Pith Number

pith:G2L47XMW

pith:2018:G2L47XMW3HGWFQ5BQ5Q7L7ANG4

not attested not anchored not stored refs pending

$L_p$-Brunn-Minkowski inequality for $p\in (1-\frac{c}{n^{\frac{3}{2}}}, 1)$

Jiakun Liu, Qi-Rui Li, Shibing Chen, Yong Huang

arxiv:1811.10181 v1 · 2018-11-26 · math.AP · 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{G2L47XMW3HGWFQ5BQ5Q7L7ANG4}

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	2026-05-17T23:59:58.483767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3697cfdd96d9cd62c3a18761f5fc0d37198b022fef97c2e64720dcbd01ac6ec9

Aliases

arxiv: 1811.10181 · arxiv_version: 1811.10181v1 · doi: 10.48550/arxiv.1811.10181 · pith_short_12: G2L47XMW3HGW · pith_short_16: G2L47XMW3HGWFQ5B · pith_short_8: G2L47XMW

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/G2L47XMW3HGWFQ5BQ5Q7L7ANG4 \
  | 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: 3697cfdd96d9cd62c3a18761f5fc0d37198b022fef97c2e64720dcbd01ac6ec9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "570aea8b7b5e85dde9dcdafc4313ec6e22994702409b287060e5f64a7f3590a6",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-11-26T05:24:18Z",
    "title_canon_sha256": "c18f2f0f8b2baed50d0d2b9a488462d83aadf6b0e037e96bca3993f9268c93d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.10181",
    "kind": "arxiv",
    "version": 1
  }
}