Pith Number

pith:MY4WKTBD

pith:2019:MY4WKTBDRO2CJXPBUDKNL3WFZB

not attested not anchored not stored refs pending

A characterization of Veech groups in terms of origamis

Shun Kumagai

arxiv:1908.09226 v2 · 2019-08-24 · math.GT · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MY4WKTBDRO2CJXPBUDKNL3WFZB}

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	2026-07-05T01:01:35.732696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6639654c238bb424dde1a0d4d5eec5c875a2d9e4e226a8458e8cd8d3e80a09f0

Aliases

arxiv: 1908.09226 · arxiv_version: 1908.09226v2 · doi: 10.48550/arxiv.1908.09226 · pith_short_12: MY4WKTBDRO2C · pith_short_16: MY4WKTBDRO2CJXPB · pith_short_8: MY4WKTBD

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/MY4WKTBDRO2CJXPBUDKNL3WFZB \
  | 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: 6639654c238bb424dde1a0d4d5eec5c875a2d9e4e226a8458e8cd8d3e80a09f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9095a48975be50e6c0786a452b65adcf0076b83d1d95e2d770c93274b5976436",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-08-24T22:59:20Z",
    "title_canon_sha256": "e3c692001201ca5a3dc5035ebb7de5d3c6501a815b5928cc6383749d7f7f53e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09226",
    "kind": "arxiv",
    "version": 2
  }
}