Pith Number

pith:27NV5Q7Z

pith:2012:27NV5Q7ZCNK4RBZSRNH6DGUIC4

not attested not anchored not stored refs pending

Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature

Artur O. Lopes, Jairo K. Mengue, Joana Mohr, Rafael R. Souza

arxiv:1210.3391 v3 · 2012-10-11 · math.DS · cond-mat.stat-mech · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27NV5Q7ZCNK4RBZSRNH6DGUIC4}

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	2026-05-18T01:35:57.671248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7db5ec3f91355c887328b4fe19a88170b45fe76695b2956f4b5d3706fda4d9f

Aliases

arxiv: 1210.3391 · arxiv_version: 1210.3391v3 · doi: 10.48550/arxiv.1210.3391 · pith_short_12: 27NV5Q7ZCNK4 · pith_short_16: 27NV5Q7ZCNK4RBZS · pith_short_8: 27NV5Q7Z

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/27NV5Q7ZCNK4RBZSRNH6DGUIC4 \
  | 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: d7db5ec3f91355c887328b4fe19a88170b45fe76695b2956f4b5d3706fda4d9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97d27088cdca70e3ab627147deb1b629b2d506949e7eccd6f06673c213be0244",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-11T23:29:48Z",
    "title_canon_sha256": "009fdf1ebee557e85257e52934627ebe9d17d11d8ebbfe85be6b82db2ad133f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3391",
    "kind": "arxiv",
    "version": 3
  }
}