Pith Number

pith:3OV4L4ES

pith:2005:3OV4L4ESYO7YDP3HTAU6OFCIZO

not attested not anchored not stored refs pending

On Uniqueness of Gibbs Measures for $P$-Adic Nonhomogeneous $\l$-Model on the Cayley Tree

Farrukh Mukhamedov, Murod Khamraev, Utkir Rozikov

arxiv:math-ph/0510021 v2 · 2005-10-06 · 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{3OV4L4ESYO7YDP3HTAU6OFCIZO}

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	2026-05-18T01:38:33.018080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbabc5f092c3bf81bf679829e71448cb87f568be4091be807dd2f2fb36ee3e03

Aliases

arxiv: math-ph/0510021 · arxiv_version: math-ph/0510021v2 · doi: 10.48550/arxiv.math-ph/0510021 · pith_short_12: 3OV4L4ESYO7Y · pith_short_16: 3OV4L4ESYO7YDP3H · pith_short_8: 3OV4L4ES

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/3OV4L4ESYO7YDP3HTAU6OFCIZO \
  | 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: dbabc5f092c3bf81bf679829e71448cb87f568be4091be807dd2f2fb36ee3e03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84d05ba51e1c806dd3827262f84f13630ca4742c9781b0b91ad657f1e449d348",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-10-06T10:54:04Z",
    "title_canon_sha256": "9965141175f702fd5c1da494143cac0460baf607e29e5f94e5d9d6c423dce0a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0510021",
    "kind": "arxiv",
    "version": 2
  }
}