Pith Number

pith:GDCP3ZIB

pith:2026:GDCP3ZIBADCBMVQY2HP4J3IMRG

not attested not anchored not stored refs pending

Generalized Howe curves of genus 4, 5, and 6 with completely decomposable Jacobians

Ryo Ohashi

Generalized Howe curves with Jacobians splitting into four elliptic curves are superspecial for genus 4 in every prime between 20001 and 999999.

arxiv:2604.18074 v3 · 2026-04-20 · math.AG · math.NT

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\usepackage{pith}
\pithnumber{GDCP3ZIBADCBMVQY2HP4J3IMRG}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 confirmed by computer the existence of such superspecial curves of genus 4 in characteristics p with 20000 < p < 10^6. Using a similar approach, we also propose constructions of superspecial curves of genera 5 and 6 from only supersingular elliptic curves.

C2weakest assumption

The superspeciality of the generalized Howe curve reduces exactly to the supersingularity of its four elliptic curve factors, and the computer enumeration correctly finds all such curves without implementation errors or missed cases.

C3one line summary

Generalized Howe curves with completely decomposable Jacobians yield superspecial genus-4 curves for all primes 20000 < p < 10^6, plus constructions and existence checks for genera 5 and 6 up to p=10^5.

Receipt and verification

First computed	2026-06-04T01:08:50.244682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30c4fde50100c4165618d1dfc4ed0c89bebe34f96f981985a047c314b0798772

Aliases

arxiv: 2604.18074 · arxiv_version: 2604.18074v3 · doi: 10.48550/arxiv.2604.18074 · pith_short_12: GDCP3ZIBADCB · pith_short_16: GDCP3ZIBADCBMVQY · pith_short_8: GDCP3ZIB

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/GDCP3ZIBADCBMVQY2HP4J3IMRG \
  | 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: 30c4fde50100c4165618d1dfc4ed0c89bebe34f96f981985a047c314b0798772

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6150de653512c7ba32a2eef9b61802d7cc9a04756c96fd808ea30fdb93c63909",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-20T10:42:50Z",
    "title_canon_sha256": "05bd51ee19c0711e0001d05dd9c3bcb63436bb2f29b971fd544c77dc0f0d5bd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18074",
    "kind": "arxiv",
    "version": 3
  }
}