Pith Number

pith:WBOLKQVL

pith:2026:WBOLKQVLNOAE57SAKWMQ3O4QFC

not attested not anchored not stored refs pending

Critical parameters of germ-monotone families of branching random walks

Daniela Bertacchi, Fabio Zucca

arxiv:2602.21062 v2 · 2026-02-24 · 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{WBOLKQVLNOAE57SAKWMQ3O4QFC}

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	2026-06-19T16:12:51.611444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b05cb542ab6b804efe4055990dbb9028874e41db074062f473819ca224c79a38

Aliases

arxiv: 2602.21062 · arxiv_version: 2602.21062v2 · doi: 10.48550/arxiv.2602.21062 · pith_short_12: WBOLKQVLNOAE · pith_short_16: WBOLKQVLNOAE57SA · pith_short_8: WBOLKQVL

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/WBOLKQVLNOAE57SAKWMQ3O4QFC \
  | 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: b05cb542ab6b804efe4055990dbb9028874e41db074062f473819ca224c79a38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6615d5a14ee232351b563f04b0e4758dbd635a9838444912fbcc0c8bf797e404",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-02-24T16:24:26Z",
    "title_canon_sha256": "4b86251c2ed59104f8703138edf5ee76594bfb634a6605a2e78a639f8cf2d983"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.21062",
    "kind": "arxiv",
    "version": 2
  }
}