docs/DATA_DICTIONARY.md

Data dictionary and provenance

These eight JSON Lines tables are presentation exports of EVE–NOCHRÆL v1.0.0 reference records. They expose 490 rows in the Hub viewer. Aggregate tables repeat information present in per-run tables, so row counts must not be added to infer experimental sample size.

Every configuration has a single partition named data. This is a repository partition and does not imply a machine-learning training, validation, or blinded test split. No model training data are supplied by these table partitions. The original improvement inputs, evaluation cases, spectra, rational certificates, and solver programs are separate files under research/results/.

Configurations and lineage

Configuration	Rows	Original source	Transformation
recursive_summary	8	research/results/summary.json	Select cycle_results; add scope, percentage, and timing-source label
recursive_runs	100	research/results/recursive_metrics.json	Flatten shared fields and acquisition counters; encode state uniformly as text
reconstruction_runs	72	research/results/reconstruction.json	Expand each shared instance into trace and bounded-baseline method rows
outside_family	2	research/results/summary.json	Select outside_family_results; add exact solve fraction and state
claim_ledger	20	research/docs/CLAIM_LEDGER.json	Retain exact wording/status; encode lists as JSON strings and prefix evidence paths
arithmetic_tasks	280	research/results/symbolic_transfer.json	Preserve arbitrary-size integers as decimal strings; label enumeration availability
ablation_summary	3	research/results/summary.json	Select no_residual_ablation; add documented run count and query budget
trainable_bridge	5	research/results/trainable_bridge.json	Flatten training and reconstruction metrics from each recorded seed

metadata/export_lineage.json records source-file SHA-256 hashes, output hashes, row counts, descriptions, and exporter version. The exporter uses Python's standard library and does not execute experiments. Its output is deterministic for these supplied files.

Conventions

• JSON numeric rates are fractions in [0, 1], unless the field explicitly says percent.
• All durations ending in _seconds are seconds from the original reference execution. They are not new packaging measurements.
• null means a value is missing or inapplicable in the original record. It never means a successful zero-cost operation.
• evaluation_state is text in all rows. Values 0, 1, 2, 3 identify in-family states; outside_after_3 identifies the separate transfer evaluation.
• cycle_index is an integer for the four in-family states and null for outside-family evaluation. Cycle zero has no update.
• All integer-valued exact arithmetic outputs in arithmetic_tasks are strings, including small values. Use Python int() to recover them. This avoids losing values such as modulus 18446744073709551616 in signed 64-bit readers.
• Lists in claim_ledger are JSON strings with _json suffixes. Decode with json.loads() for list semantics. This keeps the viewer schema flat and retains exact source lists.
• Original exact fractions elsewhere in research/results/ remain rational strings. The viewer tables do not replace the certificate transcripts.

Field reference

Identity and evaluation

Field	Type	Meaning
seed	integer	Original experiment seed; one seed can occur across methods and states
method	text	Method identifier defined below
cycle	integer	State/update index in summary or ablation tables
evaluation_state	text	Uniform state identifier in per-run or outside-family tables
cycle_index	nullable integer	Numeric index for an in-family state
scope	text	controlled_algebraic_family or outside_family
runs	integer	Number of seeded runs aggregated in a summary row
correct	integer	Tasks satisfying the declared exact all-active-mode success predicate
total	integer	Tasks evaluated for that row
accuracy	number	correct / total for a per-run or outside-family row
mean_accuracy	number	Original mean per-run solve fraction in the cycle summary
accuracy_percent	number	100 * correct / total; only the summary uses percentages
exact_frequency_checks	integer	Listed active-frequency support incidences for the evaluation tasks; not the number of executed predicates, because evaluation can short-circuit

Method names trace_residual and classical_task_quotient refer to recursive inverse solving. Names trace_completed and bounded_kronecker_prony refer to the separate reconstruction comparison. The bounded baseline has a different prior-information contract. A reconstruction_runs row's exact_success is the shared instance-level recorded success flag: the source experiment checks reconstruction equality for both methods.

