Pith Number

pith:QRFJ4OLO

pith:2026:QRFJ4OLO2M4S7SYQMWNQQQ2UBL

not attested not anchored not stored refs pending

Existence of classical minimal surfaces in $4$ and $5$-manifolds

Da Rong Cheng, Xin Zhou

arxiv:2606.24754 v1 · 2026-06-23 · 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{QRFJ4OLO2M4S7SYQMWNQQQ2UBL}

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	2026-06-24T01:15:41.215800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

844a9e396ed3392fcb10659b0843540afaeae80f5fdc58aadaa70740845b121d

Aliases

arxiv: 2606.24754 · arxiv_version: 2606.24754v1 · doi: 10.48550/arxiv.2606.24754 · pith_short_12: QRFJ4OLO2M4S · pith_short_16: QRFJ4OLO2M4S7SYQ · pith_short_8: QRFJ4OLO

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/QRFJ4OLO2M4S7SYQMWNQQQ2UBL \
  | 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: 844a9e396ed3392fcb10659b0843540afaeae80f5fdc58aadaa70740845b121d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "432be90d6709bada6142b84382a0994832bcb76fb30cb83301d69204502fcdae",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-23T16:15:38Z",
    "title_canon_sha256": "340a58ef0907b7c6b8a0f4327e4c04682dd6bf34a089f4fdcee31ed1f9824885"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24754",
    "kind": "arxiv",
    "version": 1
  }
}