Pith Number

pith:FVLW644S

pith:2025:FVLW644SAWHPOAJE3RWMOOXKBW

not attested not anchored not stored refs pending

Critical long-range percolation I: High effective dimension

Tom Hutchcroft

arxiv:2508.18807 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{FVLW644SAWHPOAJE3RWMOOXKBW}

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

6 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

Convergence of $k$-point functions in high dimensional percolation

Receipt and verification

First computed	2026-07-05T11:59:31.484038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d576f7392058ef70124dc6cc73aea0daab062fe61ba1f45617f7f027970e136

Aliases

arxiv: 2508.18807 · arxiv_version: 2508.18807v1 · doi: 10.48550/arxiv.2508.18807 · pith_short_12: FVLW644SAWHP · pith_short_16: FVLW644SAWHPOAJE · pith_short_8: FVLW644S

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/FVLW644SAWHPOAJE3RWMOOXKBW \
  | 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: 2d576f7392058ef70124dc6cc73aea0daab062fe61ba1f45617f7f027970e136

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3e7fec362ba79dc15321f036d1f47a2c244e24ee15fd04578887b253405476d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-26T08:40:49Z",
    "title_canon_sha256": "6056fa975ac3c96589908021cc91d088520c2ac2ca51feca41188de573d6d61f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.18807",
    "kind": "arxiv",
    "version": 1
  }
}