Pith Number

pith:NHWM37DA

pith:2017:NHWM37DAEYQPMHUMGTDAMGQQ46

not attested not anchored not stored refs pending

Gibbs measures and free energies of Ising-Vannimenus Model on the Cayley tree

Farrukh Mukhamedov, Hasan Akin, Otabek Khakimov

arxiv:1704.01933 v1 · 2017-04-06 · 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{NHWM37DAEYQPMHUMGTDAMGQQ46}

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	2026-05-18T00:38:08.779022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69eccdfc602620f61e8c34c6061a10e7935092a6296c826b3003223fbad08ef9

Aliases

arxiv: 1704.01933 · arxiv_version: 1704.01933v1 · doi: 10.48550/arxiv.1704.01933 · pith_short_12: NHWM37DAEYQP · pith_short_16: NHWM37DAEYQPMHUM · pith_short_8: NHWM37DA

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/NHWM37DAEYQPMHUMGTDAMGQQ46 \
  | 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: 69eccdfc602620f61e8c34c6061a10e7935092a6296c826b3003223fbad08ef9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7f97f945827edd8ae659711e92a03329b143ece477265069b8d52c32d6da88f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-04-06T17:02:03Z",
    "title_canon_sha256": "c04f107168632a671f6964bb7c25161fadd41e5dc20c5339a698702c640a24ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.01933",
    "kind": "arxiv",
    "version": 1
  }
}