Pith Number

pith:ELZ2H63O

pith:2008:ELZ2H63OML4ZCJR6YONNXPR4KN

not attested not anchored not stored refs pending

Counting growth types of automorphisms of free groups

Gilbert Levitt

arxiv:0801.4844 v2 · 2008-01-31 · 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{ELZ2H63OML4ZCJR6YONNXPR4KN}

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	2026-05-17T23:44:05.081283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22f3a3fb6e62f991263ec39adbbe3c5372da3e4828677a520fcea1027a09a023

Aliases

arxiv: 0801.4844 · arxiv_version: 0801.4844v2 · doi: 10.48550/arxiv.0801.4844 · pith_short_12: ELZ2H63OML4Z · pith_short_16: ELZ2H63OML4ZCJR6 · pith_short_8: ELZ2H63O

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/ELZ2H63OML4ZCJR6YONNXPR4KN \
  | 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: 22f3a3fb6e62f991263ec39adbbe3c5372da3e4828677a520fcea1027a09a023

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6c174986f4931b75de3c69eeb624fea9894606b69c715d8aae3709bd2a56a11",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-01-31T10:13:00Z",
    "title_canon_sha256": "537ee82469344c986e1763290fe69d8befb2d374525cd9416977e7595cb5134d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.4844",
    "kind": "arxiv",
    "version": 2
  }
}