Pith Number

pith:GWTNUHAG

pith:2022:GWTNUHAGCYVRRRDVIJTY4ZYO4X

not attested not anchored not stored refs pending

Infinite volume Gibbs states and metastates of the random field mean-field spherical model

Kalle Koskinen

arxiv:2211.08920 v2 · 2022-11-16 · math-ph · cond-mat.dis-nn · 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{GWTNUHAGCYVRRRDVIJTY4ZYO4X}

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	2026-07-05T06:11:02.081096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955

Aliases

arxiv: 2211.08920 · arxiv_version: 2211.08920v2 · doi: 10.48550/arxiv.2211.08920 · pith_short_12: GWTNUHAGCYVR · pith_short_16: GWTNUHAGCYVRRRDV · pith_short_8: GWTNUHAG

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/GWTNUHAGCYVRRRDVIJTY4ZYO4X \
  | 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: 35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c61a7baa59d32358f8058096e1ef56bfd28b196aefd601666c6e8cc8c15c7ea",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2022-11-16T14:05:23Z",
    "title_canon_sha256": "8baccb8b626d0f5a26ef7094cbfa633f349149b81fb757f9f48a3ad93219b3c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.08920",
    "kind": "arxiv",
    "version": 2
  }
}