Pith Number

pith:VI5HWAL2

pith:2024:VI5HWAL2CCVX6AEJRBO4LZIZUK

not attested not anchored not stored refs pending

Dimension jump at the uniqueness threshold for percolation in $\infty+d$ dimensions

Minghao Pan, Tom Hutchcroft

arxiv:2412.15895 v1 · 2024-12-20 · 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{VI5HWAL2CCVX6AEJRBO4LZIZUK}

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	2026-07-05T09:52:31.755171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa3a7b017a10ab7f0089885dc5e519a28bc5859fc1f2706d32c20c96edf76184

Aliases

arxiv: 2412.15895 · arxiv_version: 2412.15895v1 · doi: 10.48550/arxiv.2412.15895 · pith_short_12: VI5HWAL2CCVX · pith_short_16: VI5HWAL2CCVX6AEJ · pith_short_8: VI5HWAL2

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/VI5HWAL2CCVX6AEJRBO4LZIZUK \
  | 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: aa3a7b017a10ab7f0089885dc5e519a28bc5859fc1f2706d32c20c96edf76184

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f96dc710b8eab5618b2389723c315cdbc524578f137e6b1a88dcc9b08a581a02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-20T13:49:47Z",
    "title_canon_sha256": "17948cdc899330f0a504a4bad3123395bb03004ab0cb654b378637d896a046ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.15895",
    "kind": "arxiv",
    "version": 1
  }
}