Pith Number

pith:JPXAQ47V

pith:2006:JPXAQ47VKMAZ63IEEKFDFNH32Q

not attested not anchored not stored refs pending

Combinatorics of Partial Derivatives

Michael Hardy

arxiv:math/0601149 v1 · 2006-01-08 · math.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{JPXAQ47VKMAZ63IEEKFDFNH32Q}

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

1 paper in Pith

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration

Receipt and verification

First computed	2026-07-04T14:52:47.267920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bee0873f553019f6d04228a32b4fbd439400c855c35416237a16c1f272c1e72

Aliases

arxiv: math/0601149 · arxiv_version: math/0601149v1 · doi: 10.48550/arxiv.math/0601149 · pith_short_12: JPXAQ47VKMAZ · pith_short_16: JPXAQ47VKMAZ63IE · pith_short_8: JPXAQ47V

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/JPXAQ47VKMAZ63IEEKFDFNH32Q \
  | 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: 4bee0873f553019f6d04228a32b4fbd439400c855c35416237a16c1f272c1e72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f43f6eafaefc53e82dd4b6b9e8bdac0b8b1498a5872a6b3cce02aa1581f8d7ef",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-01-08T00:35:43Z",
    "title_canon_sha256": "64d84a523a11e722f21be4d3d44322d0fb0972e5ab2d3341d18e1e9a64862e77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601149",
    "kind": "arxiv",
    "version": 1
  }
}