Pith Number

pith:JB3LPDQW

pith:2007:JB3LPDQW4EE7MUYRIV6KB4TU3X

not attested not anchored not stored refs pending

On ground fields of arithmetic hyperbolic reflection groups

Viacheslav V. Nikulin

arxiv:0708.3991 v2 · 2007-08-29 · math.AG · 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{JB3LPDQW4EE7MUYRIV6KB4TU3X}

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	2026-05-18T04:11:39.828724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4876b78e16e109f65311457ca0f274ddf2ace61dc18e164e78e6f8cc9a596ef8

Aliases

arxiv: 0708.3991 · arxiv_version: 0708.3991v2 · doi: 10.48550/arxiv.0708.3991 · pith_short_12: JB3LPDQW4EE7 · pith_short_16: JB3LPDQW4EE7MUYR · pith_short_8: JB3LPDQW

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/JB3LPDQW4EE7MUYRIV6KB4TU3X \
  | 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: 4876b78e16e109f65311457ca0f274ddf2ace61dc18e164e78e6f8cc9a596ef8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6a9cb59e43f72d2c98027787345f21c92abbdd99bec031ad18ef7771fb50f95",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-08-29T16:48:46Z",
    "title_canon_sha256": "ff4dc250584673933414c41f3f40395733f00385ab91dc068d86b0cc12059ea0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.3991",
    "kind": "arxiv",
    "version": 2
  }
}