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Duplicate
The dataset viewer is not available for this split.
Cannot load the dataset split (in streaming mode) to extract the first rows.
Error code:   StreamingRowsError
Exception:    CastError
Message:      Couldn't cast
path: string
imports: list<item: string>
  child 0, item: string
premises: list<item: struct<full_name: string, code: string, start: list<item: int64>, end: list<item: int64>, (... 15 chars omitted)
  child 0, item: struct<full_name: string, code: string, start: list<item: int64>, end: list<item: int64>, kind: stri (... 3 chars omitted)
      child 0, full_name: string
      child 1, code: string
      child 2, start: list<item: int64>
          child 0, item: int64
      child 3, end: list<item: int64>
          child 0, item: int64
      child 4, kind: string
n_pairs: struct<min_to_max: int64, inf_to_sup: int64, add_to_mul: int64, sub_to_div: int64, zero_to_one: int6 (... 311 chars omitted)
  child 0, min_to_max: int64
  child 1, inf_to_sup: int64
  child 2, add_to_mul: int64
  child 3, sub_to_div: int64
  child 4, zero_to_one: int64
  child 5, le_to_lt: int64
  child 6, list_to_multiset: int64
  child 7, set_to_finset: int64
  child 8, nat_to_int: int64
  child 9, unprimed_to_primed: int64
  child 10, differentiable_to_hasderiv: int64
  child 11, sup_inf: int64
  child 12, top_bot: int64
  child 13, max_min: int64
  child 14, upper_lower: int64
  child 15, ceil_floor: int64
  child 16, atTop_atBot: int64
  child 17, add_mul: int64
  child 18, image_preimage: int64
  child 19, map_comap: int64
transfer: struct<full: struct<add_to_mul: struct<relation: double, plain: double, wrong: double, lift: double> (... 734 chars omitted)
  child 0, full: struct<add_to_mul: struct<relat
...
     child 4, sub_to_div: double
      child 5, zero_to_one: double
      child 6, le_to_lt: double
      child 7, list_to_multiset: double
      child 8, set_to_finset: double
      child 9, nat_to_int: double
      child 10, unprimed_to_primed: double
      child 11, differentiable_to_hasderiv: double
      child 12, sup_inf: double
      child 13, top_bot: double
      child 14, max_min: double
      child 15, upper_lower: double
      child 16, ceil_floor: double
      child 17, atTop_atBot: double
      child 18, add_mul: double
      child 19, image_preimage: double
      child 20, map_comap: double
  child 2, name: struct<_floor: double, min_to_max: double, inf_to_sup: double, add_to_mul: double, sub_to_div: doubl (... 347 chars omitted)
      child 0, _floor: double
      child 1, min_to_max: double
      child 2, inf_to_sup: double
      child 3, add_to_mul: double
      child 4, sub_to_div: double
      child 5, zero_to_one: double
      child 6, le_to_lt: double
      child 7, list_to_multiset: double
      child 8, set_to_finset: double
      child 9, nat_to_int: double
      child 10, unprimed_to_primed: double
      child 11, differentiable_to_hasderiv: double
      child 12, sup_inf: double
      child 13, top_bot: double
      child 14, max_min: double
      child 15, upper_lower: double
      child 16, ceil_floor: double
      child 17, atTop_atBot: double
      child 18, add_mul: double
      child 19, image_preimage: double
      child 20, map_comap: double
to
{'variants': List(Value('string')), 'n_pairs': {'min_to_max': Value('int64'), 'inf_to_sup': Value('int64'), 'add_to_mul': Value('int64'), 'sub_to_div': Value('int64'), 'zero_to_one': Value('int64'), 'le_to_lt': Value('int64'), 'list_to_multiset': Value('int64'), 'set_to_finset': Value('int64'), 'nat_to_int': Value('int64'), 'unprimed_to_primed': Value('int64'), 'differentiable_to_hasderiv': Value('int64'), 'sup_inf': Value('int64'), 'top_bot': Value('int64'), 'max_min': Value('int64'), 'upper_lower': Value('int64'), 'ceil_floor': Value('int64'), 'atTop_atBot': Value('int64'), 'add_mul': Value('int64'), 'image_preimage': Value('int64'), 'map_comap': Value('int64')}, 'coherence': {'full': {'_floor': Value('float64'), 'min_to_max': Value('float64'), 'inf_to_sup': Value('float64'), 'add_to_mul': Value('float64'), 'sub_to_div': Value('float64'), 'zero_to_one': Value('float64'), 'le_to_lt': Value('float64'), 'list_to_multiset': Value('float64'), 'set_to_finset': Value('float64'), 'nat_to_int': Value('float64'), 'unprimed_to_primed': Value('float64'), 'differentiable_to_hasderiv': Value('float64'), 'sup_inf': Value('float64'), 'top_bot': Value('float64'), 'max_min': Value('float64'), 'upper_lower': Value('float64'), 'ceil_floor': Value('float64'), 'atTop_atBot': Value('float64'), 'add_mul': Value('float64'), 'image_preimage': Value('float64'), 'map_comap': Value('float64')}, 'stmt': {'_floor': Value('float64'), 'min_to_max': Value('float64'), 'inf_to_sup': Value('float64'), 'add_to_
...
