Pith Number

pith:Q2M2I7NS

pith:2015:Q2M2I7NS4EZ55ILOBAEADMCY6M

not attested not anchored not stored refs pending

Representation and poly-time approximation for pressure of $\mathbb{Z}^2$ lattice models in the non-uniqueness region

Brian Marcus, Raimundo Brice\~no, Ronnie Pavlov, Stefan Adams

arxiv:1508.06590 v1 · 2015-08-26 · math.DS · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q2M2I7NS4EZ55ILOBAEADMCY6M}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:20:34.464159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8699a47db2e133dea16e080801b058f303f85cf294ed6ce7a4b6c96f496b6012

Aliases

arxiv: 1508.06590 · arxiv_version: 1508.06590v1 · doi: 10.48550/arxiv.1508.06590 · pith_short_12: Q2M2I7NS4EZ5 · pith_short_16: Q2M2I7NS4EZ55ILO · pith_short_8: Q2M2I7NS

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/Q2M2I7NS4EZ55ILOBAEADMCY6M \
  | 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: 8699a47db2e133dea16e080801b058f303f85cf294ed6ce7a4b6c96f496b6012

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9487f4de3ccfef8dc2113c0de9d9fec43d917453df6012f22b293e2f658b80ec",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-08-26T18:07:40Z",
    "title_canon_sha256": "6b661be5913902df389b945aaf26fa3ca29938533a3c8792b0982cffd757647e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.06590",
    "kind": "arxiv",
    "version": 1
  }
}