Pith Number

pith:K5UMSPQD

pith:2026:K5UMSPQDVYIN52ENMLVEG7HCXI

not attested not anchored not stored refs pending

Digesting the proof of the sharp thin-shell inequality

Boaz Klartag, Yuansi Chen

arxiv:2607.23307 v1 · 2026-07-25 · math.MG · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K5UMSPQDVYIN52ENMLVEG7HCXI}

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	2026-07-28T01:22:47.001633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5768c93e03ae10dee88d62ea437ce2ba0753a97578a08cf84543a4f1aaf00408

Aliases

arxiv: 2607.23307 · arxiv_version: 2607.23307v1 · doi: 10.48550/arxiv.2607.23307 · pith_short_12: K5UMSPQDVYIN · pith_short_16: K5UMSPQDVYIN52EN · pith_short_8: K5UMSPQD

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/K5UMSPQDVYIN52ENMLVEG7HCXI \
  | 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: 5768c93e03ae10dee88d62ea437ce2ba0753a97578a08cf84543a4f1aaf00408

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27247e7ec02b423ceaed738d010e0083c33dbb595fd439b067b9cce9dc051e77",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-07-25T17:48:30Z",
    "title_canon_sha256": "b835fe204634c7ff992e785fd9ea53704e816b65d446f95449e1a4de72473ea3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23307",
    "kind": "arxiv",
    "version": 1
  }
}