Pith Number

pith:GTEUNIQD

pith:2016:GTEUNIQD37GULKNFJO3O6CCHDS

not attested not anchored not stored refs pending

Multitype branching processes evolving in i.i.d. random environment: probability of survival for the critical case

Elena E. Dyakonova, Vladimir A. Vatutin

arxiv:1612.00681 v2 · 2016-12-02 · 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{GTEUNIQD37GULKNFJO3O6CCHDS}

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	2026-05-18T00:55:28.224082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c946a203dfcd45a9a54bb6ef08471cb155cd093f0fa571e758fad606ddd722

Aliases

arxiv: 1612.00681 · arxiv_version: 1612.00681v2 · doi: 10.48550/arxiv.1612.00681 · pith_short_12: GTEUNIQD37GU · pith_short_16: GTEUNIQD37GULKNF · pith_short_8: GTEUNIQD

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/GTEUNIQD37GULKNFJO3O6CCHDS \
  | 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: 34c946a203dfcd45a9a54bb6ef08471cb155cd093f0fa571e758fad606ddd722

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fff06a0ea785f3aabb9e4db905d33f0ebdde8898560b40d947175002646d1fae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-02T13:49:39Z",
    "title_canon_sha256": "3f77cbdcd8f28818440c5253d0289c968825076b7bf91274237df7003c44bd21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00681",
    "kind": "arxiv",
    "version": 2
  }
}