Pith Number

pith:2BVCUL4G

pith:2017:2BVCUL4G6TXNHGMAHQJ4G4Q5P7

not attested not anchored not stored refs pending

A sphere theorem for Bach-flat manifolds with positive constant scalar curvature

Wei Yuan, Yi Fang

arxiv:1704.06633 v1 · 2017-04-21 · 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{2BVCUL4G6TXNHGMAHQJ4G4Q5P7}

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	2026-05-18T00:45:59.210500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d06a2a2f86f4eed399803c13c3721d7fea43b28dd1185910fe9668e4ffcf97e8

Aliases

arxiv: 1704.06633 · arxiv_version: 1704.06633v1 · doi: 10.48550/arxiv.1704.06633 · pith_short_12: 2BVCUL4G6TXN · pith_short_16: 2BVCUL4G6TXNHGMA · pith_short_8: 2BVCUL4G

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/2BVCUL4G6TXNHGMAHQJ4G4Q5P7 \
  | 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: d06a2a2f86f4eed399803c13c3721d7fea43b28dd1185910fe9668e4ffcf97e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9f4c36d297cfbd3e8d2053288decaf5df00b5d2d04c71064966be832224a697",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-04-21T16:54:27Z",
    "title_canon_sha256": "bb0ce3c005a3a0f023915e5474fdd80a8cc2bc79c5f6f09ee2625d074eddeb6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.06633",
    "kind": "arxiv",
    "version": 1
  }
}