Pith Number

pith:KHE4GLET

pith:2026:KHE4GLETAGPMCR76LTMUUXDXN5

not attested not anchored not stored refs pending

Rainbow percolation

Benjamin Lees, Peter Gracar

arxiv:2608.12954 v1 · 2026-08-13 · 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{KHE4GLETAGPMCR76LTMUUXDXN5}

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	2026-08-14T00:59:36.546332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51c9c32c93019ec147fe5cd94a5c776f52fb84ffc4f786b190343ec9a45bc44e

Aliases

arxiv: 2608.12954 · arxiv_version: 2608.12954v1 · doi: 10.48550/arxiv.2608.12954 · pith_short_12: KHE4GLETAGPM · pith_short_16: KHE4GLETAGPMCR76 · pith_short_8: KHE4GLET

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/KHE4GLETAGPMCR76LTMUUXDXN5 \
  | 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: 51c9c32c93019ec147fe5cd94a5c776f52fb84ffc4f786b190343ec9a45bc44e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e0b03eab7e0057b2b2f1dbc92178e44f0d2e373fd30333956947d5005c61ce5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-13T08:33:15Z",
    "title_canon_sha256": "6ca28ea6e06a7fbbaeb0080268963c1c10b0e7371b7f95a493afeb46c8c0e604"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12954",
    "kind": "arxiv",
    "version": 1
  }
}