Pith Number

pith:JJ2EHBAL

pith:2015:JJ2EHBALF6Q5GAF3J6D7NFBV4A

not attested not anchored not stored refs pending

A review on symmetry properties of birth-death processes

Antonio Di Crescenzo, Barbara Martinucci

arxiv:1509.02511 v1 · 2015-09-08 · 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{JJ2EHBALF6Q5GAF3J6D7NFBV4A}

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	2026-05-18T01:33:40.752440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a7443840b2fa1d300bb4f87f69435e01d61e91c6c7b3dace282b3ccc3e350b2

Aliases

arxiv: 1509.02511 · arxiv_version: 1509.02511v1 · doi: 10.48550/arxiv.1509.02511 · pith_short_12: JJ2EHBALF6Q5 · pith_short_16: JJ2EHBALF6Q5GAF3 · pith_short_8: JJ2EHBAL

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/JJ2EHBALF6Q5GAF3J6D7NFBV4A \
  | 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: 4a7443840b2fa1d300bb4f87f69435e01d61e91c6c7b3dace282b3ccc3e350b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "388a09a7e509642652275d46f3aff5fc26dbc3a42beed927440d7938fde2db41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-08T19:48:08Z",
    "title_canon_sha256": "e8f77350369d120805db60a3e92c5affa2b974bfff49ec79dfd2fa51ea107be4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02511",
    "kind": "arxiv",
    "version": 1
  }
}