Observation and resource accounting

Field	Type	Meaning
update_calls	integer	Original scalar discovery-query count for a per-run state
mean_update_calls	number	Mean query count across the summary's seeded updates
scalar_calls	integer	Scalar query calls for a standalone reconstruction
cache_hits	integer	Queries answered through cached observations
atom_visits	nullable integer	Explicit source-row visits made by the observation backend
source_atoms	nullable integer	Source rows presented at a recursive update
defect_atoms	nullable integer	Declared remaining defective spectral orbits for an update
dimension	integer	Spectral vector dimension in a reconstruction instance
atoms	integer	Source support size in a reconstruction instance
max_derivative_order	nullable integer	Largest origin-jet order reached by that run
max_observed_derivative_order	integer	Largest observed order across runs in a summary
response_bits	nullable integer	Original total response bit-length accounting
max_response_bits	integer	Largest single response bit length in standalone reconstruction
polynomial_work_units	nullable integer	Implementation-specific polynomial-work counter; neither hardware FLOPs nor elapsed time
directions_tried	nullable integer	Candidate projection directions attempted by the adaptive trace method
memory_corrections	nullable integer	Stored symbolic corrections in the trace program
memory_eigenvalues	nullable integer	Stored task-relevant eigenvalues in the classical program
memory_serialized_bytes	nullable integer	Original serialized program-memory size
max_inverse_degree_bound	nullable integer	Reported maximum inverse-polynomial degree bound
dense_entries_formula	integer	Formula for a dense derivative-tensor scalar-entry count, not a measured computation
dense_runtime_measured	boolean	Whether dense-tensor elapsed time was actually measured; false for these records

source_atoms counts stored rows, not necessarily distinct support after all algebraic reductions. Information counts, exact arithmetic bit costs, polynomial work, and wall-clock cost are separate measures. Do not divide tensor-entry formulas by query counts and call that an intelligence gain.

Timing

Field	Meaning
update_seconds, mean_update_seconds	Original update duration for one run or its summary mean
evaluation_seconds, mean_eval_seconds	Original evaluation duration, recorded separately from update cost
acquisition_seconds	Original observation acquisition duration
total_seconds	Original standalone reconstruction duration
training_seconds	Original trainable-bridge fitting duration
reconstruction_seconds	Original trainable-bridge reconstruction duration
timing_source	Always original_reference_run; the wrapper does not retime the experiments

Machine load, interpreter version, exact-number growth, and implementation details affect these timings. Counts can support exact comparisons within their defined contracts; reference timings alone do not establish asymptotic speed guarantees.

Claims and arithmetic tasks

Field	Meaning
claim_id	Original ledger identifier, such as M1 or N3
claim	Original claim wording
status	Original claim or arithmetic-record status; the exporter adds a descriptive default only when an arithmetic status is absent
historical_novelty_status	Original individual novelty qualification or an explicit no-certification default
source_labels_json	Original manuscript theorem/statement labels encoded as a JSON list
evidence_paths_json	Original evidence paths, prefixed with research/, encoded as a JSON list
limitations_json	Original individual qualifications encoded as a JSON list
task	modular_kernel_count or large_modulus_transfer
modulus_decimal	Exact modulus, as a decimal string
exact_answer_decimal	Exact computed count, as a decimal string
independent_enumeration_decimal	Enumeration answer as text, or null for unenumerated large cases
exhaustively_enumerated	Whether independent enumeration was performed for that record
enumeration_matches	Exact equality to enumeration, or null when unavailable

The 220 enumerated records and 60 large-modulus records have different verification scopes. Missing exhaustive enumeration for large cases must not be replaced by true. A proof label means a written proof under the stated assumptions, not formal proof-assistant checking or peer review.

Ablation and trained-module bridge

Field	Meaning
successful_runs, total_runs	Successful and attempted ablation runs for the update
scalar_query_budget	Twelve scalar queries in the ablation contract
residual_filter_enabled	False in the no-filter ablation
trainable_parameters, training_steps, training_size, heldout_size	Original trained-module parameter, step, fitting-angle, and held-out-angle counts
initial_training_mse, final_training_mse, heldout_mse	Original squared prediction-error summaries
heldout_relative_frobenius_error	Held-out fit error relative to the original target, before reconstruction equivalence is considered
exact_reconstruction	Exact equality of reconstructed reduced support and stored dyadic weights
finite_certificate_passed	Acceptance under the finite exact reconstruction contract
maximum_prediction_difference	Maximum difference between reconstructed and frozen-module held-out predictions
intelligence_gain_claimed, end_to_end_speedup_claimed	Both false in these bridge records

A small target-fit error is different from equality to the frozen trained module. The maximum reconstruction prediction difference is not an LLM reasoning metric.

Access examples

Once the prepared repository is published:

from datasets import load_dataset

runs = load_dataset("PureOne/EVE-NOCHRAEL-v1.0", "recursive_runs", split="data")
outside = runs.filter(lambda row: row["scope"] == "outside_family")

For local standard-library access without any Hub dependency:

import json
from pathlib import Path

rows = [json.loads(line) for line in Path("data/arithmetic_tasks.jsonl").read_text().splitlines()]
first_modulus = int(rows[0]["modulus_decimal"])

Published evaluation cases should be treated as disclosed reference examples in future work. A new generalization claim requires new evaluation cases and an appropriate baseline and budget.