Pith Number

pith:3X2ZMUOD

pith:2025:3X2ZMUODA63WUXWVVRFQYTB26H

not attested not anchored not stored refs pending

Discreteness of the complex hyperbolic ultra-parallel triangle groups

Baohua Xie, Wei Liao

arxiv:2504.04407 v2 · 2025-04-06 · 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{3X2ZMUODA63WUXWVVRFQYTB26H}

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	2026-05-29T01:04:52.713376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddf59651c307b76a5ed5ac4b0c4c3af1f0bf5d971a22bbcadd47d82010e82955

Aliases

arxiv: 2504.04407 · arxiv_version: 2504.04407v2 · doi: 10.48550/arxiv.2504.04407 · pith_short_12: 3X2ZMUODA63W · pith_short_16: 3X2ZMUODA63WUXWV · pith_short_8: 3X2ZMUOD

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/3X2ZMUODA63WUXWVVRFQYTB26H \
  | 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: ddf59651c307b76a5ed5ac4b0c4c3af1f0bf5d971a22bbcadd47d82010e82955

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cd1c3396ea445ad64d9c6efee068a8bdada2001c66078d47e91beb9bee7d224",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-04-06T08:14:53Z",
    "title_canon_sha256": "e2a2a496fdddfea98dba343b4f9be2bcbef479050c4a905e4ce27f1b8880d58d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.04407",
    "kind": "arxiv",
    "version": 2
  }
}