Pith Number

pith:75ZYBJ2U

pith:2017:75ZYBJ2USWMNYQ2Q7UREW4SXGQ

not attested not anchored not stored refs pending

Asymptotic Behaviors for Critical Branching Processes with Immigration

Doudou Li, Mei Zhang

arxiv:1712.08892 v1 · 2017-12-24 · 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{75ZYBJ2USWMNYQ2Q7UREW4SXGQ}

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	2026-05-18T00:27:14.895427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff7380a7549598dc4350fd224b725734071e2181c9d928adb368e64756b02cb4

Aliases

arxiv: 1712.08892 · arxiv_version: 1712.08892v1 · doi: 10.48550/arxiv.1712.08892 · pith_short_12: 75ZYBJ2USWMN · pith_short_16: 75ZYBJ2USWMNYQ2Q · pith_short_8: 75ZYBJ2U

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/75ZYBJ2USWMNYQ2Q7UREW4SXGQ \
  | 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: ff7380a7549598dc4350fd224b725734071e2181c9d928adb368e64756b02cb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fe77447281e0d9cef67d059e2bb44643f8a27886750dc8e7665e4c9c75f7ede",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-12-24T08:59:06Z",
    "title_canon_sha256": "b8ebb91aaba1a73e0065aa4b019e12e8e7020e627634655adb234e0a6f902b5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.08892",
    "kind": "arxiv",
    "version": 1
  }
}