Pith Number

pith:MDGUCUUC

pith:2022:MDGUCUUCGVCFAZHHRU235YY6E7

not attested not anchored not stored refs pending

Embedding surfaces in 4-manifolds

Arunima Ray, Daniel Kasprowski, Mark Powell, Peter Teichner

arxiv:2201.03961 v3 · 2022-01-11 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDGUCUUCGVCFAZHHRU235YY6E7}

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	2026-07-05T09:02:09.864175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60cd41528235445064e78d35bee31e27f5187600cf815484669b09633e61e310

Aliases

arxiv: 2201.03961 · arxiv_version: 2201.03961v3 · doi: 10.48550/arxiv.2201.03961 · pith_short_12: MDGUCUUCGVCF · pith_short_16: MDGUCUUCGVCFAZHH · pith_short_8: MDGUCUUC

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/MDGUCUUCGVCFAZHHRU235YY6E7 \
  | 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: 60cd41528235445064e78d35bee31e27f5187600cf815484669b09633e61e310

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb836321b299863ec61571040719aea97c7992125224feb8b5758373c7e599fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2022-01-11T14:18:04Z",
    "title_canon_sha256": "8d0f1c0eb879be0d17569cb3605ebe9788637d6b9465c5a822ac2f9316e38514"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.03961",
    "kind": "arxiv",
    "version": 3
  }
}