Pith Number

pith:3NGT5RAC

pith:2015:3NGT5RAC7WOLMH6OTKJBUHJBBR

not attested not anchored not stored refs pending

The Stan Math Library: Reverse-Mode Automatic Differentiation in C++

Bob Carpenter, Daniel Lee, Marcus Brubaker, Matthew D. Hoffman, Michael Betancourt, Peter Li

arxiv:1509.07164 v1 · 2015-09-23 · cs.MS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NGT5RAC7WOLMH6OTKJBUHJBBR}

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.

Cited by

3 papers in Pith

Higher Order Automatic Differentiation of Higher Order Functions

CHAD: Combinatory Homomorphic Automatic Differentiation

Neural Ordinary Differential Equations

Receipt and verification

First computed	2026-05-18T01:32:11.211118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db4d3ec402fd9cb61fce9a921a1d210c74148ab975ac230f26b407a4eac251aa

Aliases

arxiv: 1509.07164 · arxiv_version: 1509.07164v1 · doi: 10.48550/arxiv.1509.07164 · pith_short_12: 3NGT5RAC7WOL · pith_short_16: 3NGT5RAC7WOLMH6O · pith_short_8: 3NGT5RAC

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/3NGT5RAC7WOLMH6OTKJBUHJBBR \
  | 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: db4d3ec402fd9cb61fce9a921a1d210c74148ab975ac230f26b407a4eac251aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75a9fc8eb742025943201f3fc88854bdc2f49d6d9b5938390bbeca51d65b59a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.MS",
    "submitted_at": "2015-09-23T21:34:46Z",
    "title_canon_sha256": "a636d4506626fd61d76a6645e46be1418fb68eb41d5f3d56aaad0f4dbc0e46a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07164",
    "kind": "arxiv",
    "version": 1
  }
}