Pith Number

pith:PS7TLZLO

pith:2016:PS7TLZLOTHRZEDQILUSUEG52RM

not attested not anchored not stored refs pending

Asymptotic of the distribution and harmonic moments for a supercritical branching process in a random environment

Eric Miqueu, Ion Grama, Quansheng Liu

arxiv:1606.04228 v1 · 2016-06-14 · 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{PS7TLZLOTHRZEDQILUSUEG52RM}

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	2026-05-18T01:12:25.914502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cbf35e56e99e3920e085d25421bba8b2fb6f9740d1674cb12e3e6bc4a6dafd8

Aliases

arxiv: 1606.04228 · arxiv_version: 1606.04228v1 · doi: 10.48550/arxiv.1606.04228 · pith_short_12: PS7TLZLOTHRZ · pith_short_16: PS7TLZLOTHRZEDQI · pith_short_8: PS7TLZLO

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/PS7TLZLOTHRZEDQILUSUEG52RM \
  | 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: 7cbf35e56e99e3920e085d25421bba8b2fb6f9740d1674cb12e3e6bc4a6dafd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7144bd50dba5b8a173ce9d61e38a77cf9e7bbb849533f5e63ff0e89c9c0945d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-14T07:29:46Z",
    "title_canon_sha256": "b374112d4a6a9b7c3c6ccf53f16b2fcb5ea26c8e02e0211fae9d0ab874d5dc84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04228",
    "kind": "arxiv",
    "version": 1
  }
}