Pith Number

pith:BNUGKJS6

pith:2012:BNUGKJS6MDX42G5KPBYETXZ6ZG

not attested not anchored not stored refs pending

New proofs of the Torelli theorems for Riemann surfaces

Kefeng Liu, Quanting Zhao, Sheng Rao

arxiv:1207.5697 v2 · 2012-07-24 · math.DG · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BNUGKJS6MDX42G5KPBYETXZ6ZG}

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	2026-05-18T03:27:01.586276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b6865265e60efcd1baa787049df3ec9bdf07a29da84b2b2dc78cd5561a9cc75

Aliases

arxiv: 1207.5697 · arxiv_version: 1207.5697v2 · doi: 10.48550/arxiv.1207.5697 · pith_short_12: BNUGKJS6MDX4 · pith_short_16: BNUGKJS6MDX42G5K · pith_short_8: BNUGKJS6

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/BNUGKJS6MDX42G5KPBYETXZ6ZG \
  | 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: 0b6865265e60efcd1baa787049df3ec9bdf07a29da84b2b2dc78cd5561a9cc75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "909c7fbd87976c764268a66eb760dd683214dc5d12c8a249a8ca08c14d732fa7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-07-24T13:39:20Z",
    "title_canon_sha256": "f29f20957838c22372046c85c3023d4bd7ccf5f548bc219592bc32f6a57ff35f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5697",
    "kind": "arxiv",
    "version": 2
  }
}