Pith Number

pith:QJ3JNLLJ

pith:2015:QJ3JNLLJ4LO3CASO3QXSMV4UBV

not attested not anchored not stored refs pending

Sublinearity of the number of semi-infinite branches for geometric random trees

David Coupier

arxiv:1501.04804 v3 · 2015-01-20 · 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{QJ3JNLLJ4LO3CASO3QXSMV4UBV}

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	2026-05-18T00:54:58.295423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

827696ad69e2ddb1024edc2f2657940d7c5450e1f4d3122ed3973f21d70896c2

Aliases

arxiv: 1501.04804 · arxiv_version: 1501.04804v3 · doi: 10.48550/arxiv.1501.04804 · pith_short_12: QJ3JNLLJ4LO3 · pith_short_16: QJ3JNLLJ4LO3CASO · pith_short_8: QJ3JNLLJ

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/QJ3JNLLJ4LO3CASO3QXSMV4UBV \
  | 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: 827696ad69e2ddb1024edc2f2657940d7c5450e1f4d3122ed3973f21d70896c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14a08a1f905461b813b1059ffdbb988020270ced43560f20797bf3e05b87c485",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-20T13:39:11Z",
    "title_canon_sha256": "0ea7636c2953c509d21a3b3d451b92a58c0509a64bd184c0df4e2dc9314493c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04804",
    "kind": "arxiv",
    "version": 3
  }
}