Pith Number

pith:L2IMPF7X

pith:2001:L2IMPF7X7Q5TH6UO4GX6ZYQ57B

not attested not anchored not stored refs pending

Random Electrical Networks on Complete Graphs II: Proofs

Geoffrey Grimmett, Harry Kesten

arxiv:math/0107068 v1 · 2001-07-10 · 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{L2IMPF7X7Q5TH6UO4GX6ZYQ57B}

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	2026-05-18T01:05:37.679096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e90c797f7fc3b33fa8ee1afece21df87fb400df630ef6f12c88ab16d0802c50

Aliases

arxiv: math/0107068 · arxiv_version: math/0107068v1 · doi: 10.48550/arxiv.math/0107068 · pith_short_12: L2IMPF7X7Q5T · pith_short_16: L2IMPF7X7Q5TH6UO · pith_short_8: L2IMPF7X

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/L2IMPF7X7Q5TH6UO4GX6ZYQ57B \
  | 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: 5e90c797f7fc3b33fa8ee1afece21df87fb400df630ef6f12c88ab16d0802c50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40c58bf5f28f1f30a71ef84c269ca00712a56064277136bdbec02ae396abb1c3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2001-07-10T09:34:48Z",
    "title_canon_sha256": "02c1e7c60c3098967b3141a4ddf5a6745a303d4bce821276f9e308f63b882f6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0107068",
    "kind": "arxiv",
    "version": 1
  }
}