Pith Number

pith:MH3YFDIL

pith:2002:MH3YFDIL4MM5MVKFTDRFLOI252

not attested not anchored not stored refs pending

On several varieties of cacti and their relations

Ralph M. Kaufmann

arxiv:math/0209131 v7 · 2002-09-11 · math.QA · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MH3YFDIL4MM5MVKFTDRFLOI252}

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	2026-05-18T02:41:32.874839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61f7828d0be319d6554598e255b91aee9337d29528005c350ac9006ebdeb4747

Aliases

arxiv: math/0209131 · arxiv_version: math/0209131v7 · doi: 10.48550/arxiv.math/0209131 · pith_short_12: MH3YFDIL4MM5 · pith_short_16: MH3YFDIL4MM5MVKF · pith_short_8: MH3YFDIL

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/MH3YFDIL4MM5MVKFTDRFLOI252 \
  | 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: 61f7828d0be319d6554598e255b91aee9337d29528005c350ac9006ebdeb4747

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8728328dd20f824ec927dbd8e98c5c95da62940584ff536f787e1d33ac22fe7f",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-09-11T18:42:37Z",
    "title_canon_sha256": "61df6044a8baf442a0c585fbce15f4e3c3402f9816b971ef5caa409efeeeecac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209131",
    "kind": "arxiv",
    "version": 7
  }
}