Pith Number

pith:LYEZED4X

pith:2011:LYEZED4X7M6QH7N7Y74VSYVWJP

not attested not anchored not stored refs pending

Closed Aspherical Manifolds with Center

Min Yan, Shmuel Weinberger, Sylvain Cappell

arxiv:1108.2321 v3 · 2011-08-11 · 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{LYEZED4X7M6QH7N7Y74VSYVWJP}

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	2026-05-18T02:58:00.644924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e09920f97fb3d03fdbfc7f95962b64bcef098349708791b30344cdfff8b776b

Aliases

arxiv: 1108.2321 · arxiv_version: 1108.2321v3 · doi: 10.48550/arxiv.1108.2321 · pith_short_12: LYEZED4X7M6Q · pith_short_16: LYEZED4X7M6QH7N7 · pith_short_8: LYEZED4X

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/LYEZED4X7M6QH7N7Y74VSYVWJP \
  | 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: 5e09920f97fb3d03fdbfc7f95962b64bcef098349708791b30344cdfff8b776b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51799a6298e96ea50c8c39c3e484a28568d059108ea52d0a1af294f9e19881e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-11T02:15:37Z",
    "title_canon_sha256": "2d1b015ce3b33c9b892c3743e8396abca4d6a9afc67b4e1cbe93bc24de8dcb59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2321",
    "kind": "arxiv",
    "version": 3
  }
}