Pith Number

pith:AKSPPSUF

pith:2026:AKSPPSUFP5ZMX2JCPIS2QAKP4N

not attested not anchored not stored refs pending

$\mathcal{P}(\Phi)_2$ Theory from many-body quantum Gibbs states

Phan Th\`anh Nam, Xiangchan Zhu, Zhilin Yang

arxiv:2607.23084 v1 · 2026-07-25 · math-ph · math.AP · 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{AKSPPSUFP5ZMX2JCPIS2QAKP4N}

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	2026-07-28T01:22:05.762483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02a4f7ca857f72cbe9227a25a8014fe360714eb8452ef35bac6c6860ccb9869c

Aliases

arxiv: 2607.23084 · arxiv_version: 2607.23084v1 · doi: 10.48550/arxiv.2607.23084 · pith_short_12: AKSPPSUFP5ZM · pith_short_16: AKSPPSUFP5ZMX2JC · pith_short_8: AKSPPSUF

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/AKSPPSUFP5ZMX2JCPIS2QAKP4N \
  | 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: 02a4f7ca857f72cbe9227a25a8014fe360714eb8452ef35bac6c6860ccb9869c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6cb8ffbf21f3d2357ff97a7f707a3f61254fdeb150392d511d858b240237eb9",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-25T07:22:09Z",
    "title_canon_sha256": "933c8c95164cd1a6a329cfd1532eba2e2f55d38ea55e75011b98bd177d132527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23084",
    "kind": "arxiv",
    "version": 1
  }
}