Pith Number

pith:MTBNVVR6

pith:2015:MTBNVVR67DLEHGM5KU4DU5GWJH

not attested not anchored not stored refs pending

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

Farrukh Mukhamedov, Hasan Akin

arxiv:1504.00755 v1 · 2015-04-03 · 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{MTBNVVR67DLEHGM5KU4DU5GWJH}

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	2026-05-18T02:19:42.028265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64c2dad63ef8d643999d55383a74d649e1eb82b7d8dc707fa59cf9416a1216f8

Aliases

arxiv: 1504.00755 · arxiv_version: 1504.00755v1 · doi: 10.48550/arxiv.1504.00755 · pith_short_12: MTBNVVR67DLE · pith_short_16: MTBNVVR67DLEHGM5 · pith_short_8: MTBNVVR6

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/MTBNVVR67DLEHGM5KU4DU5GWJH \
  | 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: 64c2dad63ef8d643999d55383a74d649e1eb82b7d8dc707fa59cf9416a1216f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b88fe63cd161a6092bc88605abc1e2c0e2d5df26cfe7640d6f3f8e632f886f6f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-04-03T06:51:57Z",
    "title_canon_sha256": "9ce1bb57407be56c0c820fa89312593512178df93dc113ab9e5ac0605c7949e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00755",
    "kind": "arxiv",
    "version": 1
  }
}