Pith Number

pith:4GKXQ7AZ

pith:2025:4GKXQ7AZS5ZSU7AHMP5UPNJ7CP

not attested not anchored not stored refs pending

A generalized sphere theorem and its applications

Jing Mao

arxiv:2506.01251 v1 · 2025-06-02 · 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{4GKXQ7AZS5ZSU7AHMP5UPNJ7CP}

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	2026-07-05T11:14:10.390234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e195787c1997732a7c0763fb47b53f13e6aa8fb07cf386eeebe82ef95641c428

Aliases

arxiv: 2506.01251 · arxiv_version: 2506.01251v1 · doi: 10.48550/arxiv.2506.01251 · pith_short_12: 4GKXQ7AZS5ZS · pith_short_16: 4GKXQ7AZS5ZSU7AH · pith_short_8: 4GKXQ7AZ

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/4GKXQ7AZS5ZSU7AHMP5UPNJ7CP \
  | 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: e195787c1997732a7c0763fb47b53f13e6aa8fb07cf386eeebe82ef95641c428

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "278560171538b832dc1125e7a4ace883f7faff0512f3e36ab6c5628539e8b3d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-06-02T01:59:27Z",
    "title_canon_sha256": "2241f98d33f81e4eeb97ae135aa4cccc67bec0cdf59b1fd25681d7954faca6a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.01251",
    "kind": "arxiv",
    "version": 1
  }
}