{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LKVCEYCV6C2EBHAD24UXC554XB","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":"10e377c8d495fe64e7b0568f201c7627cfa974af5a5a680b900004878fa75c00","cross_cats_sorted":["math.AP","math.DG","math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-17T15:22:49Z","title_canon_sha256":"f5ec37fdaa817b8ffb6064663ece4dc546700d8e63485a5c195f2944919c1cb9"},"schema_version":"1.0","source":{"id":"2605.17502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17502","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17502v1","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17502","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"LKVCEYCV6C2E","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"LKVCEYCV6C2EBHAD","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"LKVCEYCV","created_at":"2026-05-20T00:04:42Z"}],"graph_snapshots":[{"event_id":"sha256:6363cda02937d7e0215bf460963e21f0602f27c48c2bb4a6edeb269ab66bf34c","target":"graph","created_at":"2026-05-20T00:04:42Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"A Lagrangian kinematic construction, in which the strain rate is built from the rate of change of inner products of Lie-dragged connecting vectors, uniquely selects the deformation Laplacian for fluids whose configuration space is intrinsically the manifold."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The strain rate constructed from inner-product geometry of Lie-dragged vectors is symmetric and possesses no antisymmetric part, which is invoked to exclude the Hodge Laplacian at the kinematic step before constitutive assumptions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A Lagrangian kinematic construction from inner-product changes of Lie-dragged vectors uniquely selects the deformation Laplacian for intrinsic fluid configuration spaces on Riemannian manifolds."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A Lagrangian kinematic construction uniquely selects the deformation Laplacian as the viscous operator for fluids on Riemannian manifolds."}],"snapshot_sha256":"7eb32220558ebdb81c2700aff09e74107888c070d66b18ecf40d5c87690d2efb"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"71551af61282f1dd573fa2c35dda2a228b1d338a3a004f3d5857f523f3431954"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.613554Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:31:09.162001Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.665300Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.635931Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17502/integrity.json","findings":[],"snapshot_sha256":"1bd7872d50b702a793fc07338f906c6a79af645a6cca7ecd0e27cf74ff18ba82","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On a general Riemannian manifold the Navier-Stokes equations admit several inequivalent formulations, differing in the choice of viscous operator: the Hodge Laplacian, the Bochner Laplacian, or the deformation Laplacian. We show that a Lagrangian kinematic construction, in which the strain rate is built from the rate of change of inner products of Lie-dragged connecting vectors, uniquely selects the deformation Laplacian for fluids whose configuration space is intrinsically the manifold. The Hodge Laplacian is excluded at the kinematic step (before introducing constitutive assumptions) because","authors_text":"Samuel L. Braunstein, Zhi-Wei Wang","cross_cats":["math.AP","math.DG","math.MP","physics.flu-dyn"],"headline":"A Lagrangian kinematic construction uniquely selects the deformation Laplacian as the viscous operator for fluids on Riemannian manifolds.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-17T15:22:49Z","title":"Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle"},"references":{"count":31,"internal_anchors":0,"resolved_work":31,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Czubak, In search of the viscosity operator on Riemannian manifolds,Notices Amer","work_id":"48dbf9a6-6a69-4cae-9701-de924bbd9f4b","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"D.G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid,Ann. Math.92(1970) 102–163","work_id":"81c2b722-25bd-4018-b1e7-0fa36818059e","year":1970},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Arnold, Sur la g´ eom´ etrie diff´ erentielle des groupes de Lie de dimension infinie et ses applications ` a l’hydrodynamique des fluides parfaits,Ann","work_id":"621ff085-fb4c-44cf-9f96-ab291f08d3c8","year":1966},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evo- lution equations,Comm","work_id":"ba1f9c98-2efd-4cc1-b43f-40ce4674c228","year":1992},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Taylor,Partial Differential Equations III: Nonlinear Equations, 2nd ed., Springer, 2011","work_id":"48214952-8da3-404d-b998-a8479bffe78f","year":2011}],"snapshot_sha256":"607f74fdd83f6dbdf713b38e78924079c7134c06581cc5b4a9bb825c00928922"},"source":{"id":"2605.17502","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:22:17.754425Z","id":"361ceaef-6dad-4c72-bba0-ddf62fe4e26e","model_set":{"reader":"grok-4.3"},"one_line_summary":"A Lagrangian kinematic construction from inner-product changes of Lie-dragged vectors uniquely selects the deformation Laplacian for intrinsic fluid configuration spaces on Riemannian manifolds.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A Lagrangian kinematic construction uniquely selects the deformation Laplacian as the viscous operator for fluids on Riemannian manifolds.","strongest_claim":"A Lagrangian kinematic construction, in which the strain rate is built from the rate of change of inner products of Lie-dragged connecting vectors, uniquely selects the deformation Laplacian for fluids whose configuration space is intrinsically the manifold.","weakest_assumption":"The strain rate constructed from inner-product geometry of Lie-dragged vectors is symmetric and possesses no antisymmetric part, which is invoked to exclude the Hodge Laplacian at the kinematic step before constitutive assumptions."}},"verdict_id":"361ceaef-6dad-4c72-bba0-ddf62fe4e26e"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a90b0d243a7a34facdf8b8cc361fc5c97f8ee380d3dbab609adda8e0c3520280","target":"record","created_at":"2026-05-20T00:04:42Z","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":"10e377c8d495fe64e7b0568f201c7627cfa974af5a5a680b900004878fa75c00","cross_cats_sorted":["math.AP","math.DG","math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-17T15:22:49Z","title_canon_sha256":"f5ec37fdaa817b8ffb6064663ece4dc546700d8e63485a5c195f2944919c1cb9"},"schema_version":"1.0","source":{"id":"2605.17502","kind":"arxiv","version":1}},"canonical_sha256":"5aaa226055f0b4409c03d7297177bcb8496ec6cc015e99757b3203c241880d2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5aaa226055f0b4409c03d7297177bcb8496ec6cc015e99757b3203c241880d2a","first_computed_at":"2026-05-20T00:04:42.509931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:42.509931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uwHlAuOV/CEjlkl/OczbtzQxDfKeO/x/ZKalAhKmVAgHiZVGWyzCQYLUX3HwuYMu8/b+cd4ZCgO1Rhesrh9xCQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:42.510891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90b0d243a7a34facdf8b8cc361fc5c97f8ee380d3dbab609adda8e0c3520280","sha256:6363cda02937d7e0215bf460963e21f0602f27c48c2bb4a6edeb269ab66bf34c"],"state_sha256":"fddbb78dd0bf061e96b1dd0b3747b25d415888e9b4a6c1cf00121b772d9bc510"}