Pith Number

pith:AWG5P5HG

pith:2026:AWG5P5HGVS2B3PWT7Y7V5EQHCH

not attested not anchored not stored refs pending

Error estimates for an unregularized optimal control problem for the stationary Navier-Stokes equations

Francisco Fuica, Nicolai Jork

Error estimates are proven for variational discretization of an unregularized optimal control problem for the stationary Navier-Stokes equations, for nonsingular locally optimal controls satisfying a growth condition that implies bang-bang structure.

arxiv:2605.01633 v2 · 2026-05-02 · math.NA · cs.NA · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AWG5P5HGVS2B3PWT7Y7V5EQHCH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove a priori error estimates for locally optimal controls that are nonsingular and which satisfy a growth condition which implies a bang-bang structure.

C2weakest assumption

The locally optimal controls are nonsingular and satisfy a growth condition implying bang-bang structure (as stated in the abstract for the error estimates to hold).

C3one line summary

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T02:04:11.765465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

058dd7f4e6acb41dbed3fe3f5e920711d10bc30d8a3cd648168bb9214356561c

Aliases

arxiv: 2605.01633 · arxiv_version: 2605.01633v2 · doi: 10.48550/arxiv.2605.01633 · pith_short_12: AWG5P5HGVS2B · pith_short_16: AWG5P5HGVS2B3PWT · pith_short_8: AWG5P5HG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AWG5P5HGVS2B3PWT7Y7V5EQHCH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 058dd7f4e6acb41dbed3fe3f5e920711d10bc30d8a3cd648168bb9214356561c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d79679fb6cefce2e533f4c817739f9646a26f9302923510451b67741e758b66",
    "cross_cats_sorted": [
      "cs.NA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-02T22:48:52Z",
    "title_canon_sha256": "46a9e7f82b2002dbff7a993bc3e4fd66370f411e5059f51a4b9e0355f06190c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01633",
    "kind": "arxiv",
    "version": 2
  }
}