Pith Number

pith:XWSB5FRC

pith:2026:XWSB5FRC5ZVQKHYZSMRYGQG6CT

not attested not anchored not stored refs pending

Multi-window trace connectivity in subcritical planar Brownian loop soups

Zhengwen Qiao

arxiv:2607.21342 v1 · 2026-07-23 · 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{XWSB5FRC5ZVQKHYZSMRYGQG6CT}

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	2026-07-24T01:24:26.750129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bda41e9622ee6b051f1993238340de14ef555de07f061c3d62be3849e575a311

Aliases

arxiv: 2607.21342 · arxiv_version: 2607.21342v1 · doi: 10.48550/arxiv.2607.21342 · pith_short_12: XWSB5FRC5ZVQ · pith_short_16: XWSB5FRC5ZVQKHYZ · pith_short_8: XWSB5FRC

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/XWSB5FRC5ZVQKHYZSMRYGQG6CT \
  | 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: bda41e9622ee6b051f1993238340de14ef555de07f061c3d62be3849e575a311

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b02160281de9497789c5f06c971c03c89859437454cda6757a51b99cbd764f7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-23T14:12:50Z",
    "title_canon_sha256": "4125c18741c999f8d75f68286bf578f872c3b8e703b04031700e2aeaca01da90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21342",
    "kind": "arxiv",
    "version": 1
  }
}