Pith Number

pith:U64NPHO6

pith:2018:U64NPHO6QD2QS63VLKSKKU7P55

not attested not anchored not stored refs pending

A Geometric Theory of Higher-Order Automatic Differentiation

Michael Betancourt

arxiv:1812.11592 v1 · 2018-12-30 · stat.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U64NPHO6QD2QS63VLKSKKU7P55}

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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.

Cited by

2 papers in Pith

Archimedean Copula Inference via Taylor-Mode AD

Higher Order Automatic Differentiation of Higher Order Functions

Receipt and verification

First computed	2026-05-17T23:57:11.563097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7b8d79dde80f5097b755aa4a553efef5db86686d5f4b13e86578a6bbd3fe167

Aliases

arxiv: 1812.11592 · arxiv_version: 1812.11592v1 · doi: 10.48550/arxiv.1812.11592 · pith_short_12: U64NPHO6QD2Q · pith_short_16: U64NPHO6QD2QS63V · pith_short_8: U64NPHO6

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/U64NPHO6QD2QS63VLKSKKU7P55 \
  | 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: a7b8d79dde80f5097b755aa4a553efef5db86686d5f4b13e86578a6bbd3fe167

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b95dd1356ded92dfa25fe2a4d13c70aaf10f2392d27a6c2543f40f4282c1b3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.CO",
    "submitted_at": "2018-12-30T19:06:30Z",
    "title_canon_sha256": "ad84c6b49519daaa1c884f9780f17826e98794df5cd32f73b9374164357e44ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.11592",
    "kind": "arxiv",
    "version": 1
  }
}