Pith Number

pith:GUKN5M5K

pith:2013:GUKN5M5KWUCQKSHHLJAHFRBEV7

not attested not anchored not stored refs pending

Inside the clustering threshold for random linear equations

Michael Molloy, Pu Gao

arxiv:1309.6651 v1 · 2013-09-19 · cs.DM · math.CO · 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{GUKN5M5KWUCQKSHHLJAHFRBEV7}

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	2026-05-18T03:12:10.994383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3514deb3aab5050548e75a4072c424afde5ac4bfcfefd247cd61c9d57a97d61c

Aliases

arxiv: 1309.6651 · arxiv_version: 1309.6651v1 · doi: 10.48550/arxiv.1309.6651 · pith_short_12: GUKN5M5KWUCQ · pith_short_16: GUKN5M5KWUCQKSHH · pith_short_8: GUKN5M5K

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/GUKN5M5KWUCQKSHHLJAHFRBEV7 \
  | 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: 3514deb3aab5050548e75a4072c424afde5ac4bfcfefd247cd61c9d57a97d61c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06d3c928f594c24499eed500421e02a75e48e273fc4dbe826d687643a0026114",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2013-09-19T15:01:43Z",
    "title_canon_sha256": "68937c6800c5649f71e254faf73053925d9ffdc516a40bfaaf390bd68f53609c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6651",
    "kind": "arxiv",
    "version": 1
  }
}