Pith Number

pith:4HZFMLEH

pith:2011:4HZFMLEH42D5RF6CJ5YYANPNDJ

not attested not anchored not stored refs pending

On phase transition for one dimensional countable state $P$-adic Potts model

Farrukh Mukhamedov

arxiv:1106.5560 v1 · 2011-06-28 · math-ph · math.FA · 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{4HZFMLEH42D5RF6CJ5YYANPNDJ}

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	2026-05-18T04:19:12.952991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1f2562c87e687d897c24f718035ed1a5a5538748b09a987acc52f7919b97471

Aliases

arxiv: 1106.5560 · arxiv_version: 1106.5560v1 · doi: 10.48550/arxiv.1106.5560 · pith_short_12: 4HZFMLEH42D5 · pith_short_16: 4HZFMLEH42D5RF6C · pith_short_8: 4HZFMLEH

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/4HZFMLEH42D5RF6CJ5YYANPNDJ \
  | 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: e1f2562c87e687d897c24f718035ed1a5a5538748b09a987acc52f7919b97471

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "066dc516b8dcd490adb4c809e42d757262800bbf8da1ddeac2673f89ea148827",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-06-28T03:36:28Z",
    "title_canon_sha256": "0d2ca38800e79b526eb751cab763913fa82043c61952457c1d0fe78985fed642"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5560",
    "kind": "arxiv",
    "version": 1
  }
}