Pith Number

pith:XJYR72DU

pith:1992:XJYR72DUOFV5VZSPZB5E3KYOQX

not attested not anchored not stored refs pending

Generalizing the hyperbolic collar lemma

Ara Basmajian

arxiv:math/9207211 v1 · 1992-07-01 · math.DG · 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{XJYR72DUOFV5VZSPZB5E3KYOQX}

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	2026-05-18T01:05:52.717350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba711fe874716bdae64fc87a4dab0e85eb0f478a8ed814c67ffcba1b85b5439f

Aliases

arxiv: math/9207211 · arxiv_version: math/9207211v1 · doi: 10.48550/arxiv.math/9207211 · pith_short_12: XJYR72DUOFV5 · pith_short_16: XJYR72DUOFV5VZSP · pith_short_8: XJYR72DU

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/XJYR72DUOFV5VZSPZB5E3KYOQX \
  | 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: ba711fe874716bdae64fc87a4dab0e85eb0f478a8ed814c67ffcba1b85b5439f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ef6f201ebfd5d05a1c2f2ff2a0b173a72789badf601ba3ea9bfe31869b98b46",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1992-07-01T00:00:00Z",
    "title_canon_sha256": "fb8f88ddf57b4732269e2d9cc10594557f114a07c45b7d1ac91487229ee57dc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9207211",
    "kind": "arxiv",
    "version": 1
  }
}