Pith Number

pith:IJILZJWM

pith:2026:IJILZJWM2XSZLBFPG3R57EIJKW

not attested not anchored not stored refs pending

The stacky Batyrev-Manin conjecture and modular curves

Changho Han, Ratko Darda

The stacky Batyrev-Manin conjecture holds for the naive height on the modular stacks X_0(N) over the rationals for N where the coarse space is the projective line.

arxiv:2602.19771 v3 · 2026-02-23 · math.NT · math.AG

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\pithnumber{IJILZJWM2XSZLBFPG3R57EIJKW}

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Record completeness

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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 show that the stacky Batyrev--Manin conjecture [DY24] holds for the naive height on X_0(N) when F=Q.

C2weakest assumption

The listed values of N are precisely those for which the coarse moduli space of X_0(N) is isomorphic to P^1, and that the height in question is the naive height on the stack.

C3one line summary

The stacky Batyrev-Manin conjecture holds for naive heights on the modular stacks X_0(N) for N in {1,2,3,4,5,6,7,8,9,10,12,13,16,18,25} over Q.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:15.987697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4250bca6ccd5e59584af36e3df910955a02689ff972a9e733391a8f0be747975

Aliases

arxiv: 2602.19771 · arxiv_version: 2602.19771v3 · doi: 10.48550/arxiv.2602.19771 · pith_short_12: IJILZJWM2XSZ · pith_short_16: IJILZJWM2XSZLBFP · pith_short_8: IJILZJWM

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IJILZJWM2XSZLBFPG3R57EIJKW \
  | 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: 4250bca6ccd5e59584af36e3df910955a02689ff972a9e733391a8f0be747975

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dbb9c9f007f2b4b7e4d67a1d0d4fb3a6bf012e0655b7797006cf6c5bfcb29ea",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-02-23T12:23:39Z",
    "title_canon_sha256": "60847f3e7036029554f833555aace945ab5d293f3d7e01829db0e40e9f7061ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.19771",
    "kind": "arxiv",
    "version": 3
  }
}