Pith Number

pith:LAD65QGI

pith:2015:LAD65QGIPICNM3LMFERUF3WBYC

not attested not anchored not stored refs pending

Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane

George Stantchev, Greg McShane, Ser Peow Tan, William Goldman

arxiv:1509.03790 v3 · 2015-09-13 · math.DS · math.DG · 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{LAD65QGIPICNM3LMFERUF3WBYC}

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	2026-05-18T01:02:56.831570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5807eec0c87a04d66d6c292342eec1c08053cf313689ffc963c34106b4544d55

Aliases

arxiv: 1509.03790 · arxiv_version: 1509.03790v3 · doi: 10.48550/arxiv.1509.03790 · pith_short_12: LAD65QGIPICN · pith_short_16: LAD65QGIPICNM3LM · pith_short_8: LAD65QGI

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/LAD65QGIPICNM3LMFERUF3WBYC \
  | 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: 5807eec0c87a04d66d6c292342eec1c08053cf313689ffc963c34106b4544d55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23e649b6080a287703ca3a11b6cfdb7a1bce313ca70e2e59455063dc0200ef6a",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-13T00:37:28Z",
    "title_canon_sha256": "bc789f047a2943cdbb95f48450ca1a40a9bd27b64683a4c6fc7545f7a59e4b6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03790",
    "kind": "arxiv",
    "version": 3
  }
}