Pith Number

pith:QZ6ULMGZ

pith:2001:QZ6ULMGZXL4ICW4Y7XKFXKZUVC

not attested not anchored not stored refs pending

The Yamabe invariant for non-simply connected manifolds

Boris Botvinnik, Jonathan Rosenberg

arxiv:math/0104186 v1 · 2001-04-18 · math.DG · math.AT · math.GT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QZ6ULMGZXL4ICW4Y7XKFXKZUVC}

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	2026-05-18T04:27:03.940038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

867d45b0d9baf8815b98fdd45bab34a8ac77198a94ce9a2ad1c8667172e7fad8

Aliases

arxiv: math/0104186 · arxiv_version: math/0104186v1 · doi: 10.48550/arxiv.math/0104186 · pith_short_12: QZ6ULMGZXL4I · pith_short_16: QZ6ULMGZXL4ICW4Y · pith_short_8: QZ6ULMGZ

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/QZ6ULMGZXL4ICW4Y7XKFXKZUVC \
  | 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: 867d45b0d9baf8815b98fdd45bab34a8ac77198a94ce9a2ad1c8667172e7fad8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f2e85af7614fd4b5e574d7e51a9239c5e791ea8ea57da62985a362b1cf35cf4",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT",
      "math.KT"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2001-04-18T21:26:43Z",
    "title_canon_sha256": "8d64e008dc7b4e516be2f0259cf5c7639488dedaf2288a6215341c3a23b479ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0104186",
    "kind": "arxiv",
    "version": 1
  }
}