Pith Number

pith:ZKQL2U7I

pith:2009:ZKQL2U7ITCOKZETUGA4V3HDCLZ

not attested not anchored not stored refs pending

Homotopy groups of the moduli space of metrics of positive scalar curvature

Bernhard Hanke (TU M\"unchen), Boris Botvinnik (University of Oregon), Mark Walsh (University of Oregon), Thomas Schick (Georg-August Universit\"at G\"ottingen)

arxiv:0907.5188 v3 · 2009-07-29 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKQL2U7ITCOKZETUGA4V3HDCLZ}

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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	2026-05-18T02:38:18.785160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa0bd53e8989cac927430395d9c625e62e88f33d00d3b82aed9324e2dffb2f3

Aliases

arxiv: 0907.5188 · arxiv_version: 0907.5188v3 · doi: 10.48550/arxiv.0907.5188 · pith_short_12: ZKQL2U7ITCOK · pith_short_16: ZKQL2U7ITCOKZETU · pith_short_8: ZKQL2U7I

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/ZKQL2U7ITCOKZETUGA4V3HDCLZ \
  | 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: caa0bd53e8989cac927430395d9c625e62e88f33d00d3b82aed9324e2dffb2f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48566708c5da6fa170783d8d6e1e7ebe294cbb7dafd969dd95f34aa310b8e6e2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-07-29T18:56:30Z",
    "title_canon_sha256": "20c0ecc0fcc377e4527835b5da8ea0bc5421d34e51cc2f9b970fd97438d5cba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5188",
    "kind": "arxiv",
    "version": 3
  }
}