Pith Number

pith:AFAEB6AL

pith:2011:AFAEB6ALKUPZIIQMNCPHNNQY5N

not attested not anchored not stored refs pending

On the singularity of random Bernoulli matrices - novel integer partitions and lower bound expansions

Richard Arratia, Stephen DeSalvo

arxiv:1105.2834 v2 · 2011-05-13 · 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{AFAEB6ALKUPZIIQMNCPHNNQY5N}

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	2026-05-18T03:55:02.904788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

014040f80b551f94220c689e76b618eb63d1ed02d7444f27884d45ccc31f273e

Aliases

arxiv: 1105.2834 · arxiv_version: 1105.2834v2 · doi: 10.48550/arxiv.1105.2834 · pith_short_12: AFAEB6ALKUPZ · pith_short_16: AFAEB6ALKUPZIIQM · pith_short_8: AFAEB6AL

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/AFAEB6ALKUPZIIQMNCPHNNQY5N \
  | 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: 014040f80b551f94220c689e76b618eb63d1ed02d7444f27884d45ccc31f273e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1632297706c28d42e03bfcbe8fc168d8219d5ff4c6f9fcd1fa2f8d5b9afaef93",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-13T20:33:53Z",
    "title_canon_sha256": "b45f3b3ce49fa9f7888f4e956c1b281dbdfda2aaeb2cb3b4f6c38b8b270f652f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2834",
    "kind": "arxiv",
    "version": 2
  }
}