Pith Number

pith:RAOO2XZT

pith:2025:RAOO2XZTGHJEU342WRRPPUD2PJ

not attested not anchored not stored refs pending

Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model

Dingyun Yao, Lode Polle, Tianning Xiao, Youjin Deng, Zhijie Fan

arxiv:2512.01956 v2 · 2025-12-01 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RAOO2XZTGHJEU342WRRPPUD2PJ}

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.

Cited by

1 paper in Pith

Perturbative Renormalization and Universality Diagram for Long-Range Quantum Criticality

Receipt and verification

First computed	2026-06-04T01:08:36.986716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

881ced5f3331d24a6f9ab462f7d07a7a78880f93c1c782733a51696101535e36

Aliases

arxiv: 2512.01956 · arxiv_version: 2512.01956v2 · doi: 10.48550/arxiv.2512.01956 · pith_short_12: RAOO2XZTGHJE · pith_short_16: RAOO2XZTGHJEU342 · pith_short_8: RAOO2XZT

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/RAOO2XZTGHJEU342WRRPPUD2PJ \
  | 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: 881ced5f3331d24a6f9ab462f7d07a7a78880f93c1c782733a51696101535e36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46096d6d8f7b5a90788584fa8ed9a77d662d2d87c31a05b560c982dd6db50ad4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2025-12-01T18:06:48Z",
    "title_canon_sha256": "5eaf1ae384d1c8d688dfdb1d5088f24885fb6e15babaffeaf824baa0e619ec17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.01956",
    "kind": "arxiv",
    "version": 2
  }
}