Pith Number

pith:QDUJ3XAB

pith:2024:QDUJ3XABCHHXBLWCUINL2R3L5O

not attested not anchored not stored refs pending

Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs

Jian Ding, Zhenhao Cai

arxiv:2412.05709 v2 · 2024-12-07 · 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{QDUJ3XABCHHXBLWCUINL2R3L5O}

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

A switching identity for cable-graph loop soups and Gaussian free fields

Receipt and verification

First computed	2026-07-05T10:05:47.085945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80e89ddc0111cf70aec2a21abd476beba38ad035b0f6b066db31e6ae2f7814cd

Aliases

arxiv: 2412.05709 · arxiv_version: 2412.05709v2 · doi: 10.48550/arxiv.2412.05709 · pith_short_12: QDUJ3XABCHHX · pith_short_16: QDUJ3XABCHHXBLWC · pith_short_8: QDUJ3XAB

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/QDUJ3XABCHHXBLWCUINL2R3L5O \
  | 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: 80e89ddc0111cf70aec2a21abd476beba38ad035b0f6b066db31e6ae2f7814cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ce53480226ebe344266c48e1dbc870175471c85d483615ea08ecd17461667e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-07T17:48:37Z",
    "title_canon_sha256": "ebdb87858dbb483b67cf278985166715c1a4124bbb549c44c2720d1e683ac6e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.05709",
    "kind": "arxiv",
    "version": 2
  }
}