Pith Number

pith:2NUDZ7AL

pith:2023:2NUDZ7ALQYWJX6Q2E3FQW7QF46

not attested not anchored not stored refs pending

On the waist and width inequality in complete 3-manifolds with positive scalar curvature

Yevgeny Liokumovich, Zhichao Wang

arxiv:2308.04044 v1 · 2023-08-08 · math.DG · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2NUDZ7ALQYWJX6Q2E3FQW7QF46}

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	2026-07-05T06:39:21.552391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3683cfc0b862c9bfa1a26cb0b7e05e7a983fa347b1aa6eccf5d187e3afa95ad

Aliases

arxiv: 2308.04044 · arxiv_version: 2308.04044v1 · doi: 10.48550/arxiv.2308.04044 · pith_short_12: 2NUDZ7ALQYWJ · pith_short_16: 2NUDZ7ALQYWJX6Q2 · pith_short_8: 2NUDZ7AL

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/2NUDZ7ALQYWJX6Q2E3FQW7QF46 \
  | 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: d3683cfc0b862c9bfa1a26cb0b7e05e7a983fa347b1aa6eccf5d187e3afa95ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b83dd6af565e2adb29efe96915ebcb68079fcaf64601bc7e3e67369da561cb8",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2023-08-08T04:44:55Z",
    "title_canon_sha256": "7b3d787b254e541ec2f26cbb793795ba3b3f56efd2eea3f69c00c1abcf2bb945"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.04044",
    "kind": "arxiv",
    "version": 1
  }
}