Pith Number

pith:WHMWC7FW

pith:2026:WHMWC7FWK2367IGN7MP77DORVW

not attested not anchored not stored refs pending

(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on $\mathbb{Z^d}$, $d > 4$, and $\mathbb{T}_d$,$ d \ge 3$

Alexander Drewitz, Andreas Klippel, Christian M\"onch, Volker Betz

arxiv:2608.11198 v1 · 2026-08-11 · 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{WHMWC7FWK2367IGN7MP77DORVW}

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	2026-08-12T01:24:47.860550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1d9617cb656b7efa0cdfb1fff8dd1ad8f01296fa8b5a96db259d68871001510

Aliases

arxiv: 2608.11198 · arxiv_version: 2608.11198v1 · doi: 10.48550/arxiv.2608.11198 · pith_short_12: WHMWC7FWK236 · pith_short_16: WHMWC7FWK2367IGN · pith_short_8: WHMWC7FW

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/WHMWC7FWK2367IGN7MP77DORVW \
  | 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: b1d9617cb656b7efa0cdfb1fff8dd1ad8f01296fa8b5a96db259d68871001510

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "358aa2e1658b7abadd9fda8b4f46d440ecc2d8e1fb07d8e0c9fe1a42fec3c1a6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-11T17:56:09Z",
    "title_canon_sha256": "6f91091689dcc34d2ca344ff5b135a27a4ac4fbe3765b47ca18b33312cc29bab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.11198",
    "kind": "arxiv",
    "version": 1
  }
}