Pith Number

pith:ZSH3TF2S

pith:2016:ZSH3TF2SAQB5FE5FHZYZ75X6BJ

not attested not anchored not stored refs pending

A gap theorem of four-dimensional gradient shrinking solitons

Zhuhong Zhang

arxiv:1606.01154 v2 · 2016-06-03 · 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{ZSH3TF2SAQB5FE5FHZYZ75X6BJ}

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	2026-05-18T01:07:50.663881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc8fb997520403d293a53e719ff6fe0a62d49cb8252d1a5e4337eb2ba858c6a9

Aliases

arxiv: 1606.01154 · arxiv_version: 1606.01154v2 · doi: 10.48550/arxiv.1606.01154 · pith_short_12: ZSH3TF2SAQB5 · pith_short_16: ZSH3TF2SAQB5FE5F · pith_short_8: ZSH3TF2S

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/ZSH3TF2SAQB5FE5FHZYZ75X6BJ \
  | 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: cc8fb997520403d293a53e719ff6fe0a62d49cb8252d1a5e4337eb2ba858c6a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58af58e95611760df172c3c4858a9f2dddeb5f0f29181dfdb5a49a7b09668c58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-06-03T15:48:05Z",
    "title_canon_sha256": "62f86a7f3616ccfd9aff0c0a0c0cd02e4be3c136aff87d79928cd8d1a0e9f848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01154",
    "kind": "arxiv",
    "version": 2
  }
}