Pith Number

pith:B6BP3DZ2

pith:2016:B6BP3DZ22ZN2DESVXFF3GZXWX7

not attested not anchored not stored refs pending

Birth of a giant $(k_1,k_2)$-core in the random digraph

Boris Pittel, Dan Poole

arxiv:1608.05095 v1 · 2016-08-17 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B6BP3DZ22ZN2DESVXFF3GZXWX7}

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	2026-05-18T01:08:31.917348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f82fd8f3ad65ba19255b94bb366f6bff9abddcebff86a71df16d15f2c8f14f2

Aliases

arxiv: 1608.05095 · arxiv_version: 1608.05095v1 · doi: 10.48550/arxiv.1608.05095 · pith_short_12: B6BP3DZ22ZN2 · pith_short_16: B6BP3DZ22ZN2DESV · pith_short_8: B6BP3DZ2

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/B6BP3DZ22ZN2DESVXFF3GZXWX7 \
  | 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: 0f82fd8f3ad65ba19255b94bb366f6bff9abddcebff86a71df16d15f2c8f14f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2be403408d482c0a88b45314c6f45f7c9245e2741c75b1637bc3e6c92f9f1dce",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-08-17T20:31:29Z",
    "title_canon_sha256": "d3756aabef17309f3fa11dfa874e3680b944f3a0a0e9686a8da373653926ff8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05095",
    "kind": "arxiv",
    "version": 1
  }
}