Pith Number

pith:I4K7KQIY

pith:2011:I4K7KQIYUFUJRFUNNQUTX5WRGX

not attested not anchored not stored refs pending

Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition

Emanuel Milman

arxiv:1108.4609 v3 · 2011-08-23 · math.DG · math.FA · 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{I4K7KQIYUFUJRFUNNQUTX5WRGX}

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	2026-05-18T03:46:49.308230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4715f54118a16898968d6c293bf6d135f97656d9ed75e2f3c474739279e5176a

Aliases

arxiv: 1108.4609 · arxiv_version: 1108.4609v3 · doi: 10.48550/arxiv.1108.4609 · pith_short_12: I4K7KQIYUFUJ · pith_short_16: I4K7KQIYUFUJRFUN · pith_short_8: I4K7KQIY

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/I4K7KQIYUFUJRFUNNQUTX5WRGX \
  | 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: 4715f54118a16898968d6c293bf6d135f97656d9ed75e2f3c474739279e5176a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b6382d2c088e1b2c0567f5498b626b32192883e4fb518cb45f05372483a3291",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-08-23T14:19:31Z",
    "title_canon_sha256": "1904999cbaebaa015ed6f22e8dd831df51aa1e6ca08bd44349e699a965db4e23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4609",
    "kind": "arxiv",
    "version": 3
  }
}