Pith Number

pith:BD3MW4YV

pith:2022:BD3MW4YVYBFP3HZJUN3XHNGPT7

not attested not anchored not stored refs pending

$4$-manifolds with boundary and fundamental group $\mathbb{Z}$

Anthony Conway, Lisa Piccirillo, Mark Powell

arxiv:2205.12774 v2 · 2022-05-25 · 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{BD3MW4YVYBFP3HZJUN3XHNGPT7}

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	2026-07-05T08:56:54.570561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08f6cb7315c04afd9f29a37773b4cf9ff836ba904d43c9a920370177f0f8ada0

Aliases

arxiv: 2205.12774 · arxiv_version: 2205.12774v2 · doi: 10.48550/arxiv.2205.12774 · pith_short_12: BD3MW4YVYBFP · pith_short_16: BD3MW4YVYBFP3HZJ · pith_short_8: BD3MW4YV

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/BD3MW4YVYBFP3HZJUN3XHNGPT7 \
  | 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: 08f6cb7315c04afd9f29a37773b4cf9ff836ba904d43c9a920370177f0f8ada0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e85e64c1e43a578f568621dd64ca457b588bc3b63e0d6dbf2105582c022cd9b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2022-05-25T13:42:04Z",
    "title_canon_sha256": "97a4fe39b8da1d1b06c058a01dc9b7328f048294339071ab1da2f1632a9397b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.12774",
    "kind": "arxiv",
    "version": 2
  }
}