Pith Number

pith:UL237S5E

pith:2025:UL237S5EA4TINCCBNPJLBMCOKF

not attested not anchored not stored refs pending

Random Lozenge Waterfall: Dimensional Collapse of Gibbs Measures

Alisa Knizel, Leonid Petrov

arxiv:2507.22011 v1 · 2025-07-29 · math.PR · cond-mat.stat-mech · 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{UL237S5EA4TINCCBNPJLBMCOKF}

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	2026-07-05T11:45:11.416352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2f5bfcba407268688416bd2b0b04e514b8fde552874b08c75a6384998fd68db

Aliases

arxiv: 2507.22011 · arxiv_version: 2507.22011v1 · doi: 10.48550/arxiv.2507.22011 · pith_short_12: UL237S5EA4TI · pith_short_16: UL237S5EA4TINCCB · pith_short_8: UL237S5E

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/UL237S5EA4TINCCBNPJLBMCOKF \
  | 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: a2f5bfcba407268688416bd2b0b04e514b8fde552874b08c75a6384998fd68db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e4b203f794debb8e1ed5b98f2d2c18a3448cdbdda8e702f93db6fc1e43aaf83",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-29T17:02:16Z",
    "title_canon_sha256": "de812eeda9728d31f23f5cb75d123f64b440ae226fbd0c751ce104b8aad593b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.22011",
    "kind": "arxiv",
    "version": 1
  }
}