Pith Number

pith:N26PB7QZ

pith:2012:N26PB7QZQJB5ZZKURRYFJ3HJRR

not attested not anchored not stored refs pending

Computing bounds for entropy of stationary Z^d Markov random fields

Brian Marcus, Ronnie Pavlov

arxiv:1204.2612 v3 · 2012-04-12 · math.DS · math-ph · 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{N26PB7QZQJB5ZZKURRYFJ3HJRR}

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	2026-05-18T03:49:11.661331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ebcf0fe198243dce5548c7054ece98c712a42026981cf3b4699d353743045b9

Aliases

arxiv: 1204.2612 · arxiv_version: 1204.2612v3 · doi: 10.48550/arxiv.1204.2612 · pith_short_12: N26PB7QZQJB5 · pith_short_16: N26PB7QZQJB5ZZKU · pith_short_8: N26PB7QZ

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/N26PB7QZQJB5ZZKURRYFJ3HJRR \
  | 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: 6ebcf0fe198243dce5548c7054ece98c712a42026981cf3b4699d353743045b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d805430a0dd45980595b5f08e85989b913556334ef36ca07c4be2ac200ef8a45",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-04-12T04:01:56Z",
    "title_canon_sha256": "7c961b804e48f4344c6330db06b8b44a2ada68aaccb1bbd713e47f21ed8522a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2612",
    "kind": "arxiv",
    "version": 3
  }
}