license: gpl-3.0
task_categories:
- other
pretty_name: TDF — Trilayer, Double Favourable Calabi–Yau database
tags:
- physics
- string-theory
- flux-compactifications
- calabi-yau
- mathematics
- toric-geometry
- kreuzer-skarke
size_categories:
- 1M<n<10M
configs:
- config_name: tdf
data_files:
- split: catalog
path: tdf/catalog.parquet
- split: conifold_catalog
path: tdf/conifold_catalog.parquet
TDF — Trilayer, Double Favourable Calabi–Yau database
Toric Calabi–Yau threefold hypersurfaces from the Kreuzer–Skarke list, 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
TDF covers Calabi–Yau threefolds $X$ realised as trilayer, double favourable anti-canonical hypersurfaces in toric varieties from the Kreuzer–Skarke list [arXiv:hep-th/0002240]. Each model is uniquely identified by
ks_id— the Kreuzer–Skarke 4D reflexive-polytope identifier;triang_id— the triangulation identifier within that polytope (different triangulations generally give rise to different Calabi–Yau geometries).
For each model the dataset provides (when computed):
- Topological data: triple intersection numbers $\kappa_{ijk}$, second Chern class $c_2$, Euler characteristic $\chi$, Hodge numbers $h^{1,1}$ and $h^{2,1}$, Kähler-cone generators and hyperplanes.
- Gopakumar–Vafa invariants $n_q^0$ (and Gromov–Witten data where available).
- Conifold data: conifold curves, GV invariants of shrinking cycles, integer basis-change matrices.
- Polytope data: lattice points of the reflexive polytope.
- Extra properties: the D3 tadpole $\chi/24$ and miscellaneous precomputed fields.
Hodge ranges span $h^{1,1},, h^{2,1} \in {1,, \dots,, \sim 500}$.
Quick start
pip install stringforge
Pure I/O (no JAXVacua)
from stringforge import TDFDatabase
db = TDFDatabase() # downloads catalogue only (~10 MB)
df = db.query(h11=2, has_conifolds=True) # catalogue-level filter, no shard I/O
# Inspect a single polytope's lattice points without loading the geometry
poly = db.get_polytope(ks_id=int(df.iloc[0]["ks_id"]), h11=2)
Model loading in mirror convention (recommended for JAXVacua)
from stringforge import LCSDatabase
lcs = LCSDatabase(dataset="tdf") # mirror-convention wrapper
df = lcs.query(h12=2, has_conifolds=True) # h12 in mirror convention
tree = lcs.load(
ks_id = int(df.iloc[0]["ks_id"]),
triang_id= int(df.iloc[0]["triang_id"]),
h11 = int(df.iloc[0]["h11"]), # mirror h11
h12 = int(df.iloc[0]["h12"]), # mirror h12
include_gv = True,
include_conifolds = True,
)
# Or construct a fully initialised FluxVacuaFinder directly
finder = lcs.load_model(
ks_id = int(df.iloc[0]["ks_id"]),
triang_id= int(df.iloc[0]["triang_id"]),
include_gv = True,
include_conifolds = True,
maximum_degree = 2,
)
Streaming batches without local-disk accumulation
from stringforge import LCSDatabase
lcs_lean = LCSDatabase(dataset="tdf", cache_mode="none")
for tree in lcs_lean.iter_batch(h11=2, include_gv=True):
...
A full walkthrough — including offline mode, batched loading, and vacua persistence — is in the stringforge documentation.
Sub-dataset layout
tdf/
README.md ← this file
catalog.parquet ← main index, ~10 MB
conifold_catalog.parquet ← per-conifold sub-catalogue
schema.json ← schema version + description
manifest.json ← incremental-build manifest
lcs_data/h11_{N}/ ← geometry data, sharded by h^{1,1}
data-00000.parquet
data-00001.parquet
...
gv/h11_{N}/ ← Gopakumar–Vafa invariants, sharded by h^{1,1}
data-00000.parquet
...
conifolds/h11_{N}/ ← conifold-limit data, sharded by h^{1,1}
data-00000.parquet
...
polytope/ ← reflexive polytope data (one row per ks_id)
data-00000.parquet
...
extra/ ← miscellaneous precomputed fields
data-00000.parquet
...
Why $h^{1,1}$-bucketed?
The row size for lcs_data, gv, and conifolds scales strongly with $h^{1,1}$: intersection-number tensors are $O(h^3)$, GV charge vectors have length $h$, conifold curves are $h$-vectors. Placing small- and large-$h^{1,1}$ rows in the same Parquet file would force fixed-width columns sized for the largest entry, wasting space and I/O.
Bucketing by $h^{1,1}$ also means a query like db.load_batch(h11=3) pulls only the h11_3 sub-directories — small-$h^{1,1}$ users never need to download large-$h^{1,1}$ shards.
