Pith Number

pith:XJQ4GURH

pith:2007:XJQ4GURHZ4F6XYMC6SOIIU5CTT

not attested not anchored not stored refs pending

On ground fields of arithmetic hyperbolic reflection groups. III

Viacheslav V. Nikulin

arxiv:0710.2340 v3 · 2007-10-11 · 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{XJQ4GURHZ4F6XYMC6SOIIU5CTT}

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	2026-05-18T02:58:12.188593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba61c35227cf0bebe182f49c8453a29cd048f85b95b2c2b74d24a77388c4c9fc

Aliases

arxiv: 0710.2340 · arxiv_version: 0710.2340v3 · doi: 10.48550/arxiv.0710.2340 · pith_short_12: XJQ4GURHZ4F6 · pith_short_16: XJQ4GURHZ4F6XYMC · pith_short_8: XJQ4GURH

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/XJQ4GURHZ4F6XYMC6SOIIU5CTT \
  | 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: ba61c35227cf0bebe182f49c8453a29cd048f85b95b2c2b74d24a77388c4c9fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b53db190f6c6205ee39115a57b61dbadb65d08bc7645d541540e4519c5f5b20",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-10-11T20:06:57Z",
    "title_canon_sha256": "e903ce4884a9956ee40f7e0db3a117dca1676e748cbe7b20a252b55780263a90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.2340",
    "kind": "arxiv",
    "version": 3
  }
}