Pith Number

pith:UCJWHRSL

pith:2007:UCJWHRSLUFC6P3EHKFBFJ4ECCN

not attested not anchored not stored refs pending

On the type of triangle groups

Carlos H. Grossi

arxiv:0707.3628 v1 · 2007-07-24 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UCJWHRSLUFC6P3EHKFBFJ4ECCN}

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	2026-05-18T04:09:56.624351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a09363c64ba145e7ec87514254f082136ff01dc2134657c8942238c76c009026

Aliases

arxiv: 0707.3628 · arxiv_version: 0707.3628v1 · doi: 10.48550/arxiv.0707.3628 · pith_short_12: UCJWHRSLUFC6 · pith_short_16: UCJWHRSLUFC6P3EH · pith_short_8: UCJWHRSL

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/UCJWHRSLUFC6P3EHKFBFJ4ECCN \
  | 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: a09363c64ba145e7ec87514254f082136ff01dc2134657c8942238c76c009026

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c49c192c168ddc320ef1ed48401e9f616f6a63cd4f41fd413162b1781f16198",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2007-07-24T19:09:38Z",
    "title_canon_sha256": "0df162c70bac49e8833e138378dbb79e1999530ae9682ba52d9c51f98a5d5d31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.3628",
    "kind": "arxiv",
    "version": 1
  }
}