Pith Number

pith:4DKX6B5R

pith:2016:4DKX6B5RF6454MT5FJE2K3DWUE

not attested not anchored not stored refs pending

An algebraic multigrid method for $Q_2-Q_1$ mixed discretizations of the Navier-Stokes equations

Andrey Prokopenko, Raymond S. Tuminaro

arxiv:1607.02489 v2 · 2016-07-08 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4DKX6B5RF6454MT5FJE2K3DWUE}

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	2026-06-04T18:09:52.585249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0d57f07b12fb9de327d2a49a56c76a111523d01946f5c0960900368b07bb074

Aliases

arxiv: 1607.02489 · arxiv_version: 1607.02489v2 · doi: 10.48550/arxiv.1607.02489 · pith_short_12: 4DKX6B5RF645 · pith_short_16: 4DKX6B5RF6454MT5 · pith_short_8: 4DKX6B5R

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/4DKX6B5RF6454MT5FJE2K3DWUE \
  | 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: e0d57f07b12fb9de327d2a49a56c76a111523d01946f5c0960900368b07bb074

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e364a041fd78515d5a13314aa21046d80c1d8dfa98689edbb30facc929fe6f6b",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-07-08T18:42:38Z",
    "title_canon_sha256": "c830c53f683d01ea0e4f2fb9429aba716e0c70018836b4dde0ff9fadc9a0dbbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02489",
    "kind": "arxiv",
    "version": 2
  }
}