Pith Number

pith:HB26NF5Q

pith:2009:HB26NF5QQQQZPYH2R6ABUPIK5N

not attested not anchored not stored refs pending

Euler's fluid equations: Optimal Control vs Optimization

Darryl D. Holm

arxiv:0904.4289 v4 · 2009-04-28 · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HB26NF5QQQQZPYH2R6ABUPIK5N}

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	2026-05-18T02:13:56.833678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3875e697b0842197e0fa8f801a3d0aeb48f6f31ef92dbfa502cf10d4285a9e82

Aliases

arxiv: 0904.4289 · arxiv_version: 0904.4289v4 · doi: 10.48550/arxiv.0904.4289 · pith_short_12: HB26NF5QQQQZ · pith_short_16: HB26NF5QQQQZPYH2 · pith_short_8: HB26NF5Q

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/HB26NF5QQQQZPYH2R6ABUPIK5N \
  | 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: 3875e697b0842197e0fa8f801a3d0aeb48f6f31ef92dbfa502cf10d4285a9e82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbbc7bf41e0524e61724bf1e6fefc21a22e7b3813a27fd77f866ff37f01402a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.CD",
    "submitted_at": "2009-04-28T01:13:25Z",
    "title_canon_sha256": "f84548b4836a2412ce2439e1201943e3efd5e0c0b7ea4635f8495c2b8db6fe55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.4289",
    "kind": "arxiv",
    "version": 4
  }
}