Pith Number

pith:R4L4CEE5

pith:2010:R4L4CEE5RQP4WEZL4TOYVU5PFV

not attested not anchored not stored refs pending

Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

Akimichi Takemura, Hiromasa Nakayama, Katsuyoshi Ohara, Kenta Nishiyama, Masayuki Noro, Nobuki Takayama, Tomonari Sei

arxiv:1005.5273 v2 · 2010-05-28 · cs.SC · math.OC · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R4L4CEE5RQP4WEZL4TOYVU5PFV}

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	2026-05-18T03:36:46.911089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f17c1109d8c1fcb132be4dd8ad3af2d450f6ddb6726e4980271e076a003dc26

Aliases

arxiv: 1005.5273 · arxiv_version: 1005.5273v2 · doi: 10.48550/arxiv.1005.5273 · pith_short_12: R4L4CEE5RQP4 · pith_short_16: R4L4CEE5RQP4WEZL · pith_short_8: R4L4CEE5

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/R4L4CEE5RQP4WEZL4TOYVU5PFV \
  | 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: 8f17c1109d8c1fcb132be4dd8ad3af2d450f6ddb6726e4980271e076a003dc26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d19ea26b87c77be066000be294ad513634e465abe06e83a75924df64d4d9abea",
    "cross_cats_sorted": [
      "math.OC",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2010-05-28T12:02:21Z",
    "title_canon_sha256": "692ac2a10ecc437cf9ecb282572f49dc31e7a17f4aec68d4a62eb4b1153d8a8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.5273",
    "kind": "arxiv",
    "version": 2
  }
}