Pith Number

pith:VMQCIL62

pith:2024:VMQCIL62FE36J2TXTDMA2UTXG5

not attested not anchored not stored refs pending

Essential annuli in genus two handlebody exteriors

Makoto Ozawa, Yi-Sheng Wang, Yuya Koda

arxiv:2404.04503 v1 · 2024-04-06 · 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{VMQCIL62FE36J2TXTDMA2UTXG5}

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.

Cited by

1 paper in Pith

On symmetry and exterior problems of knotted handlebodies

Receipt and verification

First computed	2026-07-05T08:05:17.685246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab20242fda2937e4ea7798d80d5277377dd4d988796a812525e1b76281c0fafc

Aliases

arxiv: 2404.04503 · arxiv_version: 2404.04503v1 · doi: 10.48550/arxiv.2404.04503 · pith_short_12: VMQCIL62FE36 · pith_short_16: VMQCIL62FE36J2TX · pith_short_8: VMQCIL62

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/VMQCIL62FE36J2TXTDMA2UTXG5 \
  | 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: ab20242fda2937e4ea7798d80d5277377dd4d988796a812525e1b76281c0fafc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1864a077d49f694dfeca84b6e72151e49bab99fec2ad32688500c4a22130334",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-04-06T04:58:08Z",
    "title_canon_sha256": "3cf5a6b31c112b058b4839173e748e81dff5bcb4c6aa462fac15479e786a99d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.04503",
    "kind": "arxiv",
    "version": 1
  }
}