The polytope and extra splits are flat (not $h^{1,1}$-bucketed) because their rows are small and uniform.
Shard sizing
Shard sizes are adaptive per (split, $h^{1,1}$) bucket, targeting ≈ 30 shards per bucket, clamped to $[500,; 50,000]$ rows. Without this, conifolds/h11_{10}/ with millions of rows would explode into thousands of tiny files.
Catalogue schema
The main catalog.parquet is the entry point. One row per $(\text{ks_id},, \text{triang_id})$ pair, with shard pointers into the data splits.
| Column | Type | Description |
|---|---|---|
ks_id |
int64 |
Kreuzer–Skarke polytope identifier |
triang_id |
int64 |
Triangulation identifier within the polytope |
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 |
Shard index in lcs_data/h11_{h11}/ |
lcs_row_index |
int64 |
Row within that shard |
gv_shard_id |
Int64 (nullable) |
Shard index in gv/h11_{h11}/ — null if GV data unavailable |
gv_row_index |
Int64 (nullable) |
Row within that shard |
has_gv |
bool |
Whether GV data is present |
n_conifolds |
int64 |
Number of conifold limits available |
conifold_shard_id |
Int64 (nullable) |
First shard index in conifolds/h11_{h11}/ — null if n_conifolds == 0 |
polytope_shard_id |
int64 |
Shard index in polytope/ (shared across triangulations of the same ks_id) |
polytope_row_index |
int64 |
Row within that shard |
D3_tadpole |
int64 |
$\chi/24$ |
A smaller conifold_catalog.parquet lists one row per $(\text{ks_id},, \text{triang_id},, \text{conifold_id})$ triple, with columns ks_id, triang_id, conifold_id, h11, h12, ncf, conifold_curve, conifold_shard_id, conifold_row_index.
Mirror convention. The catalogue exposes Hodge numbers in catalogue convention (typically small
h11, largeh12). Usestringforge.LCSDatabase(dataset="tdf")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 |
|---|---|
ks_id, triang_id, h11, h12, chi |
Identity |
intnums |
Triple intersection numbers $\kappa_{ijk}$ of the mirror (dense tensor) |
c2 |
Second Chern class $c_{2,i}$ |
generators_kahler_cone |
Kähler-cone generators |
rays_kahler_cone, tip_of_stretched_kahler_cone |
Kähler-cone geometry |
hyperplanes |
Hyperplane constraints defining the cone |
gv/h11_{N}/
Gopakumar–Vafa invariants, one row per model that has GV data.
| Column | Description |
|---|---|
ks_id, triang_id, h11, h12 |
Identity |
GVs, GWs |
Dictionaries of GV and GW invariants keyed by effective-curve charge |
grading_vector |
Grading vector used during the computation |
conifolds/h11_{N}/
One row per $(\text{ks_id},, \text{triang_id},, \text{conifold_id})$ triple.
| Column | Description |
|---|---|
ks_id, triang_id, h11, h12, conifold_id |
Identity |
ncf |
GV invariant of the shrinking curve |
conifold_curve |
Charge vector $c \in \mathbb{Z}^{h^{1,1}}$ of the shrinking cycle |
basis_change |
Integer basis rotation matrix placing the conifold modulus first |
polytope/
One row per ks_id (shared across all triangulations of that polytope).
| Column | Description |
|---|---|
ks_id |
Identity |
polytope_points |
Lattice points of the reflexive polytope (2D integer array) |
extra/
Miscellaneous scalar fields that vary per model.
| Column | Description |
|---|---|
ks_id, triang_id, h11, h12 |
Identity |
chi |
Euler characteristic |
D3_tadpole |
$\chi/24$ |
| ... | Additional precomputed properties |
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 = "tdf/catalog.parquet",
repo_type = "dataset",
)
catalog = pd.read_parquet(catalog_path)
# Resolve a specific model's geometry shard
row = catalog.query("ks_id == 716 and triang_id == 1").iloc[0]
lcs_path = hf_hub_download(
repo_id = "aschachner/cy-database",
filename = f"tdf/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.TDFDatabase (pure I/O) and stringforge.LCSDatabase(dataset="tdf") (JAXVacua-compatible model loading) wrap this pattern with a consistent API, caching, mirror-convention handling, and filtering.
Scope and limitations specific to TDF
- Only trilayer, double favourable toric hypersurfaces are included. Other toric and non-toric constructions live in separate sub-datasets (e.g.
cicy/). - GV invariants are precomputed only for a subset of models — use
has_gv=Truein queries to filter. - Conifold data is present only for models with at least one conifold limit — use
has_conifolds=Truein queries.
Building / updating
Produced from a local collection of per-model pickle files by the build_tdf_database notebook under stringforge/private/database/. Builds are incremental: models already in the manifest (by content hash) are skipped; only new or changed models are appended to the existing shards.
Additional references
For citation, licence, and contact details, see the umbrella cy-database card.