Pith Number

pith:7NP5T5QR

pith:2026:7NP5T5QRD5LPDO24PIMFMSHOME

not attested not anchored not stored refs pending

The unirationality of $S_9^-$ and moduli spaces of pointed spin curves

Alessandro Verra, Gavril Farkas

The moduli space of odd spin curves of genus 9 is unirational.

arxiv:2604.18719 v2 · 2026-04-20 · math.AG

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\usepackage{pith}
\pithnumber{7NP5T5QRD5LPDO24PIMFMSHOME}

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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.

Claims

C1strongest claim

We show that the moduli space of odd spin curves of genus 9 is unirational. This is the highest genus for which such a result is known.

C2weakest assumption

The birational realization of the moduli space of odd spin curves of genus g<10 as a locally trivial projective bundle over a finite quotient of the moduli space of n-pointed odd stable spin curves of genus g'<g is valid.

C3one line summary

The moduli space of odd spin curves of genus 9 is unirational.

Receipt and verification

First computed	2026-05-20T00:04:32.136529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb5fd9f6111f56f1bb5c7a185648ee613e83a42c2a34f028338b412be100e517

Aliases

arxiv: 2604.18719 · arxiv_version: 2604.18719v2 · doi: 10.48550/arxiv.2604.18719 · pith_short_12: 7NP5T5QRD5LP · pith_short_16: 7NP5T5QRD5LPDO24 · pith_short_8: 7NP5T5QR

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/7NP5T5QRD5LPDO24PIMFMSHOME \
  | 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: fb5fd9f6111f56f1bb5c7a185648ee613e83a42c2a34f028338b412be100e517

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12da4d24919f4041b04c10ed9ea7eb2dda6277c82f7c5178d40bef9715453ca8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-20T18:18:43Z",
    "title_canon_sha256": "01a5a76955fddcbd05107d81a1f7637ff3b6189f200921c45d1fc3a1a79bc4b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18719",
    "kind": "arxiv",
    "version": 2
  }
}