Pith Number

pith:S5GD2VGZ

pith:2017:S5GD2VGZOZ6NLWGB2A7FANUU4T

not attested not anchored not stored refs pending

Approximate controllability for Navier--Stokes equations in $\mathrm{3D}$ rectangles under Lions boundary conditions

Duy Phan, S\'ergio S. Rodrigues

arxiv:1712.04900 v1 · 2017-12-13 · 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{S5GD2VGZOZ6NLWGB2A7FANUU4T}

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.

Receipt and verification

First computed	2026-05-18T00:10:47.123466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

974c3d54d9767cd5d8c1d03e503694e4f49ff04e8cb177970e365bff3524c5b5

Aliases

arxiv: 1712.04900 · arxiv_version: 1712.04900v1 · doi: 10.48550/arxiv.1712.04900 · pith_short_12: S5GD2VGZOZ6N · pith_short_16: S5GD2VGZOZ6NLWGB · pith_short_8: S5GD2VGZ

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/S5GD2VGZOZ6NLWGB2A7FANUU4T \
  | 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: 974c3d54d9767cd5d8c1d03e503694e4f49ff04e8cb177970e365bff3524c5b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c91569bdc2a2a887834f6ac70ea95c53ceab789f0b76d8fd859b1b4718a7299",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-12-13T18:12:21Z",
    "title_canon_sha256": "aa7c21a846b37b59213d79b13af88a4eacfcd1c3f8fa2847688526bc3d519e19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.04900",
    "kind": "arxiv",
    "version": 1
  }
}