Pith Number

pith:HCQGP4PU

pith:2026:HCQGP4PUN4HWTAYELPBTCYVHZZ

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A complete classification of modular compactifications of the universal Jacobian

Filippo Viviani, Marco Fava, Nicola Pagani

All modular compactifications of the universal Jacobian over the moduli space of curves are parametrized by V-functions on a stability domain of half-vine types.

arxiv:2603.05455 v3 · 2026-03-05 · math.AG · math.CO

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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

Our main result gives a combinatorial parametrization of compactified universal Jacobian stacks by V-functions on a stability domain D_{g,n} of half-vine types; under this correspondence, fine compactifications are exactly the general V-functions.

C2weakest assumption

The classification assumes that every modular compactification arises from a V-function on the given stability domain of half-vine types; if some compactifications exist outside this combinatorial setup, the parametrization would be incomplete.

C3one line summary

All modular compactifications of the universal Jacobian are parametrized by V-functions on a stability domain of half-vine types, with classical numerical polarization cases recovered as special instances.

Formal links

3 machine-checked theorem links

Cited by

1 paper in Pith

Universal compactified Jacobians: cohomological invariance and boundary combinatorics

Receipt and verification

First computed	2026-06-02T01:03:44.657056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38a067f1f46f0f6983045bc33162a7ce5f75c0146b322ff5bdaa2d2c7b5799bf

Aliases

arxiv: 2603.05455 · arxiv_version: 2603.05455v3 · doi: 10.48550/arxiv.2603.05455 · pith_short_12: HCQGP4PUN4HW · pith_short_16: HCQGP4PUN4HWTAYE · pith_short_8: HCQGP4PU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HCQGP4PUN4HWTAYELPBTCYVHZZ \
  | 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: 38a067f1f46f0f6983045bc33162a7ce5f75c0146b322ff5bdaa2d2c7b5799bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75f498518b500bab62b850cc8da37dfc3a0e1fcbe09c1215322a07fb705c8af5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-03-05T18:26:43Z",
    "title_canon_sha256": "4a95d436e4000f2649c49313230b77174779062eb8b7d18bc50883c542f0a509"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.05455",
    "kind": "arxiv",
    "version": 3
  }
}