Pith Number

pith:WBP2RZNY

pith:2025:WBP2RZNYMZ5W2XLRDXEW4VSLGN

not attested not anchored not stored refs pending

Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes

Benedikt Placke, Grace M. Sommers, Nikolas P. Breuckmann, Tibor Rakovszky, Vedika Khemani

arxiv:2507.13342 v1 · 2025-07-17 · cond-mat.stat-mech · cond-mat.dis-nn · math-ph · 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{WBP2RZNYMZ5W2XLRDXEW4VSLGN}

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

Coupled-Layer Construction of Quantum Product Codes

Receipt and verification

First computed	2026-07-05T11:38:59.510625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b05fa8e5b8667b6d5d711dc96e564b337507fa1df57bbf1f99948a3b47246ab3

Aliases

arxiv: 2507.13342 · arxiv_version: 2507.13342v1 · doi: 10.48550/arxiv.2507.13342 · pith_short_12: WBP2RZNYMZ5W · pith_short_16: WBP2RZNYMZ5W2XLR · pith_short_8: WBP2RZNY

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/WBP2RZNYMZ5W2XLRDXEW4VSLGN \
  | 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: b05fa8e5b8667b6d5d711dc96e564b337507fa1df57bbf1f99948a3b47246ab3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ae52cdf6fbf76e358a64028c07f6a313aa922c470eb418cdb95cec9a3f1c7a2",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2025-07-17T17:58:42Z",
    "title_canon_sha256": "5e000cb3020e714171ed024d9ee4b78d007f39e2981c5cfc3dbd5ba2a7282ab7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13342",
    "kind": "arxiv",
    "version": 1
  }
}