Pith Number

pith:DKTW5ZUS

pith:2010:DKTW5ZUS4VAGPRSGBK3PR65WZZ

not attested not anchored not stored refs pending

A refinement of Johnson's bounding for the stable genera of Heegaard splittings

Kazuto Takao

arxiv:1005.1467 v2 · 2010-05-10 · 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{DKTW5ZUS4VAGPRSGBK3PR65WZZ}

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	2026-05-18T04:05:46.035291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1aa76ee692e54067c6460ab6f8fbb6ce4982fc6b58091a73b549e1cacea486b0

Aliases

arxiv: 1005.1467 · arxiv_version: 1005.1467v2 · doi: 10.48550/arxiv.1005.1467 · pith_short_12: DKTW5ZUS4VAG · pith_short_16: DKTW5ZUS4VAGPRSG · pith_short_8: DKTW5ZUS

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/DKTW5ZUS4VAGPRSGBK3PR65WZZ \
  | 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: 1aa76ee692e54067c6460ab6f8fbb6ce4982fc6b58091a73b549e1cacea486b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "834c221a0113bc71110812695370f5e3ddede4fe22df9f58d3b3f22327441b2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-05-10T08:09:19Z",
    "title_canon_sha256": "b0c67f3d44c6745e466aa474b1cba04bff57bc00980ed0cc009aaec795aea3e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.1467",
    "kind": "arxiv",
    "version": 2
  }
}