Pith Number

pith:PPHJFN6R

pith:2015:PPHJFN6RS33DF4Q2CFZ2DFWBGS

not attested not anchored not stored refs pending

A short proof of the Kac-Ward formula

Marcin Lis

arxiv:1502.04322 v2 · 2015-02-15 · math-ph · math.CO · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPHJFN6RS33DF4Q2CFZ2DFWBGS}

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	2026-05-18T01:33:56.781890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bce92b7d196f632f21a1173a196c134be1706120f520acd596f421bf0c66768

Aliases

arxiv: 1502.04322 · arxiv_version: 1502.04322v2 · doi: 10.48550/arxiv.1502.04322 · pith_short_12: PPHJFN6RS33D · pith_short_16: PPHJFN6RS33DF4Q2 · pith_short_8: PPHJFN6R

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/PPHJFN6RS33DF4Q2CFZ2DFWBGS \
  | 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: 7bce92b7d196f632f21a1173a196c134be1706120f520acd596f421bf0c66768

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc5437049fd9b994d3f5aea70c3ac75ff1014659f13b455cb165a23286f768f3",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-02-15T15:26:58Z",
    "title_canon_sha256": "cad4ee0e398ff44f22541a81f41a9f59acf4ae3c78434e33a349f776e84d9fc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.04322",
    "kind": "arxiv",
    "version": 2
  }
}