Pith Number

pith:4KHDTFUT

pith:2025:4KHDTFUTG2WVHBATKTAK36GZQK

not attested not anchored not stored refs pending

The percolation energy field and its logarithmic partner

Federico Camia, Yu Feng

arxiv:2508.16047 v2 · 2025-08-22 · 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{4KHDTFUTG2WVHBATKTAK36GZQK}

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

1 paper in Pith

Critical long-range percolation II: Low effective dimension

Receipt and verification

First computed	2026-06-02T02:04:47.615015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e28e39969336ad53841354c0adf8d98290a6100b658efbb302399042c057d967

Aliases

arxiv: 2508.16047 · arxiv_version: 2508.16047v2 · doi: 10.48550/arxiv.2508.16047 · pith_short_12: 4KHDTFUTG2WV · pith_short_16: 4KHDTFUTG2WVHBAT · pith_short_8: 4KHDTFUT

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/4KHDTFUTG2WVHBATKTAK36GZQK \
  | 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: e28e39969336ad53841354c0adf8d98290a6100b658efbb302399042c057d967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bf1fa6d6477a4d1f8cb2f2ff220920519ad14a05a1acb1f0bfd85fc754e7415",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-22T02:53:06Z",
    "title_canon_sha256": "c76daab2af7b96c31326164f409998b6ad8140c40143ac513e231886c2d599c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.16047",
    "kind": "arxiv",
    "version": 2
  }
}