Pith Number

pith:AB2K5UZT

pith:2015:AB2K5UZTRGDZIXX2PCJXNFCY3L

not attested not anchored not stored refs pending

The limit set for discrete complex hyperbolic groups

Angel Cano, Bingyuan Liu, Marlon M. L\'opez

arxiv:1506.08113 v5 · 2015-06-26 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AB2K5UZTRGDZIXX2PCJXNFCY3L}

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	2026-05-18T01:12:30.771881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0074aed3338987945efa7893769458dac9af0196ecd40ebe969e4a55c6d1c873

Aliases

arxiv: 1506.08113 · arxiv_version: 1506.08113v5 · doi: 10.48550/arxiv.1506.08113 · pith_short_12: AB2K5UZTRGDZ · pith_short_16: AB2K5UZTRGDZIXX2 · pith_short_8: AB2K5UZT

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/AB2K5UZTRGDZIXX2PCJXNFCY3L \
  | 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: 0074aed3338987945efa7893769458dac9af0196ecd40ebe969e4a55c6d1c873

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aac9ffe06b5f738b3a12727438132e1347f61cd2d5351b62354c8439298ae1c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-06-26T15:17:17Z",
    "title_canon_sha256": "474faf77501467dff58af2a7048709e8ff5c79cfe0ccd1c6e1fda0cc6082f3ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08113",
    "kind": "arxiv",
    "version": 5
  }
}