Pith Number

pith:CCVACGVX

pith:2026:CCVACGVXCHWVIMOKBGFDIDWW6F

not attested not anchored not stored refs pending

A Characterization of Level-k Realizability for Clustering Systems

Shilong Dai, Yangjing Long

arxiv:2605.21945 v1 · 2026-05-21 · q-bio.MN

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CCVACGVXCHWVIMOKBGFDIDWW6F}

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	2026-05-22T01:04:16.195806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10aa011ab711ed5431ca098a340ed6f14b94ce0b2ae195b780413518b43bf798

Aliases

arxiv: 2605.21945 · arxiv_version: 2605.21945v1 · doi: 10.48550/arxiv.2605.21945 · pith_short_12: CCVACGVXCHWV · pith_short_16: CCVACGVXCHWVIMOK · pith_short_8: CCVACGVX

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/CCVACGVXCHWVIMOKBGFDIDWW6F \
  | 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: 10aa011ab711ed5431ca098a340ed6f14b94ce0b2ae195b780413518b43bf798

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95e173880eafbabbfdeb1d9f558c98eaa1bca58cc7c0a43cb889ad794a864c88",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-bio.MN",
    "submitted_at": "2026-05-21T03:25:18Z",
    "title_canon_sha256": "d437afc3f8e90e70edce6eeed217194161c459b45727eed7356e655184404dc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21945",
    "kind": "arxiv",
    "version": 1
  }
}