Pith Number

pith:4HJLUHWU

pith:2025:4HJLUHWUI2ZESN7W7TSC5IHDLQ

not attested not anchored not stored refs pending

The Boundary Principle of a Single Big Jump: Refined Asymptotics for Branching Processes with Immigration

Yunfan Zhao

arxiv:2509.05650 v1 · 2025-09-06 · 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{4HJLUHWUI2ZESN7W7TSC5IHDLQ}

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	2026-07-05T12:06:21.814198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1d2ba1ed446b24937f6fce42ea0e35c0526a6e1137a5861cdf5126ad7622fdf

Aliases

arxiv: 2509.05650 · arxiv_version: 2509.05650v1 · doi: 10.48550/arxiv.2509.05650 · pith_short_12: 4HJLUHWUI2ZE · pith_short_16: 4HJLUHWUI2ZESN7W · pith_short_8: 4HJLUHWU

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/4HJLUHWUI2ZESN7W7TSC5IHDLQ \
  | 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: e1d2ba1ed446b24937f6fce42ea0e35c0526a6e1137a5861cdf5126ad7622fdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f207f06486d0220334aa8cfc3bc7359892c35f04b71a815cceec65a21eebc86",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-09-06T09:02:20Z",
    "title_canon_sha256": "c195ba8c217c9eeb9661d3474fcbaef872814170a48c5ea8d3356e622fe64fad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05650",
    "kind": "arxiv",
    "version": 1
  }
}