Pith Number

pith:4UTETK3Y

pith:2010:4UTETK3YSDBCI35GS4GBLXEAQY

not attested not anchored not stored refs pending

Full analytical solution and complete phase diagram analysis of the Verhulst-like two-species population dynamics model

Alexandre Souto Martinez, Brenno Caetano Troca Cabella, Fabiano Ribeiro

arxiv:1010.3361 v2 · 2010-10-16 · q-bio.PE · cond-mat.dis-nn · cond-mat.stat-mech · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UTETK3YSDBCI35GS4GBLXEAQY}

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	2026-05-18T02:23:45.500898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e52649ab7890c2246fa6970c15dc8086142ac7c146ac9d7cafa927811e212ee1

Aliases

arxiv: 1010.3361 · arxiv_version: 1010.3361v2 · doi: 10.48550/arxiv.1010.3361 · pith_short_12: 4UTETK3YSDBC · pith_short_16: 4UTETK3YSDBCI35G · pith_short_8: 4UTETK3Y

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/4UTETK3YSDBCI35GS4GBLXEAQY \
  | 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: e52649ab7890c2246fa6970c15dc8086142ac7c146ac9d7cafa927811e212ee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68119138a7dcec1e65f0b2f15a41f30c5204155f918c8ba793147807c5dc0700",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2010-10-16T15:27:33Z",
    "title_canon_sha256": "d83377d670753ff251ce149c3b376af838125f5aaeb2b78e35138a6c32beed8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3361",
    "kind": "arxiv",
    "version": 2
  }
}