Pith Number

pith:D75M6GH7

pith:2010:D75M6GH7IG5A2ND3Y3JFXRNT3R

not attested not anchored not stored refs pending

Limit sets of relatively hyperbolic groups

Wen-yuan Yang

arxiv:1009.1647 v3 · 2010-09-08 · 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{D75M6GH7IG5A2ND3Y3JFXRNT3R}

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	2026-05-18T04:26:43.488046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ffacf18ff41ba0d347bc6d25bc5b3dc505ce1cade480223934024df3f1610c4

Aliases

arxiv: 1009.1647 · arxiv_version: 1009.1647v3 · doi: 10.48550/arxiv.1009.1647 · pith_short_12: D75M6GH7IG5A · pith_short_16: D75M6GH7IG5A2ND3 · pith_short_8: D75M6GH7

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/D75M6GH7IG5A2ND3Y3JFXRNT3R \
  | 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: 1ffacf18ff41ba0d347bc6d25bc5b3dc505ce1cade480223934024df3f1610c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a93c335c29ee6612d16e796035faa43f26072847e014018fdb69cccc3fa1a056",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-08T20:37:46Z",
    "title_canon_sha256": "92f5e703619f1dcccb1c1d54b7e4f11c988d087d34f5af3703ac34c437c88cbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1647",
    "kind": "arxiv",
    "version": 3
  }
}