Pith Number

pith:ZZG7D7KL

pith:2013:ZZG7D7KLO7OODVYTKYIZSOJN7X

not attested not anchored not stored refs pending

Determining the long-term behavior of cell populations: A new procedure for detecting ergodicity in large stochastic reaction networks

Ankit Gupta, Mustafa Khammash

arxiv:1312.2879 v1 · 2013-12-10 · math.PR · q-bio.MN · q-bio.QM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZZG7D7KLO7OODVYTKYIZSOJN7X}

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	2026-05-18T03:05:08.167545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce4df1fd4b77dce1d713561199392dfdc0978cb4f59db73ebaae5803b0947762

Aliases

arxiv: 1312.2879 · arxiv_version: 1312.2879v1 · doi: 10.48550/arxiv.1312.2879 · pith_short_12: ZZG7D7KLO7OO · pith_short_16: ZZG7D7KLO7OODVYT · pith_short_8: ZZG7D7KL

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/ZZG7D7KLO7OODVYTKYIZSOJN7X \
  | 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: ce4df1fd4b77dce1d713561199392dfdc0978cb4f59db73ebaae5803b0947762

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb8b24fef8f4b289084a2817df990b93f480df6c93166599dffb3584b6d6c9e0",
    "cross_cats_sorted": [
      "q-bio.MN",
      "q-bio.QM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-10T17:08:09Z",
    "title_canon_sha256": "15f3cd34e1158d5e4ad218be966982e7bdc72427565fda9de63b0ca348ab4577"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2879",
    "kind": "arxiv",
    "version": 1
  }
}