}}, 'stmt': {'duality_x_duality': Value('float64'), 'control_x_control': Value('float64'), 'duality_x_control': Value('float64'), 'pairs': {'sup_inf|top_bot': Value('float64'), 'sup_inf|max_min': Value('float64'), 'sup_inf|upper_lower': Value('float64'), 'sup_inf|ceil_floor': Value('float64'), 'sup_inf|atTop_atBot': Value('float64'), 'top_bot|max_min': Value('float64'), 'top_bot|upper_lower': Value('float64'), 'top_bot|ceil_floor': Value('float64'), 'top_bot|atTop_atBot': Value('float64'), 'max_min|upper_lower': Value('float64'), 'max_min|ceil_floor': Value('float64'), 'max_min|atTop_atBot': Value('float64'), 'upper_lower|ceil_floor': Value('float64'), 'upper_lower|atTop_atBot': Value('float64'), 'ceil_floor|atTop_atBot': Value('float64')}}, 'name': {'duality_x_duality': Value('float64'), 'control_x_control': Value('float64'), 'duality_x_control': Value('float64'), 'pairs': {'sup_inf|top_bot': Value('float64'), 'sup_inf|max_min': Value('float64'), 'sup_inf|upper_lower': Value('float64'), 'sup_inf|ceil_floor': Value('float64'), 'sup_inf|atTop_atBot': Value('float64'), 'top_bot|max_min': Value('float64'), 'top_bot|upper_lower': Value('float64'), 'top_bot|ceil_floor': Value('float64'), 'top_bot|atTop_atBot': Value('float64'), 'max_min|upper_lower': Value('float64'), 'max_min|ceil_floor': Value('float64'), 'max_min|atTop_atBot': Value('float64'), 'upper_lower|ceil_floor': Value('float64'), 'upper_lower|atTop_atBot': Value('float64'), 'ceil_floor|atTop_atBot': Value('float64')}}}}
because column names don't match
Traceback:    Traceback (most recent call last):
                File "/src/services/worker/src/worker/utils.py", line 147, in get_rows_or_raise
                  return get_rows(
                      dataset=dataset,
                  ...<4 lines>...
                      column_names=column_names,
                  )
                File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
                  return func(*args, **kwargs)
                File "/src/services/worker/src/worker/utils.py", line 127, in get_rows
                  rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
                File "/src/services/worker/src/worker/utils.py", line 483, in safe_iter
                  yield from ds.decode(False) if ds.features else ds
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2840, in __iter__
                  for key, example in ex_iterable:
                                      ^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2373, in __iter__
                  for key, pa_table in self._iter_arrow():
                                       ~~~~~~~~~~~~~~~~^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2398, in _iter_arrow
                  for key, pa_table in self.ex_iterable._iter_arrow():
                                       ~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 536, in _iter_arrow
                  for key, pa_table in iterator:
                                       ^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 419, in _iter_arrow
                  for key, pa_table in self.generate_tables_fn(**gen_kwags):
                                       ~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
                  self._cast_table(pa_table, json_field_paths=json_field_paths),
                  ~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
                  pa_table = table_cast(pa_table, self.info.features.arrow_schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2306, in cast_table_to_schema
                  raise CastError(
                  ...<3 lines>...
                  )
              datasets.table.CastError: Couldn't cast
              path: string
              imports: list<item: string>
                child 0, item: string
              premises: list<item: struct<full_name: string, code: string, start: list<item: int64>, end: list<item: int64>, (... 15 chars omitted)
                child 0, item: struct<full_name: string, code: string, start: list<item: int64>, end: list<item: int64>, kind: stri (... 3 chars omitted)
                    child 0, full_name: string
                    child 1, code: string
                    child 2, start: list<item: int64>
                        child 0, item: int64
                    child 3, end: list<item: int64>
                        child 0, item: int64
                    child 4, kind: string
              n_pairs: struct<min_to_max: int64, inf_to_sup: int64, add_to_mul: int64, sub_to_div: int64, zero_to_one: int6 (... 311 chars omitted)
                child 0, min_to_max: int64
                child 1, inf_to_sup: int64
                child 2, add_to_mul: int64
                child 3, sub_to_div: int64
                child 4, zero_to_one: int64
                child 5, le_to_lt: int64
                child 6, list_to_multiset: int64
                child 7, set_to_finset: int64
                child 8, nat_to_int: int64
                child 9, unprimed_to_primed: int64
                child 10, differentiable_to_hasderiv: int64
                child 11, sup_inf: int64
                child 12, top_bot: int64
                child 13, max_min: int64
                child 14, upper_lower: int64
                child 15, ceil_floor: int64
                child 16, atTop_atBot: int64
                child 17, add_mul: int64
                child 18, image_preimage: int64
                child 19, map_comap: int64
              transfer: struct<full: struct<add_to_mul: struct<relation: double, plain: double, wrong: double, lift: double> (... 734 chars omitted)
