Pith Number

pith:UK624PRP

pith:2008:UK624PRP6MLVLQTLQ22M55VZHL

not attested not anchored not stored refs pending

Trees of cylinders and canonical splittings

Gilbert Levitt, Vincent Guirardel

arxiv:0811.2383 v2 · 2008-11-14 · 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{UK624PRP6MLVLQTLQ22M55VZHL}

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	2026-05-18T01:22:31.064211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2bdae3e2ff31755c26b86b4cef6b93af245465608fef71dc7520a5f68824a73

Aliases

arxiv: 0811.2383 · arxiv_version: 0811.2383v2 · doi: 10.48550/arxiv.0811.2383 · pith_short_12: UK624PRP6MLV · pith_short_16: UK624PRP6MLVLQTL · pith_short_8: UK624PRP

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/UK624PRP6MLVLQTLQ22M55VZHL \
  | 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: a2bdae3e2ff31755c26b86b4cef6b93af245465608fef71dc7520a5f68824a73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f17142fc31adfb56f4ba64ab38fe896b4264066c7e3e79623e1e9866533cd535",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-11-14T17:05:23Z",
    "title_canon_sha256": "a2bf2a1ba8b7c1e6c9ce018410a82175d77cf9a856ef35b1a1f1c980918611ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.2383",
    "kind": "arxiv",
    "version": 2
  }
}