Pith Number

pith:IM3VFZN5

pith:2006:IM3VFZN5XDUT3CD7I2ASTPDMRZ

not attested not anchored not stored refs pending

Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces

Viacheslav V. Nikulin

arxiv:math/0609256 v2 · 2006-09-09 · 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{IM3VFZN5XDUT3CD7I2ASTPDMRZ}

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	2026-05-18T01:38:23.789522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

433752e5bdb8e93d887f468129bc6c8e7abd8ae568b7faadd6fcc24e5df23e55

Aliases

arxiv: math/0609256 · arxiv_version: math/0609256v2 · doi: 10.48550/arxiv.math/0609256 · pith_short_12: IM3VFZN5XDUT · pith_short_16: IM3VFZN5XDUT3CD7 · pith_short_8: IM3VFZN5

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/IM3VFZN5XDUT3CD7I2ASTPDMRZ \
  | 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: 433752e5bdb8e93d887f468129bc6c8e7abd8ae568b7faadd6fcc24e5df23e55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9086fb15f7b06fafe328f3684c20464d55000a16658a7a441dd6300d4fe18af7",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-09-09T12:26:50Z",
    "title_canon_sha256": "437405b88730ddf08356494aa8fff2ccc966fb434a003e780176d2c95b3419cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609256",
    "kind": "arxiv",
    "version": 2
  }
}