Pith Number

pith:JQIVIYET

pith:2026:JQIVIYET5XEKH7SSXEMKG4UWHC

not attested not anchored not stored refs pending

Rational curves on cubic hypersurfaces in positive characteristic

Natsume Kitagawa

The Kontsevich moduli space of stable maps to a smooth cubic hypersurface is irreducible for dimension at least 4.

arxiv:2604.26556 v2 · 2026-04-29 · math.AG

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\usepackage{pith}
\pithnumber{JQIVIYET5XEKH7SSXEMKG4UWHC}

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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 prove that for every integer d≥1 the Kontsevich moduli space of stable maps on a smooth cubic hypersurface X of degree d is irreducible if the dimension of X is greater than or equal to 4.

C2weakest assumption

The hypersurface is smooth and the characteristic is not 2 or 3; the proof likely relies on these to avoid singularities and characteristic-dependent degenerations in the moduli space construction.

C3one line summary

The Kontsevich moduli space of stable maps to a smooth cubic hypersurface of dimension at least 4 is irreducible for any degree d in characteristic not 2 or 3.

Receipt and verification

First computed	2026-06-09T01:05:18.312400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c11546093edc8a3fe52b918a37296388583b8b2f63c3ee9df0d19c60b5522eb

Aliases

arxiv: 2604.26556 · arxiv_version: 2604.26556v2 · doi: 10.48550/arxiv.2604.26556 · pith_short_12: JQIVIYET5XEK · pith_short_16: JQIVIYET5XEKH7SS · pith_short_8: JQIVIYET

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/JQIVIYET5XEKH7SSXEMKG4UWHC \
  | 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: 4c11546093edc8a3fe52b918a37296388583b8b2f63c3ee9df0d19c60b5522eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdeecbf15415d9d13c83a032685da5f89aeeed7b41277481594884b3a36489cd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-29T11:43:47Z",
    "title_canon_sha256": "a759ebd458b70349a251b4d0761d9101ef85476baf26539e267fac8eb05caa78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26556",
    "kind": "arxiv",
    "version": 2
  }
}