license: gpl-3.0
task_categories:
- other
pretty_name: CICY — Complete-intersection Calabi–Yau threefold database
tags:
- physics
- string-theory
- flux-compactifications
- calabi-yau
- complete-intersection
- mathematics
size_categories:
- 1K<n<10K
configs:
- config_name: cicy
data_files:
- split: catalog
path: cicy/catalog.parquet
CICY — Complete-intersection Calabi–Yau threefold database
Complete-intersection Calabi–Yau (CICY) threefolds, precomputed for use with stringforge and jaxvacua.
This is one sub-dataset of the larger cy-database repository. For shared conventions (lazy access, cache modes, offline mode, schema versioning, mirror convention) see the umbrella card.
Scope
CICY covers the 7,890 complete-intersection Calabi–Yau threefolds first classified by Candelas et al., realised as the vanishing locus of a set of homogeneous polynomials inside a product of complex projective spaces. Each model is uniquely identified by
cicy_id— the integer index in the CICY list, with $1 \le \text{cicy_id} \le 7,890$.
For each model the dataset provides (when computed):
- Topological data: triple intersection numbers $\kappa_{ijk}$ (stored in coordinate / "COO" form), second Chern class $c_2$, $a$-matrix, Hodge numbers $h^{1,1}$ and $h^{2,1}$, Euler characteristic $\chi$, Kähler-cone generators and rays, Mori-cone rays, hyperplane constraints, and an integer basis change to a tractable working basis.
- Gopakumar–Vafa invariants $n_q^0$ in sparse form (
gv_charges,gv_invariants) together with the grading vector used during the computation. - Extra data: per-model auxiliary fields stored as a dictionary column (
extra_data).
The current catalogue contains 7,406 models with Hodge ranges $h^{1,1} \in {0,, \dots,, 101}$ and $h^{2,1} \in {0,, \dots,, 19}$ in catalogue convention (equivalently, $h^{1,1} \in {0,, \dots,, 19}$ and $h^{2,1} \in {0,, \dots,, 101}$ in mirror convention). Of these, 4,511 models carry precomputed GV invariants.
Quick start
pip install stringforge
Pure I/O (no JAXVacua)
from stringforge import CICYDatabase
db = CICYDatabase() # downloads catalogue only
df = db.query(h11=3) # catalogue-level filter
print(df.head())
Model loading in mirror convention (recommended for JAXVacua)
from stringforge import LCSDatabase
lcs = LCSDatabase(dataset="cicy") # mirror-convention wrapper
df = lcs.query(h12=3, has_gv=True) # h12 in mirror convention
tree = lcs.load(
cicy_id = int(df.iloc[0]["cicy_id"]),
include_gv = True,
)
# Or construct a fully initialised FluxVacuaFinder
finder = lcs.load_model(
cicy_id = int(df.iloc[0]["cicy_id"]),
include_gv = True,
maximum_degree = 2,
)
Streaming batches without local-disk accumulation
from stringforge import LCSDatabase
lcs_lean = LCSDatabase(dataset="cicy", cache_mode="none")
for tree in lcs_lean.iter_batch(h12=3, include_gv=True):
...
Sub-dataset layout
cicy/
README.md ← this file
catalog.parquet ← main index, one row per cicy_id
schema.json ← schema version + description
manifest.json ← incremental-build manifest
lcs_data/h11_{N}/ ← geometry data, sharded by h^{1,1}
data-00000.parquet
...
gv/ ← Gopakumar–Vafa invariants (flat split)
data-00000.parquet
...
Unlike the TDF sub-dataset, CICY does not carry per-conifold or polytope splits: the construction is a complete intersection in an ambient projective product, so reflexive-polytope data and shrinking-curve / conifold metadata are not part of the standard model identity.
Why $h^{1,1}$-bucketed?
The lcs_data split is bucketed by $h^{1,1}$ because the per-row sizes (intersection-number tensors $O(h^3)$, $a$-matrices $O(h^2)$, GV charge vectors $O(h)$) scale strongly with the rank. Bucketing keeps fixed-width Parquet columns at the size appropriate for each rank, and lets db.load_batch(h11=k) pull only the h11_k/ directory.
The gv split is flat (not $h^{1,1}$-bucketed) because GV invariants are stored in sparse coordinate form, so each row's size is determined by the number of effective curves rather than by $h$.
