Pith Number

pith:CNPR6DKN

pith:2008:CNPR6DKNWQWPVYIGVZWEGQDU7P

not attested not anchored not stored refs pending

Hierarchical size-structured populations: The linearized semigroup approach

Jozsef Z. Farkas, Thomas C. Hagen

arxiv:0812.1367 v1 · 2008-12-07 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CNPR6DKNWQWPVYIGVZWEGQDU7P}

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	2026-05-17T23:50:43.154134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

135f1f0d4db42cfae106ae6c434074fbce4b0d7e17056aed51f4cbff7e5d0764

Aliases

arxiv: 0812.1367 · arxiv_version: 0812.1367v1 · doi: 10.48550/arxiv.0812.1367 · pith_short_12: CNPR6DKNWQWP · pith_short_16: CNPR6DKNWQWPVYIG · pith_short_8: CNPR6DKN

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/CNPR6DKNWQWPVYIGVZWEGQDU7P \
  | 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: 135f1f0d4db42cfae106ae6c434074fbce4b0d7e17056aed51f4cbff7e5d0764

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "891dfc8d498bb15e821021272e8e965132b098e12b162e3d958a7b0fa675786d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-12-07T17:04:06Z",
    "title_canon_sha256": "2cfe09e652b8bb3e2093a97f848df863cd4a4a3a537ee2f30f077d607687141e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1367",
    "kind": "arxiv",
    "version": 1
  }
}