                child 0, full: struct<add_to_mul: struct<relat
              ...
                   child 4, sub_to_div: double
                    child 5, zero_to_one: double
                    child 6, le_to_lt: double
                    child 7, list_to_multiset: double
                    child 8, set_to_finset: double
                    child 9, nat_to_int: double
                    child 10, unprimed_to_primed: double
                    child 11, differentiable_to_hasderiv: double
                    child 12, sup_inf: double
                    child 13, top_bot: double
                    child 14, max_min: double
                    child 15, upper_lower: double
                    child 16, ceil_floor: double
                    child 17, atTop_atBot: double
                    child 18, add_mul: double
                    child 19, image_preimage: double
                    child 20, map_comap: double
                child 2, name: struct<_floor: double, min_to_max: double, inf_to_sup: double, add_to_mul: double, sub_to_div: doubl (... 347 chars omitted)
                    child 0, _floor: double
                    child 1, min_to_max: double
                    child 2, inf_to_sup: double
                    child 3, add_to_mul: double
                    child 4, sub_to_div: double
                    child 5, zero_to_one: double
                    child 6, le_to_lt: double
                    child 7, list_to_multiset: double
                    child 8, set_to_finset: double
                    child 9, nat_to_int: double
                    child 10, unprimed_to_primed: double
                    child 11, differentiable_to_hasderiv: double
                    child 12, sup_inf: double
                    child 13, top_bot: double
                    child 14, max_min: double
                    child 15, upper_lower: double
                    child 16, ceil_floor: double
                    child 17, atTop_atBot: double
                    child 18, add_mul: double
                    child 19, image_preimage: double
                    child 20, map_comap: double
              to
              {'variants': List(Value('string')), 'n_pairs': {'min_to_max': Value('int64'), 'inf_to_sup': Value('int64'), 'add_to_mul': Value('int64'), 'sub_to_div': Value('int64'), 'zero_to_one': Value('int64'), 'le_to_lt': Value('int64'), 'list_to_multiset': Value('int64'), 'set_to_finset': Value('int64'), 'nat_to_int': Value('int64'), 'unprimed_to_primed': Value('int64'), 'differentiable_to_hasderiv': Value('int64'), 'sup_inf': Value('int64'), 'top_bot': Value('int64'), 'max_min': Value('int64'), 'upper_lower': Value('int64'), 'ceil_floor': Value('int64'), 'atTop_atBot': Value('int64'), 'add_mul': Value('int64'), 'image_preimage': Value('int64'), 'map_comap': Value('int64')}, 'coherence': {'full': {'_floor': Value('float64'), 'min_to_max': Value('float64'), 'inf_to_sup': Value('float64'), 'add_to_mul': Value('float64'), 'sub_to_div': Value('float64'), 'zero_to_one': Value('float64'), 'le_to_lt': Value('float64'), 'list_to_multiset': Value('float64'), 'set_to_finset': Value('float64'), 'nat_to_int': Value('float64'), 'unprimed_to_primed': Value('float64'), 'differentiable_to_hasderiv': Value('float64'), 'sup_inf': Value('float64'), 'top_bot': Value('float64'), 'max_min': Value('float64'), 'upper_lower': Value('float64'), 'ceil_floor': Value('float64'), 'atTop_atBot': Value('float64'), 'add_mul': Value('float64'), 'image_preimage': Value('float64'), 'map_comap': Value('float64')}, 'stmt': {'_floor': Value('float64'), 'min_to_max': Value('float64'), 'inf_to_sup': Value('float64'), 'add_to_
              ...
              }}, 'stmt': {'duality_x_duality': Value('float64'), 'control_x_control': Value('float64'), 'duality_x_control': Value('float64'), 'pairs': {'sup_inf|top_bot': Value('float64'), 'sup_inf|max_min': Value('float64'), 'sup_inf|upper_lower': Value('float64'), 'sup_inf|ceil_floor': Value('float64'), 'sup_inf|atTop_atBot': Value('float64'), 'top_bot|max_min': Value('float64'), 'top_bot|upper_lower': Value('float64'), 'top_bot|ceil_floor': Value('float64'), 'top_bot|atTop_atBot': Value('float64'), 'max_min|upper_lower': Value('float64'), 'max_min|ceil_floor': Value('float64'), 'max_min|atTop_atBot': Value('float64'), 'upper_lower|ceil_floor': Value('float64'), 'upper_lower|atTop_atBot': Value('float64'), 'ceil_floor|atTop_atBot': Value('float64')}}, 'name': {'duality_x_duality': Value('float64'), 'control_x_control': Value('float64'), 'duality_x_control': Value('float64'), 'pairs': {'sup_inf|top_bot': Value('float64'), 'sup_inf|max_min': Value('float64'), 'sup_inf|upper_lower': Value('float64'), 'sup_inf|ceil_floor': Value('float64'), 'sup_inf|atTop_atBot': Value('float64'), 'top_bot|max_min': Value('float64'), 'top_bot|upper_lower': Value('float64'), 'top_bot|ceil_floor': Value('float64'), 'top_bot|atTop_atBot': Value('float64'), 'max_min|upper_lower': Value('float64'), 'max_min|ceil_floor': Value('float64'), 'max_min|atTop_atBot': Value('float64'), 'upper_lower|ceil_floor': Value('float64'), 'upper_lower|atTop_atBot': Value('float64'), 'ceil_floor|atTop_atBot': Value('float64')}}}}
              because column names don't match

