Pith Number

pith:P4I3NPVD

pith:2006:P4I3NPVDQB3DEF3XX7BGLJFQWE

not attested not anchored not stored refs pending

Discrete versus continuous models in evolutionary dynamics: from simple to simpler -- and even simpler -- models

Fabio A.C.C. Chalub, Max O. Souza

arxiv:math/0608041 v1 · 2006-08-02 · math.AP · 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{P4I3NPVDQB3DEF3XX7BGLJFQWE}

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	2026-05-18T03:36:05.303822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f11b6bea38076321777bfc265a4b0b13736ed56da102404089dce530db11bfe

Aliases

arxiv: math/0608041 · arxiv_version: math/0608041v1 · doi: 10.48550/arxiv.math/0608041 · pith_short_12: P4I3NPVDQB3D · pith_short_16: P4I3NPVDQB3DEF3X · pith_short_8: P4I3NPVD

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/P4I3NPVDQB3DEF3XX7BGLJFQWE \
  | 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: 7f11b6bea38076321777bfc265a4b0b13736ed56da102404089dce530db11bfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a5eaacb8a85f3b2c2cd674ec29c46afcd9320127eaa7bfc4745bb97a6b815b4",
    "cross_cats_sorted": [
      "q-bio.PE"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2006-08-02T02:19:09Z",
    "title_canon_sha256": "562c5a68dfe48829ea2886be93953a712ea6470d54ca212c0f361009a6aca233"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608041",
    "kind": "arxiv",
    "version": 1
  }
}