Pith Number

pith:NZTXMGMK

pith:2020:NZTXMGMKGGZ3MNJQ7TQMI2F23I

not attested not anchored not stored refs pending

Proper actions of discrete groups of affine transformations

Ilia Smilga, Jeffrey Danciger, Todd A. Drumm, William M. Goldman

arxiv:2002.09520 v1 · 2020-02-21 · math.GR · 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{NZTXMGMKGGZ3MNJQ7TQMI2F23I}

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.

Cited by

1 paper in Pith

Entropy and affine actions for surface groups

Receipt and verification

First computed	2026-07-05T00:43:08.586295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e6776198a31b3b63530fce0c468bada3a86ab999ef6cba328bf0dceebba5268

Aliases

arxiv: 2002.09520 · arxiv_version: 2002.09520v1 · doi: 10.48550/arxiv.2002.09520 · pith_short_12: NZTXMGMKGGZ3 · pith_short_16: NZTXMGMKGGZ3MNJQ · pith_short_8: NZTXMGMK

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/NZTXMGMKGGZ3MNJQ7TQMI2F23I \
  | 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: 6e6776198a31b3b63530fce0c468bada3a86ab999ef6cba328bf0dceebba5268

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c9293c491e979957b4ea90b78aa5ff388957eb9492f3d21d44d39d7f4f6f658",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2020-02-21T19:30:46Z",
    "title_canon_sha256": "c52afdccbf1fb846b7b70bfa2768efacf513bf6e9eb2e8993be70fee06819eb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.09520",
    "kind": "arxiv",
    "version": 1
  }
}