Pith Number

pith:ZFCDG6EG

pith:2019:ZFCDG6EGOSJ25JSQWAYAXAHWSN

not attested not anchored not stored refs pending

Branching processes in random environment with immigration stopped at zero

Doudou Li, Elena Dyakonova, Mei Zhang, Vladimir Vatutin

arxiv:1905.03535 v1 · 2019-05-09 · 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{ZFCDG6EGOSJ25JSQWAYAXAHWSN}

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	2026-05-17T23:46:37.519149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f

Aliases

arxiv: 1905.03535 · arxiv_version: 1905.03535v1 · doi: 10.48550/arxiv.1905.03535 · pith_short_12: ZFCDG6EGOSJ2 · pith_short_16: ZFCDG6EGOSJ25JSQ · pith_short_8: ZFCDG6EG

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/ZFCDG6EGOSJ25JSQWAYAXAHWSN \
  | 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: c9443378867493aea650b0300b80f6934ba0d8fdad5119e09144e4be2c83691f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "315923627d1aa60ff7eb8495f83d2803464ae34cfb2b695b34401f4afc8574ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-05-09T11:18:16Z",
    "title_canon_sha256": "094b956d1a83398a143a5d37ffd0bd5ee1e3f4ab0e496816998f464cb50a20ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.03535",
    "kind": "arxiv",
    "version": 1
  }
}