Pith Number

pith:I4MSOI7V

pith:2021:I4MSOI7V6GROWE6UUJVEENFRQ2

not attested not anchored not stored refs pending

Torelli-type theorems for gravitational instantons with quadratic volume growth

Gao Chen, Jeff Viaclovsky, Ruobing Zhang

arxiv:2112.07504 v2 · 2021-12-14 · math.DG · math-ph · math.AG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I4MSOI7V6GROWE6UUJVEENFRQ2}

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	2026-07-05T04:48:39.774233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43

Aliases

arxiv: 2112.07504 · arxiv_version: 2112.07504v2 · doi: 10.48550/arxiv.2112.07504 · pith_short_12: I4MSOI7V6GRO · pith_short_16: I4MSOI7V6GROWE6U · pith_short_8: I4MSOI7V

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/I4MSOI7V6GROWE6UUJVEENFRQ2 \
  | 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: 47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c2bf2f96158c06c7c1683f93b8defe91386b14014d50e2ddbb1c76734b355ba",
    "cross_cats_sorted": [
      "math-ph",
      "math.AG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-12-14T16:08:29Z",
    "title_canon_sha256": "f992aa89e77b6db9c9e66601fdfc1566b33fc4c8ab947136e5fb58eeea369d9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.07504",
    "kind": "arxiv",
    "version": 2
  }
}