Pith Number

pith:UIZY2MMU

pith:2017:UIZY2MMUH3RPHRWOH3ZF6FJQJP

not attested not anchored not stored refs pending

Weighted isoperimetric inequalities in warped product manifolds

Kwok-Kun Kwong

arxiv:1708.06682 v1 · 2017-08-22 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UIZY2MMUH3RPHRWOH3ZF6FJQJP}

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	2026-05-18T00:37:32.920020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2338d31943ee2f3c6ce3ef25f15304be2d7a17678a99a0e5d012145bddc4ec0

Aliases

arxiv: 1708.06682 · arxiv_version: 1708.06682v1 · doi: 10.48550/arxiv.1708.06682 · pith_short_12: UIZY2MMUH3RP · pith_short_16: UIZY2MMUH3RPHRWO · pith_short_8: UIZY2MMU

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/UIZY2MMUH3RPHRWOH3ZF6FJQJP \
  | 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: a2338d31943ee2f3c6ce3ef25f15304be2d7a17678a99a0e5d012145bddc4ec0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47fbd8c17b73b5bfdfb9d01aced2dcc9be03291f38be7fc87ef7d9e80f7657c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-08-22T15:47:36Z",
    "title_canon_sha256": "01f5ea050ed333f9a6427f2e6c7e4d15331050f269b20ebc9b84adeda8500bc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.06682",
    "kind": "arxiv",
    "version": 1
  }
}