Pith Number

pith:QX4C2BJF

pith:2005:QX4C2BJFHLPR7TGXNO5X2O7RZ4

not attested not anchored not stored refs pending

Exact controllability in projections for three-dimensional Navier-Stokes equations

Armen Shirikyan

arxiv:math/0512600 v1 · 2005-12-27 · math.AP · 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{QX4C2BJFHLPR7TGXNO5X2O7RZ4}

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	2026-05-18T00:27:05.082027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85f82d05253adf1fccd76bbb7d3bf1cf125b83391c956a81cdb01726652f73ed

Aliases

arxiv: math/0512600 · arxiv_version: math/0512600v1 · doi: 10.48550/arxiv.math/0512600 · pith_short_12: QX4C2BJFHLPR · pith_short_16: QX4C2BJFHLPR7TGX · pith_short_8: QX4C2BJF

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/QX4C2BJFHLPR7TGXNO5X2O7RZ4 \
  | 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: 85f82d05253adf1fccd76bbb7d3bf1cf125b83391c956a81cdb01726652f73ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1e4d73703708a7d8ca95ce5df329b75a9a0a6ca3c02ed397c545cedc7c4adbd",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2005-12-27T14:10:28Z",
    "title_canon_sha256": "7ca58f2224b31bf359967768f6ea7b88d11e4b440723166e8691a4a6cbfb896a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512600",
    "kind": "arxiv",
    "version": 1
  }
}