Pith Number

pith:WCVTPC6R

pith:2021:WCVTPC6RE65QQHQEH7WRQ6IZGH

not attested not anchored not stored refs pending

Uryson width of three dimensional mean convex domain with non-negative Ricci curvature

Bo Zhu, Zhichao Wang

arxiv:2109.12715 v1 · 2021-09-26 · math.DG · math.GT · 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{WCVTPC6RE65QQHQEH7WRQ6IZGH}

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	2026-07-05T03:17:35.678401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0ab378bd127bb081e043fed18791931dd438b0b70de273aed3ae0e07ae1550a

Aliases

arxiv: 2109.12715 · arxiv_version: 2109.12715v1 · doi: 10.48550/arxiv.2109.12715 · pith_short_12: WCVTPC6RE65Q · pith_short_16: WCVTPC6RE65QQHQE · pith_short_8: WCVTPC6R

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/WCVTPC6RE65QQHQEH7WRQ6IZGH \
  | 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: b0ab378bd127bb081e043fed18791931dd438b0b70de273aed3ae0e07ae1550a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94877c0ccb555a19daa1ce7ded2c8f3d77f99b764cbe5083eb423356a12fe5b3",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-09-26T22:31:42Z",
    "title_canon_sha256": "2e9fddb8a54f031d5b913ac6736ee0b4a8b6274285efe5ae9a396959770e9e80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.12715",
    "kind": "arxiv",
    "version": 1
  }
}