Pith Number

pith:PZJBXEVE

pith:2011:PZJBXEVEFFWTKK6AQLO7LJBBH4

not attested not anchored not stored refs pending

Nonconventional averages along arithmetic progressions and lattice spin systems

C. Giardina, F. Redig, G. Carinci, J.-R. Chazottes

arxiv:1110.2354 v3 · 2011-10-11 · math.PR · math-ph · 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{PZJBXEVEFFWTKK6AQLO7LJBBH4}

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	2026-05-18T03:56:10.600808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e521b92a4296d352bc082ddf5a4213f3549ff4729f4d217083ec43816f00dc1

Aliases

arxiv: 1110.2354 · arxiv_version: 1110.2354v3 · doi: 10.48550/arxiv.1110.2354 · pith_short_12: PZJBXEVEFFWT · pith_short_16: PZJBXEVEFFWTKK6A · pith_short_8: PZJBXEVE

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/PZJBXEVEFFWTKK6AQLO7LJBBH4 \
  | 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: 7e521b92a4296d352bc082ddf5a4213f3549ff4729f4d217083ec43816f00dc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f09d221428370dbeb68f4240787a025baf81871ca8e674ba7a2e936d22e94a36",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-11T12:45:20Z",
    "title_canon_sha256": "ebcb058fe61368e996b6e257fb325f4b876817e02ee1b0ef265026f04013166d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2354",
    "kind": "arxiv",
    "version": 3
  }
}