Pith Number

pith:DSU4PZ3J

pith:2026:DSU4PZ3JP3CNE4KXPWQUVWQVZD

not attested not anchored not stored refs pending

On free boundary minimal submanifolds with boundary on concentric spheres in Euclidean spac

Tianyu Ma, Vladimir Medvedev

arxiv:2606.23930 v1 · 2026-06-22 · 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{DSU4PZ3JP3CNE4KXPWQUVWQVZD}

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	2026-06-24T00:14:30.506338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ca9c7e7697ec4d271577da14ada15c8d27b13a6af91a444ab4f2d296efac78d

Aliases

arxiv: 2606.23930 · arxiv_version: 2606.23930v1 · doi: 10.48550/arxiv.2606.23930 · pith_short_12: DSU4PZ3JP3CN · pith_short_16: DSU4PZ3JP3CNE4KX · pith_short_8: DSU4PZ3J

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/DSU4PZ3JP3CNE4KXPWQUVWQVZD \
  | 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: 1ca9c7e7697ec4d271577da14ada15c8d27b13a6af91a444ab4f2d296efac78d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "668c7d6d43ab4b517ea7211a1c1c377e3189bbe3e25a7b55646b80dce14cb42d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-22T20:50:10Z",
    "title_canon_sha256": "3f51cdcd17fb16f0f39d0aa0327573cc265a7b2391f6dd47069d8c00fcd4ce35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23930",
    "kind": "arxiv",
    "version": 1
  }
}