Pith Number

pith:4GCCYHVS

pith:2016:4GCCYHVSMFH3U6HNXPU2DXBCO3

not attested not anchored not stored refs pending

The Discrete Adjoint Method for Exponential Integration

Eldad Haber, Kai Rothauge, Uri Ascher

arxiv:1610.02596 v1 · 2016-10-08 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GCCYHVSMFH3U6HNXPU2DXBCO3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:02:51.168855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1842c1eb2614fba78edbbe9a1dc2276e22759b4e8dd86861218dc2586905566

Aliases

arxiv: 1610.02596 · arxiv_version: 1610.02596v1 · doi: 10.48550/arxiv.1610.02596 · pith_short_12: 4GCCYHVSMFH3 · pith_short_16: 4GCCYHVSMFH3U6HN · pith_short_8: 4GCCYHVS

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/4GCCYHVSMFH3U6HNXPU2DXBCO3 \
  | 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: e1842c1eb2614fba78edbbe9a1dc2276e22759b4e8dd86861218dc2586905566

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7c04faa59d97c68c6607a3823e598d0630830af171a0a98d68955c8ff62e1eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-10-08T23:25:00Z",
    "title_canon_sha256": "fc5c2e8a5866b19563270c96632db8ed2b4f06ec33f49e571661367a9d5b3a21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02596",
    "kind": "arxiv",
    "version": 1
  }
}