Pith Number

pith:FXE7NTAJ

pith:2025:FXE7NTAJZSONMSCTAQPYBXDAGK

not attested not anchored not stored refs pending

Critical long-range percolation III: The upper critical dimension

Tom Hutchcroft

arxiv:2508.18809 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{FXE7NTAJZSONMSCTAQPYBXDAGK}

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	2026-07-05T11:59:31.520490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dc9f6cc09cc9cd64853041f80dc60329e7a5f6675cc221ad601784c51bf1f86

Aliases

arxiv: 2508.18809 · arxiv_version: 2508.18809v1 · doi: 10.48550/arxiv.2508.18809 · pith_short_12: FXE7NTAJZSON · pith_short_16: FXE7NTAJZSONMSCT · pith_short_8: FXE7NTAJ

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/FXE7NTAJZSONMSCTAQPYBXDAGK \
  | 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: 2dc9f6cc09cc9cd64853041f80dc60329e7a5f6675cc221ad601784c51bf1f86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08b956f82d539aaa817e9eace59e218d3aaa8dbbce5ecba6370f30fa4dcf7322",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-26T08:41:02Z",
    "title_canon_sha256": "aacb9a8dfd4424feb6200d1547186c1bb59ad92116d7032ec37d6a749a5f107d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.18809",
    "kind": "arxiv",
    "version": 1
  }
}