Pith Number

pith:VV2GAH64

pith:2008:VV2GAH64YX2VX74EN2XNVQTP5H

not attested not anchored not stored refs pending

Notes on Sela's work: Limit groups and Makanin-Razborov diagrams

Mark Feighn, Mladen Bestvina

arxiv:0809.0467 v2 · 2008-09-02 · math.GR · 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{VV2GAH64YX2VX74EN2XNVQTP5H}

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	2026-05-18T04:09:36.474659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad74601fdcc5f55bff846eaedac26fe9de0d5246dfd5adcc98063343648a7b64

Aliases

arxiv: 0809.0467 · arxiv_version: 0809.0467v2 · doi: 10.48550/arxiv.0809.0467 · pith_short_12: VV2GAH64YX2V · pith_short_16: VV2GAH64YX2VX74E · pith_short_8: VV2GAH64

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/VV2GAH64YX2VX74EN2XNVQTP5H \
  | 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: ad74601fdcc5f55bff846eaedac26fe9de0d5246dfd5adcc98063343648a7b64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a51a68a36886880433314d3e54b5fc9cef4308b171366ddeb12154e92242c59",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-09-02T16:38:14Z",
    "title_canon_sha256": "0f82ce00381eed8607468c4b773e45da246808985d5f7ac72ab88aeb18d874b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.0467",
    "kind": "arxiv",
    "version": 2
  }
}