Pith Number

pith:4F5D7LWW

pith:2011:4F5D7LWWABPTP5JQKV5RO3XFY3

not attested not anchored not stored refs pending

Gompertz and Verhulst frameworks for growth and decay description

BE), Marcel Ausloos (Liege

arxiv:1109.1269 v2 · 2011-08-25 · physics.bio-ph · physics.soc-ph · q-bio.PE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4F5D7LWWABPTP5JQKV5RO3XFY3}

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	2026-05-18T02:21:36.904594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e17a3faed6005f37f530557b176ee5c6d7e152335e98d7fd3c00c47d4a9b0361

Aliases

arxiv: 1109.1269 · arxiv_version: 1109.1269v2 · doi: 10.48550/arxiv.1109.1269 · pith_short_12: 4F5D7LWWABPT · pith_short_16: 4F5D7LWWABPTP5JQ · pith_short_8: 4F5D7LWW

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/4F5D7LWWABPTP5JQKV5RO3XFY3 \
  | 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: e17a3faed6005f37f530557b176ee5c6d7e152335e98d7fd3c00c47d4a9b0361

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "259ee4657d94bc2b6b1649a7870e1557abe401e7d5ee93e8cb84bead4ac6bde1",
    "cross_cats_sorted": [
      "physics.soc-ph",
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.bio-ph",
    "submitted_at": "2011-08-25T21:05:48Z",
    "title_canon_sha256": "907e3339ed6d26e073e58726d894a7c2a72c32480f838c1dac9a3803b4315202"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1269",
    "kind": "arxiv",
    "version": 2
  }
}