Pith Number

pith:2GRGGO4Z

pith:2012:2GRGGO4ZK3KRBCIAXQ3SCC55CY

not attested not anchored not stored refs pending

Multiply twisted products

Yong Wang

arxiv:1207.0199 v1 · 2012-07-01 · 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{2GRGGO4ZK3KRBCIAXQ3SCC55CY}

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	2026-05-18T02:46:31.578222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1a2633b9956d5108900bc37210bbd1630c1323c1ee86d3b27af5ccafc87d3fb

Aliases

arxiv: 1207.0199 · arxiv_version: 1207.0199v1 · doi: 10.48550/arxiv.1207.0199 · pith_short_12: 2GRGGO4ZK3KR · pith_short_16: 2GRGGO4ZK3KRBCIA · pith_short_8: 2GRGGO4Z

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/2GRGGO4ZK3KRBCIAXQ3SCC55CY \
  | 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: d1a2633b9956d5108900bc37210bbd1630c1323c1ee86d3b27af5ccafc87d3fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1acecbb56ef048e0a7c68cc7d7a2e3269b028228daacaa82ac29df33cbc3457e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-07-01T11:45:08Z",
    "title_canon_sha256": "a0e99f4c5fd72130b277bf56267cfd533d14681e9fa5fdd27c15b74af9455fb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0199",
    "kind": "arxiv",
    "version": 1
  }
}