Pith Number

pith:TQIW63MA

pith:2005:TQIW63MAQ22WE2CRA6QG5QTJVM

not attested not anchored not stored refs pending

Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams

Daniel Groves

arxiv:math/0503045 v2 · 2005-03-02 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQIW63MAQ22WE2CRA6QG5QTJVM}

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	2026-05-18T02:37:59.803074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c116f6d8086b562685107a06ec269ab129ec5ac0d3507fd4de69d1f6119c8d2

Aliases

arxiv: math/0503045 · arxiv_version: math/0503045v2 · doi: 10.48550/arxiv.math/0503045 · pith_short_12: TQIW63MAQ22W · pith_short_16: TQIW63MAQ22WE2CR · pith_short_8: TQIW63MA

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/TQIW63MAQ22WE2CRA6QG5QTJVM \
  | 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: 9c116f6d8086b562685107a06ec269ab129ec5ac0d3507fd4de69d1f6119c8d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39abce96c8169538870e5303234cc2d1707c728a5c696c033b167536238f7de0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-03-02T17:02:57Z",
    "title_canon_sha256": "e15ff4c8dd998d5e5e2be1ba9ab6df257bc14bc8220b2613c40b1bb69e304df7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0503045",
    "kind": "arxiv",
    "version": 2
  }
}