Pith Number

pith:3EPY6QCE

pith:2025:3EPY6QCEGTCN4RWKMG267W6RYW

not attested not anchored not stored refs pending

Self-expanders of positive genus

Guanhua Shao, Jiahua Zou

arxiv:2507.19428 v2 · 2025-07-25 · 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{3EPY6QCEGTCN4RWKMG267W6RYW}

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

Calibration energy and mean curvature flow

Receipt and verification

First computed	2026-07-05T11:49:58.279403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d91f8f404434c4de46ca61b5efdbd1c595f84ae8d89e26f6da9d0f7fc0fb741c

Aliases

arxiv: 2507.19428 · arxiv_version: 2507.19428v2 · doi: 10.48550/arxiv.2507.19428 · pith_short_12: 3EPY6QCEGTCN · pith_short_16: 3EPY6QCEGTCN4RWK · pith_short_8: 3EPY6QCE

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/3EPY6QCEGTCN4RWKMG267W6RYW \
  | 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: d91f8f404434c4de46ca61b5efdbd1c595f84ae8d89e26f6da9d0f7fc0fb741c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6e0864729c1646ae82578de74839f5384c507f9f72228de85628a6145d9c0b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-25T16:53:40Z",
    "title_canon_sha256": "eb3af116934b0d91d9753fcc99f58f283671539f158ff526a5c14cb568b3850e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.19428",
    "kind": "arxiv",
    "version": 2
  }
}