Pith Number

pith:SH7XQNK3

pith:1999:SH7XQNK3EYKGV4TYGZSFDGUM4V

not attested not anchored not stored refs pending

Kleinian groups and the complex of curves

Yair N. Minsky

arxiv:math/9907070 v2 · 1999-07-12 · 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{SH7XQNK3EYKGV4TYGZSFDGUM4V}

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	2026-05-18T02:37:59.229163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91ff78355b26146af2783664519a8ce5513dd9bef2e4f1f4cf9f9385f9f73c61

Aliases

arxiv: math/9907070 · arxiv_version: math/9907070v2 · doi: 10.48550/arxiv.math/9907070 · pith_short_12: SH7XQNK3EYKG · pith_short_16: SH7XQNK3EYKGV4TY · pith_short_8: SH7XQNK3

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/SH7XQNK3EYKGV4TYGZSFDGUM4V \
  | 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: 91ff78355b26146af2783664519a8ce5513dd9bef2e4f1f4cf9f9385f9f73c61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b8e237c90292ed2adf3da2888e8216bcc4fd9102b12113292ff1ceaf96d2931",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-07-12T13:15:54Z",
    "title_canon_sha256": "68d9f4996c2b6a1cc34a041bb064212555039bbb3fa26af6e2fea432b4e2fbb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907070",
    "kind": "arxiv",
    "version": 2
  }
}