Pith Number

pith:PGLTV35T

pith:2005:PGLTV35TIYUDTUYJQMSJGSI7PD

not attested not anchored not stored refs pending

Asymptotics of counts of small components in random structures and models of coagulation-fragmentation

Boris L. Granovsky

arxiv:math/0511381 v4 · 2005-11-15 · 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{PGLTV35TIYUDTUYJQMSJGSI7PD}

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	2026-05-18T04:01:23.919628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79973aefb3462839d309832493491f78d726d5f66f53f0d4649fa912c8c987b5

Aliases

arxiv: math/0511381 · arxiv_version: math/0511381v4 · doi: 10.48550/arxiv.math/0511381 · pith_short_12: PGLTV35TIYUD · pith_short_16: PGLTV35TIYUDTUYJ · pith_short_8: PGLTV35T

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/PGLTV35TIYUDTUYJQMSJGSI7PD \
  | 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: 79973aefb3462839d309832493491f78d726d5f66f53f0d4649fa912c8c987b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4eb87c8d350c748f41d3aeb0a2610206dec0422f612bfb7bcbb1a20648bc615e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2005-11-15T13:47:37Z",
    "title_canon_sha256": "c0ccdaf370abfaa2e7aa834afbe07df96eab33a7900432b80bf5b22dc6a49ca6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0511381",
    "kind": "arxiv",
    "version": 4
  }
}