Pith Number

pith:BCKTDZBB

pith:2026:BCKTDZBBF5EGOVQOEAELEHLM4O

not attested not anchored not stored refs pending

Gaussian free field in annulus: BPZ equations and crossing probabilities for level lines

Chongzhi Huang, Hao Wu, Mingchang Liu

arxiv:2607.27786 v1 · 2026-07-30 · 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{BCKTDZBBF5EGOVQOEAELEHLM4O}

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	2026-07-31T01:30:47.014567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

089531e4212f4867560e2008b21d6ce3b8985e28f374db768658889b9fd8c270

Aliases

arxiv: 2607.27786 · arxiv_version: 2607.27786v1 · doi: 10.48550/arxiv.2607.27786 · pith_short_12: BCKTDZBBF5EG · pith_short_16: BCKTDZBBF5EGOVQO · pith_short_8: BCKTDZBB

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/BCKTDZBBF5EGOVQOEAELEHLM4O \
  | 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: 089531e4212f4867560e2008b21d6ce3b8985e28f374db768658889b9fd8c270

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edbe4bcc6d026114c63bef1694d94957abcf6f7a901981ec2d7bde47f3ec6f06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-30T07:17:48Z",
    "title_canon_sha256": "948b1bac67a0c39a28a2aeef1f2d1dc6add05774dff0f2161164c411554db4da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27786",
    "kind": "arxiv",
    "version": 1
  }
}