Catalogue schema
The main catalog.parquet is the entry point. One row per cicy_id, with shard pointers into the data splits.
| Column | Type | Description |
|---|---|---|
cicy_id |
int64 |
CICY list index, $1 \le \text{cicy_id} \le 7,890$ |
h11 |
int64 |
Hodge number $h^{1,1}(X)$ (catalogue convention) |
h12 |
int64 |
Hodge number $h^{2,1}(X)$ (catalogue convention) |
chi |
int64 |
Euler characteristic $\chi(X) = 2,(h^{1,1} - h^{2,1})$ |
lcs_shard_id |
Int64 (nullable) |
Shard index in lcs_data/h11_{h11}/ |
lcs_row_index |
Int64 (nullable) |
Row within that shard |
gv_shard_id |
Int64 (nullable) |
Shard index in gv/ — null if GV data unavailable |
gv_row_index |
Int64 (nullable) |
Row within that shard |
has_gv |
bool |
Whether GV data is present |
Mirror convention. The catalogue exposes Hodge numbers in catalogue convention. Use
stringforge.LCSDatabase(dataset="cicy")for the mirror convention used byjaxvacua.lcs.lcs_tree; it swaps the two columns at the boundary.
Data splits
lcs_data/h11_{N}/
One row per model. Contains the topological data needed to build the Kähler cone and the LCS prepotential.
| Column | Description |
|---|---|
cicy_id, h11, h12, chi |
Identity |
intnums_coo_i, intnums_coo_j, intnums_coo_k, intnums_coo_v |
Triple intersection numbers $\kappa_{ijk}$ in coordinate (COO) sparse form |
c2 |
Second Chern class $c_{2,i}$ |
a_matrix |
Symmetrised second-derivative matrix $a_{ij}$ entering the LCS prepotential |
hyperplanes |
Hyperplane constraints defining the Kähler cone |
kahler_generators |
Kähler-cone generators in the working basis |
kahler_rays |
Rays of the Kähler cone |
mori_rays |
Rays of the Mori cone |
basis_change |
Integer change-of-basis matrix to the working basis |
extra_data |
Per-model auxiliary fields, stored as a dictionary column |
gv/
Gopakumar–Vafa invariants in sparse form, one row per model that has GV data.
| Column | Description |
|---|---|
cicy_id, h11, h12 |
Identity |
gv_charges |
Array of effective-curve charge vectors $q \in \mathbb{Z}^{h^{1,1}}$ |
gv_invariants |
Array of integer GV invariants $n_q^0$, aligned with gv_charges |
grading_vector |
Grading vector used during the computation |
Loading without stringforge
Plain Parquet access with pandas + huggingface_hub:
import pandas as pd
from huggingface_hub import hf_hub_download
# Download only the catalogue
catalog_path = hf_hub_download(
repo_id = "aschachner/cy-database",
filename = "cicy/catalog.parquet",
repo_type = "dataset",
)
catalog = pd.read_parquet(catalog_path)
# Resolve one model's geometry shard
row = catalog.query("cicy_id == 7884").iloc[0]
lcs_path = hf_hub_download(
repo_id = "aschachner/cy-database",
filename = f"cicy/lcs_data/h11_{int(row['h11'])}/data-{int(row['lcs_shard_id']):05d}.parquet",
repo_type = "dataset",
)
lcs = pd.read_parquet(lcs_path)
model_row = lcs.iloc[int(row["lcs_row_index"])]
stringforge.CICYDatabase (pure I/O) and stringforge.LCSDatabase(dataset="cicy") (JAXVacua-compatible model loading) wrap this pattern with a consistent API, caching, mirror-convention handling, and filtering.
Scope and limitations specific to CICY
- Models are stored in the working basis defined by
basis_change; downstream code that needs the original CICY-list basis should apply the inverse rotation. - GV invariants are precomputed only for a subset of models — use
has_gv=Truein queries to filter. - CICY threefolds in the standard list do not carry conifold or polytope metadata: this dataset has no
conifold_catalog.parquet, noconifolds/split, and nopolytope/split. Conifold-aware workflows should use the TDF sub-dataset. - The catalogue currently lists 7,406 models out of the canonical 7,890; missing entries reflect ongoing computation of the topological data and will be back-filled in incremental rebuilds.
Building / updating
Produced by build_cicy_database.ipynb under stringforge/private/database/ from a local collection of per-model computations. Builds are incremental: models already in the manifest (by content hash) are skipped; only new or changed models are appended to the existing shards.
References
- P. Candelas, A. M. Dale, C. A. Lütken, R. Schimmrigk, Complete Intersection Calabi–Yau Manifolds, Nucl. Phys. B 298 (1988) 493.
For citation, licence, and contact details, see the umbrella cy-database card.