Pith Number

pith:BFRNJTTK

pith:2019:BFRNJTTKCYUHMQQB4AC2QW3SHE

not attested not anchored not stored refs pending

Morse index, Betti numbers and singular set of bounded area minimal hypersurfaces

Antoine Song

arxiv:1911.09166 v3 · 2019-11-20 · 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{BFRNJTTKCYUHMQQB4AC2QW3SHE}

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.

Cited by

1 paper in Pith

On the Parallels Between Minimal Surfaces and Einstein Four-Manifolds

Receipt and verification

First computed	2026-07-05T04:50:29.984970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0962d4ce6a1628764201e005a85b72393883d42699f5eba30cee3a429b2d01cf

Aliases

arxiv: 1911.09166 · arxiv_version: 1911.09166v3 · doi: 10.48550/arxiv.1911.09166 · pith_short_12: BFRNJTTKCYUH · pith_short_16: BFRNJTTKCYUHMQQB · pith_short_8: BFRNJTTK

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/BFRNJTTKCYUHMQQB4AC2QW3SHE \
  | 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: 0962d4ce6a1628764201e005a85b72393883d42699f5eba30cee3a429b2d01cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4a19766212298f78fe30c5ef728a2a66e5f10ec512cda028c0280a9e3d2e92d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-11-20T20:50:49Z",
    "title_canon_sha256": "00d20ace63aff4a79b8c8b659a0d9c424db1f22e0489ae4d94b475d3965d8757"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.09166",
    "kind": "arxiv",
    "version": 3
  }
}