Pith Number

pith:2XUJE2HX

pith:2026:2XUJE2HXG54WVON7VWOVM2NBHR

not attested not anchored not stored refs pending

On the dependence of the zero-free region of a partition function on the external field

Alexander Barvinok

arxiv:2608.03687 v1 · 2026-08-04 · math-ph · math.CO · 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{2XUJE2HXG54WVON7VWOVM2NBHR}

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	2026-08-05T01:36:53.626011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5e89268f737796ab9bfad9d5669a13c4114aa24e0efc365e922944c5885890a

Aliases

arxiv: 2608.03687 · arxiv_version: 2608.03687v1 · doi: 10.48550/arxiv.2608.03687 · pith_short_12: 2XUJE2HXG54W · pith_short_16: 2XUJE2HXG54WVON7 · pith_short_8: 2XUJE2HX

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/2XUJE2HXG54WVON7VWOVM2NBHR \
  | 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: d5e89268f737796ab9bfad9d5669a13c4114aa24e0efc365e922944c5885890a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3662957e99cf8df713bfdafecedca9447e4341f7dede9d36efa7056e7d1606e6",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-08-04T13:56:28Z",
    "title_canon_sha256": "4d8994d590304f52072802972ff10e6d43fbf1c6642b48491d3662231e33e896"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03687",
    "kind": "arxiv",
    "version": 1
  }
}