Pith Number

pith:64UJV7X6

pith:2021:64UJV7X6YIZDE43WBAJSY5VK2B

not attested not anchored not stored refs pending

CMC hypersurfaces with bounded Morse index

Ben Sharp, Giuseppe Tinaglia, Theodora Bourni

arxiv:2102.02651 v3 · 2021-02-04 · 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{64UJV7X6YIZDE43WBAJSY5VK2B}

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	2026-07-05T02:14:01.181745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7289afefec23232737608132c76aad06f17466da5feba3b72cbebb44b8ca625

Aliases

arxiv: 2102.02651 · arxiv_version: 2102.02651v3 · doi: 10.48550/arxiv.2102.02651 · pith_short_12: 64UJV7X6YIZD · pith_short_16: 64UJV7X6YIZDE43W · pith_short_8: 64UJV7X6

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/64UJV7X6YIZDE43WBAJSY5VK2B \
  | 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: f7289afefec23232737608132c76aad06f17466da5feba3b72cbebb44b8ca625

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "997a1158a5a6e146bfca0acc21ed0199ec6fbac0850849f34cfdd7c3dd5a5585",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-02-04T14:45:16Z",
    "title_canon_sha256": "f989636f5c2ab5a01cd14dd2d5374d5d8b18cff8b88853eb3ed71fe2b43baa0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.02651",
    "kind": "arxiv",
    "version": 3
  }
}