Pith Number

pith:XD2LY5QW

pith:2011:XD2LY5QWURT3YB4VD36XOLJGWS

not attested not anchored not stored refs pending

On Smooth Closed 3-manifolds with Finite Fundamental Groups

Ming Yang

arxiv:1103.2824 v2 · 2011-03-15 · 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{XD2LY5QWURT3YB4VD36XOLJGWS}

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	2026-05-18T03:47:08.931585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8f4bc7616a467bc07951efd772d26b4bd245673544562b73c26912365771af9

Aliases

arxiv: 1103.2824 · arxiv_version: 1103.2824v2 · doi: 10.48550/arxiv.1103.2824 · pith_short_12: XD2LY5QWURT3 · pith_short_16: XD2LY5QWURT3YB4V · pith_short_8: XD2LY5QW

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/XD2LY5QWURT3YB4VD36XOLJGWS \
  | 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: b8f4bc7616a467bc07951efd772d26b4bd245673544562b73c26912365771af9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ca47525fce6d4290627d6386eff734b4494ba816c9532a1af69ef33b5ac041c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-03-15T01:34:55Z",
    "title_canon_sha256": "3008e92bd80fe5e9820ebd8593f9d33cad9bb9a3fabf86751ba435ed5d9026a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2824",
    "kind": "arxiv",
    "version": 2
  }
}