Pith Number

pith:D4HG33Z3

pith:2022:D4HG33Z3IUK5VROTXDLWQWZQPK

not attested not anchored not stored refs pending

Min-max minimal hypersurfaces with higher multiplicity

Xin Zhou, Zhichao Wang

arxiv:2201.06154 v1 · 2022-01-16 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D4HG33Z3IUK5VROTXDLWQWZQPK}

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	2026-07-05T03:48:55.323904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f0e6def3b4515dac5d3b8d7685b307abb681d68d6e92e6051ddb8e68b4a23b2

Aliases

arxiv: 2201.06154 · arxiv_version: 2201.06154v1 · doi: 10.48550/arxiv.2201.06154 · pith_short_12: D4HG33Z3IUK5 · pith_short_16: D4HG33Z3IUK5VROT · pith_short_8: D4HG33Z3

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/D4HG33Z3IUK5VROTXDLWQWZQPK \
  | 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: 1f0e6def3b4515dac5d3b8d7685b307abb681d68d6e92e6051ddb8e68b4a23b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d71289cf27387aaa1e76e014b6dc7f5049d01a4249ac74a9dd77de01aba8ef0f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2022-01-16T23:30:35Z",
    "title_canon_sha256": "2a809533056c7116f41017df3dbc083cfe55ad69abd65c76d17517a0a741461c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.06154",
    "kind": "arxiv",
    "version": 1
  }
}