba23a8fac0add3cdc14f"],"state_sha256":"b92555570920bed9378f3477b0eb1d1b8c725ad28b880224a4506f2438ed8d6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/AIqFmkrTfmYjmlDB2+jY8efLJrGmH3OD9WgWBRPFnEu3BXyK9TOHvBykWD2duJs2pi3YI7wZj1U/vq1PbrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:53:31.494081Z","bundle_sha256":"f6ef5bb118d5ca14815a43b55423b3a8acd75c8a0e8d8069179924b2e56e616c"}}