Pith Number

pith:Y5LKPYFK

pith:2025:Y5LKPYFKCDZDIXOZCH5IBINHGP

not attested not anchored not stored refs pending

Critical long-range percolation II: Low effective dimension

Tom Hutchcroft

arxiv:2508.18808 v1 · 2025-08-26 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5LKPYFKCDZDIXOZCH5IBINHGP}

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

5 papers in Pith

Perturbative Renormalization and Universality Diagram for Long-Range Quantum Criticality

Percolation on hierarchical lattices

A random walk approach to high-dimensional critical phenomena

A Scaling Limit of Random Walks in the Rational Adeles

Receipt and verification

First computed	2026-07-05T11:59:31.501398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c756a7e0aa10f2345dd911fa80a1a733dc3df5a65c113060209bf51413ebc407

Aliases

arxiv: 2508.18808 · arxiv_version: 2508.18808v1 · doi: 10.48550/arxiv.2508.18808 · pith_short_12: Y5LKPYFKCDZD · pith_short_16: Y5LKPYFKCDZDIXOZ · pith_short_8: Y5LKPYFK

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/Y5LKPYFKCDZDIXOZCH5IBINHGP \
  | 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: c756a7e0aa10f2345dd911fa80a1a733dc3df5a65c113060209bf51413ebc407

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36dca03450ec1acc8b6cde9edc3a0b2f61529f4e07767402729bba36b1504f33",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-26T08:40:56Z",
    "title_canon_sha256": "cf4f8bd2ab649be2b969343344ae7e4232862e4faf2a0a0aea1eb4c4ff0be450"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.18808",
    "kind": "arxiv",
    "version": 1
  }
}