Pith Number

pith:4MZUIQ6K

pith:2012:4MZUIQ6KE7JVMYBTI7PK32QB7U

not attested not anchored not stored refs pending

Dirichlet fundamental domains and complex-projective varieties

Michael Kapovich

arxiv:1201.3129 v1 · 2012-01-15 · math.AG · 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{4MZUIQ6KE7JVMYBTI7PK32QB7U}

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	2026-05-18T01:58:49.055919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3334443ca27d356603347deadea01fd0be9f95f28c0fa6a5445163b41f7d270

Aliases

arxiv: 1201.3129 · arxiv_version: 1201.3129v1 · doi: 10.48550/arxiv.1201.3129 · pith_short_12: 4MZUIQ6KE7JV · pith_short_16: 4MZUIQ6KE7JVMYBT · pith_short_8: 4MZUIQ6K

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/4MZUIQ6KE7JVMYBTI7PK32QB7U \
  | 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: e3334443ca27d356603347deadea01fd0be9f95f28c0fa6a5445163b41f7d270

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de8b1e507c8e0431840868bd8ae87c16a9c1235c73020872bae8578eb8b5d8d5",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-01-15T21:43:32Z",
    "title_canon_sha256": "2dafa77130461e2ff3795f448327216c3cc2d7133da4f7ed682ecc6f4883fa9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3129",
    "kind": "arxiv",
    "version": 1
  }
}