Pith Number

pith:2R45ZNTH

pith:2025:2R45ZNTHHAPVCSJPMKDO5SGJ5N

not attested not anchored not stored refs pending

Large deviation rates for supercritical multitype branching processes with immigration

Junping Li, Liuyan Li

arxiv:2508.15428 v1 · 2025-08-21 · 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{2R45ZNTHHAPVCSJPMKDO5SGJ5N}

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	2026-07-05T11:57:12.229715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d479dcb667381f51492f6286eec8c9eb7e630490cca4e43137bb8d6a211343b4

Aliases

arxiv: 2508.15428 · arxiv_version: 2508.15428v1 · doi: 10.48550/arxiv.2508.15428 · pith_short_12: 2R45ZNTHHAPV · pith_short_16: 2R45ZNTHHAPVCSJP · pith_short_8: 2R45ZNTH

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/2R45ZNTHHAPVCSJPMKDO5SGJ5N \
  | 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: d479dcb667381f51492f6286eec8c9eb7e630490cca4e43137bb8d6a211343b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "940320063794502cb85054466eff818b1c74f8ea89403a608568898ca934f6f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-21T10:29:49Z",
    "title_canon_sha256": "8d47bfe45cc1a40bb4959b300af0aadbb09d27e55b388f63bdfb4a474d4895ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.15428",
    "kind": "arxiv",
    "version": 1
  }
}