Pith Number

pith:3RG6XUNZ

pith:2026:3RG6XUNZI2H2JJNXEOGD2MRJ6M

not attested not anchored not stored refs pending

New results on the domain of analyticity of the free energy for the Ising model

Nguyen Dang Thien Thu, Nguyen Tong Xuan

arxiv:2608.08396 v1 · 2026-08-09 · math-ph · math.CO · 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{3RG6XUNZI2H2JJNXEOGD2MRJ6M}

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	2026-08-11T01:22:32.046160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc4debd1b9468fa4a5b7238c3d3229f336a06ca99a2f7f7e179b3285542cbfe4

Aliases

arxiv: 2608.08396 · arxiv_version: 2608.08396v1 · doi: 10.48550/arxiv.2608.08396 · pith_short_12: 3RG6XUNZI2H2 · pith_short_16: 3RG6XUNZI2H2JJNX · pith_short_8: 3RG6XUNZ

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/3RG6XUNZI2H2JJNXEOGD2MRJ6M \
  | 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: dc4debd1b9468fa4a5b7238c3d3229f336a06ca99a2f7f7e179b3285542cbfe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "173b548b51d071804ba139bb06c220ba8b5172b70ca53eafa5504f68ab3f075a",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-08-09T01:21:22Z",
    "title_canon_sha256": "bddc337e213646e49dc15526176f90f63123750a84a490ca35ae3bbedd5bbdcc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08396",
    "kind": "arxiv",
    "version": 1
  }
}