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vector_behavior — data bundle

Companion data for https://github.com/david-busbib/vector_behavior-

Four theorem embedding spaces over the same 99,552 Mathlib theorems, restricted to the rows the study uses and written in pool order, float32. Also carries the proof-dependency graph, reduced to what the scripts actually read.

directory space dim size
embeddings_mistral/ e5_mistral — intfloat/e5-mistral-7b-instruct 4096 1.6 GB
embeddings_corpus/ e5_large — intfloat/e5-large-v2 1024 407 MB
embeddings_fixed/ e5_large_stmt — same model, different text source 1024 407 MB
embeddings_deepseek/ deepseek_proverdegenerate, contrast only 4096 1.6 GB
results_shared/ pool.json, subset.json, neighbors.npz 27 MB
graph_uses.json.gz proof dependency graph, 55,575 theorems 2.4 MB

Setup

git clone https://github.com/david-busbib/vector_behavior-.git
cd vector_behavior-
pip install -r requirements.txt

huggingface-cli download davidbusbib/vector-behavior-data \
    --repo-type dataset --local-dir vb_data

cp vb_data/results_shared/* results/shared/
export VB_DATA=$PWD/vb_data

python scripts/19_read_mutual.py

Pulling only what you need

Each space is ~0.4-1.6 GB. To take one:

huggingface-cli download davidbusbib/vector-behavior-data \
    --repo-type dataset --local-dir vb_data \
    --include "embeddings_corpus/*" "results_shared/*" "graph_uses.json.gz" "to_additive.json"

Scripts filter themselves to whichever spaces are present, so a partial download runs the whole pipeline over the subset you took.

Notes

  • Rows are pool-ordered, so pool["rows"][space] is the identity. This is why the arrays are smaller than the originals (99,552 rather than 180,907 / 104,050 rows) and why no script needs changing.
  • float32 throughout. float16 moves the numbers.
  • deepseek_prover is degenerate — 81% of its variance sits in one direction after centring, and it was extracted under fp16. It is in the study as a contrast, never as evidence. See RESULTS.md.
  • Proofs and the dependency graph are held back as validation in this project. graph_uses.json.gz is here so Phase 3 can be rerun; it is not an encoder input.
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