Pith Number

pith:P3AZCIJR

pith:2018:P3AZCIJR67KPK3VCVZNXZFXENW

not attested not anchored not stored refs pending

Populations with interaction and environmental dependence: from few, (almost) independent, members into deterministic evolution of high densities

F.C. Klebaner, P. Chigansky, P. Jagers

arxiv:1806.03506 v1 · 2018-06-09 · 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{P3AZCIJR67KPK3VCVZNXZFXENW}

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	2026-05-18T00:13:43.165601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ec1912131f7d4f56ea2ae5b7c96e46dbc027b01dd269855cc50006d56f18c28

Aliases

arxiv: 1806.03506 · arxiv_version: 1806.03506v1 · doi: 10.48550/arxiv.1806.03506 · pith_short_12: P3AZCIJR67KP · pith_short_16: P3AZCIJR67KPK3VC · pith_short_8: P3AZCIJR

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/P3AZCIJR67KPK3VCVZNXZFXENW \
  | 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: 7ec1912131f7d4f56ea2ae5b7c96e46dbc027b01dd269855cc50006d56f18c28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4189db96c7b5a1a295c65ee54cb1238b416648d0f19c9fdd806e39e5366a5114",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-06-09T16:56:39Z",
    "title_canon_sha256": "e14d44dfb235c328fd5ec4580ca5c1b1074b2e128fa71639a37d66f1a2b00685"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.03506",
    "kind": "arxiv",
    "version": 1
  }
}