Pith Number

pith:F4BPZ2BZ

pith:2015:F4BPZ2BZNXX4CZUP7KK3TVGA77

not attested not anchored not stored refs pending

Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more

J. M. Sanz-Serna

arxiv:1503.04021 v2 · 2015-03-13 · math.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{F4BPZ2BZNXX4CZUP7KK3TVGA77}

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	2026-05-18T01:42:47.646354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f02fce8396defc1668ffa95b9d4c0fffc6b4e3207c20d719cf96c04b45e3480

Aliases

arxiv: 1503.04021 · arxiv_version: 1503.04021v2 · doi: 10.48550/arxiv.1503.04021 · pith_short_12: F4BPZ2BZNXX4 · pith_short_16: F4BPZ2BZNXX4CZUP · pith_short_8: F4BPZ2BZ

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/F4BPZ2BZNXX4CZUP7KK3TVGA77 \
  | 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: 2f02fce8396defc1668ffa95b9d4c0fffc6b4e3207c20d719cf96c04b45e3480

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d39b2095ad7e003a56862364a319acec8fea0b596923d810616b0e05285f3dc5",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-03-13T10:59:17Z",
    "title_canon_sha256": "e0ae34cdc70b13b0b21cbe083d1b2fcc5188b0611ba75c550c92b59a77f489dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04021",
    "kind": "arxiv",
    "version": 2
  }
}