Pith Number

pith:5WOLY6IY

pith:2013:5WOLY6IY46BPHAXGJETGYJFZXV

not attested not anchored not stored refs pending

Second-order Markov random fields for independent sets on the infinite Cayley tree

David A. Goldberg

arxiv:1301.1762 v4 · 2013-01-09 · math.PR · cs.CC · cs.DM · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5WOLY6IY46BPHAXGJETGYJFZXV}

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	2026-05-18T01:42:57.750390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed9cbc7918e782f382e649266c24b9bd5860b00d2447900d603b226b9338977b

Aliases

arxiv: 1301.1762 · arxiv_version: 1301.1762v4 · doi: 10.48550/arxiv.1301.1762 · pith_short_12: 5WOLY6IY46BP · pith_short_16: 5WOLY6IY46BPHAXG · pith_short_8: 5WOLY6IY

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/5WOLY6IY46BPHAXGJETGYJFZXV \
  | 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: ed9cbc7918e782f382e649266c24b9bd5860b00d2447900d603b226b9338977b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f56a2bdb50222d38647b12cb2c1a739735530dcc7bb22c7986771058cb575df4",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DM",
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-01-09T07:19:24Z",
    "title_canon_sha256": "8262d00b1d626f81dceba7499f0ddebf9e901cbc3c1ae387bc22ee394deacc58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1762",
    "kind": "arxiv",
    "version": 4
  }
}