Pith Number

pith:XUIH7YFI

pith:2026:XUIH7YFIKNVOSO4RUHJHDZDCXY

not attested not anchored not stored refs pending

Counting and Sampling Anti-Ferromagnetic Potts Models on Random Regular Bipartite Graphs in the Non-uniqueness Regime

Kuan Yang, Siyu Liu, Zhidan Li

arxiv:2606.21250 v1 · 2026-06-19 · cs.DS · 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{XUIH7YFIKNVOSO4RUHJHDZDCXY}

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	2026-06-23T01:12:34.711424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd107fe0a8536ae93b91a1d271e462be1e4805ea00c6d7cbc3f232d4504004f0

Aliases

arxiv: 2606.21250 · arxiv_version: 2606.21250v1 · doi: 10.48550/arxiv.2606.21250 · pith_short_12: XUIH7YFIKNVO · pith_short_16: XUIH7YFIKNVOSO4R · pith_short_8: XUIH7YFI

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/XUIH7YFIKNVOSO4RUHJHDZDCXY \
  | 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: bd107fe0a8536ae93b91a1d271e462be1e4805ea00c6d7cbc3f232d4504004f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c0f16528bced79ee0d49f0224d6323939ce7c9d5953c8c289a714101c2b7b89",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-06-19T09:28:45Z",
    "title_canon_sha256": "9350e631504b1b34fbe696fb78514ce27ed631bb51c4613adac36aa2d3819932"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21250",
    "kind": "arxiv",
    "version": 1
  }
}