Pith Number

pith:NPRUTRGS

pith:2026:NPRUTRGSMGB3AG76BR6VTJOB7H

not attested not anchored not stored refs pending

On rank two Kleinian groups with three parabolics

Alex Elzenaar

arxiv:2607.07424 v1 · 2026-07-08 · math.GR · 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{NPRUTRGSMGB3AG76BR6VTJOB7H}

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	2026-07-09T01:20:24.557570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6be349c4d26183b01bfe0c7d59a5c1f9c47703662e27f678159efa8688779fb2

Aliases

arxiv: 2607.07424 · arxiv_version: 2607.07424v1 · doi: 10.48550/arxiv.2607.07424 · pith_short_12: NPRUTRGSMGB3 · pith_short_16: NPRUTRGSMGB3AG76 · pith_short_8: NPRUTRGS

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/NPRUTRGSMGB3AG76BR6VTJOB7H \
  | 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: 6be349c4d26183b01bfe0c7d59a5c1f9c47703662e27f678159efa8688779fb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a811235b75c19f1c028d2aa7b985f3e3e79a8e5287b5200268cc9c1e25e17f2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-08T13:52:27Z",
    "title_canon_sha256": "15c02c11a0b7b1905af83355331faa26b8381d3573a348c55e21a829878e8489"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07424",
    "kind": "arxiv",
    "version": 1
  }
}