Pith Number

pith:JB7EW6HR

pith:2010:JB7EW6HRS35NUKRS6QOCAZOWHF

not attested not anchored not stored refs pending

Counting in Graph Covers: A Combinatorial Characterization of the Bethe Entropy Function

Pascal O. Vontobel

arxiv:1012.0065 v2 · 2010-12-01 · cs.IT · cond-mat.stat-mech · cs.AI · math.CO · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JB7EW6HRS35NUKRS6QOCAZOWHF}

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	2026-05-18T03:08:14.879297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

487e4b78f196fada2a32f41c2065d63974850e43a78a5460b60cc528672ab8a0

Aliases

arxiv: 1012.0065 · arxiv_version: 1012.0065v2 · doi: 10.48550/arxiv.1012.0065 · pith_short_12: JB7EW6HRS35N · pith_short_16: JB7EW6HRS35NUKRS · pith_short_8: JB7EW6HR

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/JB7EW6HRS35NUKRS6QOCAZOWHF \
  | 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: 487e4b78f196fada2a32f41c2065d63974850e43a78a5460b60cc528672ab8a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6c9d74592ad4d9bbd8fdb0a85697142aad6ffb933a196200e322f9099891c46",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.AI",
      "math.CO",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2010-12-01T00:00:05Z",
    "title_canon_sha256": "fd544ad1f696eba669485fc72d24705315517666b4bfc6e2cca25df5cadb88fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0065",
    "kind": "arxiv",
    "version": 2
  }
}