Pith Number

pith:GXJ7BGPM

pith:2017:GXJ7BGPMV7DZF4R4DBBMRMRNHL

not attested not anchored not stored refs pending

A compactness theorem for four-dimensional shrinking gradient Ricci solitons

Yongjia Zhang

arxiv:1706.03163 v2 · 2017-06-10 · 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{GXJ7BGPMV7DZF4R4DBBMRMRNHL}

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	2026-05-18T00:40:01.200468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35d3f099ecafc792f23c1842c8b22d3adf8c0e367baae2cd9f1662c9eba1f653

Aliases

arxiv: 1706.03163 · arxiv_version: 1706.03163v2 · doi: 10.48550/arxiv.1706.03163 · pith_short_12: GXJ7BGPMV7DZ · pith_short_16: GXJ7BGPMV7DZF4R4 · pith_short_8: GXJ7BGPM

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/GXJ7BGPMV7DZF4R4DBBMRMRNHL \
  | 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: 35d3f099ecafc792f23c1842c8b22d3adf8c0e367baae2cd9f1662c9eba1f653

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45a31ea9aa46853ee61c8c4e0519a6b5990ed25d066de43d58be72ed13a2e4c0",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-06-10T01:23:13Z",
    "title_canon_sha256": "a620c63af9410e1972e8b694f3ebe64652706d524dbd5ebddcb5734df1260146"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.03163",
    "kind": "arxiv",
    "version": 2
  }
}