Pith Number

pith:KEB7ODWJ

pith:2026:KEB7ODWJGCOI3QKHGWO4RDBTCG

not attested not anchored not stored refs pending

Two-Dimensional Phase Transitions in Classical Systems: 60 Years after the Hohenberg-Mermin-Wagner Theorem

Ruijian Zhu, Yanting Wang

arxiv:2606.24091 v1 · 2026-06-23 · cond-mat.stat-mech · cond-mat.soft

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KEB7ODWJGCOI3QKHGWO4RDBTCG}

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	2026-06-24T01:14:40.089027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5103f70ec9309c8dc147359dc88c3311bde4fb1bf48ba1545a10062140487696

Aliases

arxiv: 2606.24091 · arxiv_version: 2606.24091v1 · doi: 10.48550/arxiv.2606.24091 · pith_short_12: KEB7ODWJGCOI · pith_short_16: KEB7ODWJGCOI3QKH · pith_short_8: KEB7ODWJ

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/KEB7ODWJGCOI3QKHGWO4RDBTCG \
  | 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: 5103f70ec9309c8dc147359dc88c3311bde4fb1bf48ba1545a10062140487696

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fd1b47d7d99a2d2992750671bb55dc04c10106b92aff4d4df1696b70de7badb",
    "cross_cats_sorted": [
      "cond-mat.soft"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-06-23T03:14:06Z",
    "title_canon_sha256": "9b13b1b9d6d6a8450b8fe72dc84cd08b84f35b4f8cd2cb7800f16ced796c001d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24091",
    "kind": "arxiv",
    "version": 1
  }
}