Pith Number

pith:P64MHTYN

pith:2018:P64MHTYNVWQZUAQ4FVBRLHYODW

not attested not anchored not stored refs pending

Weak convergence of the number of vertices at intermediate levels of random recursive trees

Alexander Iksanov, Zakhar Kabluchko

arxiv:1806.10872 v1 · 2018-06-28 · 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{P64MHTYNVWQZUAQ4FVBRLHYODW}

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	2026-05-18T00:12:07.727001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fb8c3cf0dada19a021c2d43159f0e1d97f4db2274c8023636ec9a4135deebc3

Aliases

arxiv: 1806.10872 · arxiv_version: 1806.10872v1 · doi: 10.48550/arxiv.1806.10872 · pith_short_12: P64MHTYNVWQZ · pith_short_16: P64MHTYNVWQZUAQ4 · pith_short_8: P64MHTYN

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/P64MHTYNVWQZUAQ4FVBRLHYODW \
  | 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: 7fb8c3cf0dada19a021c2d43159f0e1d97f4db2274c8023636ec9a4135deebc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92a9a80b1b77cd1fe7d582798abe232718f74166192618e5c771c1c6e757400e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-06-28T10:43:54Z",
    "title_canon_sha256": "a8d977a5aaf69d1a7f1036f774051b31741cc62214e87115d3158609c3603a63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.10872",
    "kind": "arxiv",
    "version": 1
  }
}