Pith Number

pith:4IO2AFLZ

pith:2008:4IO2AFLZCQO5WAHHTAURBATCDR

not attested not anchored not stored refs pending

On several problems about automorphisms of the free group of rank two

Donghi Lee

arxiv:0802.0584 v1 · 2008-02-05 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IO2AFLZCQO5WAHHTAURBATCDR}

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	2026-05-18T04:23:13.516527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e21da01579141ddb00e798291082621c7b789f42fde8bb0310ef8cede2e0974a

Aliases

arxiv: 0802.0584 · arxiv_version: 0802.0584v1 · doi: 10.48550/arxiv.0802.0584 · pith_short_12: 4IO2AFLZCQO5 · pith_short_16: 4IO2AFLZCQO5WAHH · pith_short_8: 4IO2AFLZ

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/4IO2AFLZCQO5WAHHTAURBATCDR \
  | 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: e21da01579141ddb00e798291082621c7b789f42fde8bb0310ef8cede2e0974a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b15f36aab62e062d3c2b17221bdf31eb3a81f4a74476786c9ee04ffdb652fd39",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-02-05T10:37:13Z",
    "title_canon_sha256": "554f8f09263f53f51eaccc5f6e1752ca8cb113108c68bcf9ac71f00a5481b977"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.0584",
    "kind": "arxiv",
    "version": 1
  }
}