Pith Number

pith:TPP6YNT6

pith:2015:TPP6YNT6CUAULOTAMWGZXF34N6

not attested not anchored not stored refs pending

Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables

Akimichi Takemura, Tamio Koyama

arxiv:1503.00378 v3 · 2015-03-01 · 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{TPP6YNT6CUAULOTAMWGZXF34N6}

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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.

Receipt and verification

First computed	2026-05-18T01:34:35.017525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bdfec367e150145ba60658d9b977c6f80059e6d2b03c8cb255befc1e19b3af9

Aliases

arxiv: 1503.00378 · arxiv_version: 1503.00378v3 · doi: 10.48550/arxiv.1503.00378 · pith_short_12: TPP6YNT6CUAU · pith_short_16: TPP6YNT6CUAULOTA · pith_short_8: TPP6YNT6

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/TPP6YNT6CUAULOTAMWGZXF34N6 \
  | 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: 9bdfec367e150145ba60658d9b977c6f80059e6d2b03c8cb255befc1e19b3af9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19376103240480847e3f3f83395aefda31006a2704842182c543be1c9615f417",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2015-03-01T23:56:25Z",
    "title_canon_sha256": "1498812fd979ab4b3e92cafb19af64bdaefaff44d1e6e5bbf8102e3a49fc3215"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.00378",
    "kind": "arxiv",
    "version": 3
  }
}