Pith Number

pith:EPIYRDOZ

pith:2013:EPIYRDOZF2DTQTXPWLISVWM7VU

not attested not anchored not stored refs pending

The harmonic measure of balls in random trees

Jean-Fran\c{c}ois Le Gall, Nicolas Curien

arxiv:1304.7190 v4 · 2013-04-26 · 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{EPIYRDOZF2DTQTXPWLISVWM7VU}

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	2026-05-18T00:41:08.672270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23d1888dd92e87384eefb2d12ad99fad06d3b68b89e33b722afea259f1c4cfc5

Aliases

arxiv: 1304.7190 · arxiv_version: 1304.7190v4 · doi: 10.48550/arxiv.1304.7190 · pith_short_12: EPIYRDOZF2DT · pith_short_16: EPIYRDOZF2DTQTXP · pith_short_8: EPIYRDOZ

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/EPIYRDOZF2DTQTXPWLISVWM7VU \
  | 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: 23d1888dd92e87384eefb2d12ad99fad06d3b68b89e33b722afea259f1c4cfc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb372150369a14febd3f60a5f7a2c283caa8e7d8e057a86077a49609b7dd0b5c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-26T14:40:29Z",
    "title_canon_sha256": "d7c849a93993943f361006ba595ffb44054e4cd0cd28dea2c35b9d924785066d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7190",
    "kind": "arxiv",
    "version": 4
  }
}