Pith Number

pith:ZNNZGCIU

pith:2016:ZNNZGCIUBZWDAVOICCZ4QE4SUZ

not attested not anchored not stored refs pending

Isoperimetric characterization of upper curvature bounds

Alexander Lytchak, Stefan Wenger

arxiv:1611.05261 v1 · 2016-11-16 · math.DG · 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{ZNNZGCIUBZWDAVOICCZ4QE4SUZ}

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	2026-05-18T00:58:27.494570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb5b9309140e6c3055c810b3c81392a640c970308d9a4e9410683bdfe0d32673

Aliases

arxiv: 1611.05261 · arxiv_version: 1611.05261v1 · doi: 10.48550/arxiv.1611.05261 · pith_short_12: ZNNZGCIUBZWD · pith_short_16: ZNNZGCIUBZWDAVOI · pith_short_8: ZNNZGCIU

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/ZNNZGCIUBZWDAVOICCZ4QE4SUZ \
  | 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: cb5b9309140e6c3055c810b3c81392a640c970308d9a4e9410683bdfe0d32673

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2a2a9a3eb0946753a0c008b9fb32b778635382421342d672957ac2db72a880a",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-11-16T13:02:25Z",
    "title_canon_sha256": "29299d55ff56f49585da453c0963f8d06df65b31b7757c4a37bd31b3f62e1643"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05261",
    "kind": "arxiv",
    "version": 1
  }
}