Pith Number

pith:IPQIKEBZ

pith:2008:IPQIKEBZUV5BR4B6WG7ICY2JR4

not attested not anchored not stored refs pending

The universal Cannon--Thurston maps and the boundary of the curve complex

Christopher J. Leininger, Mahan Mj, Saul Schleimer

arxiv:0808.3521 v2 · 2008-08-26 · math.GT · 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{IPQIKEBZUV5BR4B6WG7ICY2JR4}

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	2026-05-18T04:10:09.282468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43e0851039a57a18f03eb1be8163498f1e6522f53288d334240a15a68a018028

Aliases

arxiv: 0808.3521 · arxiv_version: 0808.3521v2 · doi: 10.48550/arxiv.0808.3521 · pith_short_12: IPQIKEBZUV5B · pith_short_16: IPQIKEBZUV5BR4B6 · pith_short_8: IPQIKEBZ

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/IPQIKEBZUV5BR4B6WG7ICY2JR4 \
  | 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: 43e0851039a57a18f03eb1be8163498f1e6522f53288d334240a15a68a018028

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2381616603f2f98cf7867ecda67f0215738068325a1feb53caf87a58cc25412",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-08-26T15:31:21Z",
    "title_canon_sha256": "df94e0177f89bf2b919cafc702b057c40037425f653026addc3885d61a940094"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.3521",
    "kind": "arxiv",
    "version": 2
  }
}