Pith Number

pith:QLX4BQV2

pith:2011:QLX4BQV2I4KVB5MW4ZIZE3FKWN

not attested not anchored not stored refs pending

Fluctuation limits of strongly degenerate branching systems

Yuqiang Li

arxiv:1108.1319 v2 · 2011-08-05 · 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{QLX4BQV2I4KVB5MW4ZIZE3FKWN}

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	2026-05-18T02:01:02.438224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82efc0c2ba471550f596e651926caab372825925d8d8e23354dc2e60ac96ba6e

Aliases

arxiv: 1108.1319 · arxiv_version: 1108.1319v2 · doi: 10.48550/arxiv.1108.1319 · pith_short_12: QLX4BQV2I4KV · pith_short_16: QLX4BQV2I4KVB5MW · pith_short_8: QLX4BQV2

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/QLX4BQV2I4KVB5MW4ZIZE3FKWN \
  | 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: 82efc0c2ba471550f596e651926caab372825925d8d8e23354dc2e60ac96ba6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b8b419290db79924060e70e63062f394c8b81299d45c5e140ade95423e32c44",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-05T12:28:41Z",
    "title_canon_sha256": "cb766b53f527c48c7fbd111682d7a87b4e8f19c24fc923eb9d9ef51f8e860489"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1319",
    "kind": "arxiv",
    "version": 2
  }
}