Pith Number

pith:N5HVDM4I

pith:2010:N5HVDM4IDL555KYNC3UWHMET65

not attested not anchored not stored refs pending

On dynamical systems and phase transitions for $Q+1$-state $P$-adic Potts model on the Cayley tree

Farrukh Mukhamedov

arxiv:1011.1395 v1 · 2010-11-05 · math-ph · cond-mat.stat-mech · math.DS · math.MP · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N5HVDM4IDL555KYNC3UWHMET65}

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	2026-05-18T04:36:58.526335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f4f51b3881afbdeab0d16e963b093f7713710226216da2e6e490bb3042df4ca

Aliases

arxiv: 1011.1395 · arxiv_version: 1011.1395v1 · doi: 10.48550/arxiv.1011.1395 · pith_short_12: N5HVDM4IDL55 · pith_short_16: N5HVDM4IDL555KYN · pith_short_8: N5HVDM4I

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/N5HVDM4IDL555KYNC3UWHMET65 \
  | 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: 6f4f51b3881afbdeab0d16e963b093f7713710226216da2e6e490bb3042df4ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73413e48d6a13b3fc2e49cf4e066fcd9c0d4822759a8efca35c8a29684b53f8e",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.DS",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-11-05T13:39:39Z",
    "title_canon_sha256": "94b8dc18acb5eb707b72657ea4dc5beaf39db3589a1971a656492d1b659b777d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1395",
    "kind": "arxiv",
    "version": 1
  }
}