Pith Number

pith:ZKXXKNS6

pith:2024:ZKXXKNS6BKKCDGFQVJTXWRFVNG

not attested not anchored not stored refs pending

Quasi-multiplicativity and regularity for metric graph Gaussian free fields

Jian Ding, Zhenhao Cai

arxiv:2412.05706 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{ZKXXKNS6BKKCDGFQVJTXWRFVNG}

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	2026-07-05T10:05:47.062651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caaf75365e0a942198b0aa677b44b56981428c4f4c3d678b20cd9b5e039e206e

Aliases

arxiv: 2412.05706 · arxiv_version: 2412.05706v2 · doi: 10.48550/arxiv.2412.05706 · pith_short_12: ZKXXKNS6BKKC · pith_short_16: ZKXXKNS6BKKCDGFQ · pith_short_8: ZKXXKNS6

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/ZKXXKNS6BKKCDGFQVJTXWRFVNG \
  | 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: caaf75365e0a942198b0aa677b44b56981428c4f4c3d678b20cd9b5e039e206e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efd486d7d90a6d53d8244c797a3fa2cf7eff80f784737faa95590fc90177b15c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-07T17:30:32Z",
    "title_canon_sha256": "cee43652fc84791db8c9bddf4ebbab472687994970e5ee352e611b753e646148"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.05706",
    "kind": "arxiv",
    "version": 2
  }
}