Pith Number

pith:3PMX4LD2

pith:2014:3PMX4LD2JOSN7FQHBZ2VTCHZOF

not attested not anchored not stored refs pending

On $p$-adic Gibbs measures for the SOS model on a Cayley tree

Otabek Khakimov

arxiv:1406.5140 v1 · 2014-04-16 · 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{3PMX4LD2JOSN7FQHBZ2VTCHZOF}

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	2026-05-18T02:49:20.869236Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbd97e2c7a4ba4df96070e755988f97160a54e193cdfadd969f56b5fd6ff4ad4

Aliases

arxiv: 1406.5140 · arxiv_version: 1406.5140v1 · doi: 10.48550/arxiv.1406.5140 · pith_short_12: 3PMX4LD2JOSN · pith_short_16: 3PMX4LD2JOSN7FQH · pith_short_8: 3PMX4LD2

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/3PMX4LD2JOSN7FQHBZ2VTCHZOF \
  | 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: dbd97e2c7a4ba4df96070e755988f97160a54e193cdfadd969f56b5fd6ff4ad4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16e3e17cc945ab9d75419117252efaea897c305ae50d7d12fcb9f4bd6bda33f6",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-04-16T06:29:07Z",
    "title_canon_sha256": "01ae53624211c2b19c55cd7c9ae0e92a1b3286b466a1afd77bcb457c64322556"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.5140",
    "kind": "arxiv",
    "version": 1
  }
}