Pith Number

pith:KAAOHYQD

pith:2005:KAAOHYQDTHMMFRLPVHPJOUD3E5

not attested not anchored not stored refs pending

Virtually Haken surgeries on once-punctured torus bundles

Joseph D. Masters

arxiv:math/0506443 v3 · 2005-06-22 · 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{KAAOHYQDTHMMFRLPVHPJOUD3E5}

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	2026-05-18T01:05:23.377951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5000e3e20399d8c2c56fa9de97507b27516527f524b5bbe0a89adbd140a29bb8

Aliases

arxiv: math/0506443 · arxiv_version: math/0506443v3 · doi: 10.48550/arxiv.math/0506443 · pith_short_12: KAAOHYQDTHMM · pith_short_16: KAAOHYQDTHMMFRLP · pith_short_8: KAAOHYQD

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/KAAOHYQDTHMMFRLPVHPJOUD3E5 \
  | 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: 5000e3e20399d8c2c56fa9de97507b27516527f524b5bbe0a89adbd140a29bb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59e3a6b9a603cd42529d835f6db50e934ae51ee2b9256d515a97465c1e07120c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2005-06-22T16:15:22Z",
    "title_canon_sha256": "48ac31eb83597ec5787634141c8c0fb9c554a1e73a3ca2b114172805d2e056f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506443",
    "kind": "arxiv",
    "version": 3
  }
}