docs/DATA_DICTIONARY.md

# Data dictionary

The files in `results/` are outputs of fixed-design **synthetic finite known-model studies**. They are neither human gameplay records nor model weights. There are no training/validation/test splits, no learned neural model, and no commercial-game benchmark. Trial tables expose simulation draws; aggregate tables summarize those draws or exact finite computations. Combining rows from different designs does not create a shared benchmark population.

All counts below describe the delivered v3 reference outputs. Deterministic reproduction can regenerate the main files. Scientific definitions are implemented in `experiments/run_all.py` and the modules under `src/infinite_players/`.

## Shared conventions

| Convention | Meaning |
|---|---|
| Probabilities, accuracy, TV, gain fractions | Dimensionless numbers, usually represented on the 0–1 scale rather than as percentages |
| `ci_low`, `ci_high` in binomial studies | Two-sided nominal 95% Wilson interval for the simulated success proportion |
| `paired_gain_ci_low`, `paired_gain_ci_high` | Descriptive paired t interval over 16 arena-seed gains, not an external population guarantee |
| `trial`, `seed`, `revision`, `index` | Zero-based identifiers within the stated study design unless otherwise stated |
| `iteration` in `nullspace_updates.csv` | One-based projected-policy update number, from 1 through 24 |
| Event/lag/horizon counts | Simulation events or decisions; they are not seconds, milliseconds, frames, or a proposed universal AI clock |
| `theta`, `world` | Synthetic signs in {-1,+1}; binary type and mechanics hypothesis labels |
| Floating residuals | Absolute numerical errors in the indicated probability, logscore, or equality-constraint quantity |
| Payload bytes | NumPy array payload only where specified; excludes Python objects, allocator overhead, and unrelated input storage |

The main pseudorandom seed is 1,860,317. Different studies use offsets from it; the arena family separately calls `make_arena(4100 + seed)`. `results/config.json` records the main experimental design. Study definitions are fixed rather than selected by searching for the strongest displayed outcome.

## Result-file map

| Family | Aggregate/diagnostic files | Trial or structured detail |
|---|---|---|
| Temporal alignment | `continuous_lag.csv` | `continuous_lag_trials.csv` |
| Sequence inference | `sequence_inference.csv`, `sequence_inference_audit.json` | `sequence_inference_trials.csv` |
| Local source correction | `local_revisions.csv`, `runtime_telemetry.json` | `local_revision_trials.csv` |
| Future-query memory | `memory_graphs.csv`, `retrospective_memory.csv`, `lossy_memory_bound.json` | No separate retrospective-query trial CSV is retained |
| Semantic-law policy improvement | `shield_summary.csv`, `semantic_horizons.csv`, `calibration_unlock.json` | `shield_arena.csv`, `nullspace_updates.csv`, `policy_examples.json` |
| Approximate operators | `approximation_summary.json` | `approximation_trials.csv` |
| Lifetime promotion audits | `lifetime_audit.csv` | No separate lifetime-history trial CSV is retained |
| Exact finite verification | `exact_audits.json` | Enumerated assertions and rational values, not a generic gameplay dataset |
| Combined configuration/results | `config.json`, `summary.json` | These duplicate or collect study outputs rather than introducing extra independent evidence |

## Temporal alignment and lag

`continuous_lag.csv` has **7 rows**, one each for lags 0, 1, 2, 3, 4, 6, and 9. Each condition contains 16,000 trajectories of 64 events, for 112,000 trajectories overall. The generator uses Markov persistence 0.72 and sign reliabilities 0.6 and 0.75. Overlapping trajectory segments are generated jointly; endpoint pairs are not assumed independent.

| Fields | Definition and units |
|---|---|
| `lag` | Offset between observation streams, in simulation events |
| `n` | Events contributing to each signed score; 64 here |
| `trials`, `correct` | Trajectory count and number classified correctly |
| `accuracy` | `correct / trials`; ties are resolved by a random fair sign |
| `ci_low`, `ci_high` | Wilson interval for simulated classification accuracy |
| `mean_score`, `theory_mean` | Observed mean and exact declared-model mean of the sum of n signed products; score units |
| `variance`, `theory_variance` | Sample variance with `ddof=1` and exact declared-model variance of that score; squared-score units |
| `error_bound` | Conservative one-trajectory classification-error upper bound returned by `lag_moments`; dimensionless and not an empirical error rate |

`continuous_lag_trials.csv` has **112,000 rows**. Its key is `(lag, trial)`; `score` is the signed integer score and `correct` is 0 or 1. These trajectories are synthetic alignment fixtures, not measurements of human response latency.

## Sequence inference

`sequence_inference.csv` has **9 rows**: three methods at each of 8, 16, and 32 events per record. There are 1,000 records at each length, for 3,000 underlying records. The three method rows within each length are evaluated on the same records, so they are paired comparisons rather than 9,000 independent recordings.

| `method` | Meaning |
|---|---|
| `operator_tree` | Ordered scaled-operator tree inference after the simulated mechanics calibration |
| `full_HMM_replay` | Separately implemented exact full forward replay using the same hypotheses, likelihoods, and calibration |
| `paired_product` | Simpler sign-product estimator on those same synthetic records |

Aggregate fields are `events`, `method`, `trials`, `correct`, `accuracy`, `ci_low`, and `ci_high`. `events` is the source-record length. Accuracy is correct recovery of the synthetic binary `theta` after the actual simulated `world` sign is supplied as a calibration probe. These values do not measure human identity reconstruction.

`sequence_inference_trials.csv` has **3,000 rows**, keyed by `(n, trial)`:

| Fields | Meaning |
|---|---|
| `n` | Events in this record; corresponds to aggregate `events` |
| `trial` | Record index within this length condition |
| `theta`, `world` | Generating type and mechanics signs |
| `posterior_positive` | Tree posterior probability of `theta = +1` after the mechanics probe |
| `tree_correct`, `full_replay_correct`, `product_correct` | Per-method 0/1 correctness on the same record |

`sequence_inference_audit.json` records `independent_records` (3,000), `maximum_tree_replay_posterior_error` (maximum coordinatewise posterior discrepancy), and `maximum_precalibration_identity_error_from_half` (largest departure from the symmetric 0.5 type posterior before calibration). The tree is an update/inference organization, not a better posterior than the same exact Bayesian model.

## Local evidence correction and resource cost

`local_revisions.csv` has **3 rows**, for archived lengths 256, 2,048, and 16,384 events. Each length receives 16 local factor replacements under a fixed four-hypothesis, two-hidden-state model.

| Fields | Meaning and units |
|---|---|
| `events`, `hypotheses`, `hidden_states`, `revisions` | Archive length and the finite inference dimensions/counts |
| `tree_compositions_per_revision` | Tree-depth count of batched operator compositions after replacing one leaf |
| `replay_steps_per_revision` | Event-wise vector-forward steps for full replay |
| `tree_payload_bytes` | Reported conceptual operator-node payload bytes, including scaling arrays and padding/unused node slots |
| `raw_two_sign_payload_bytes` | Baseline payload of two raw int8 sign streams, `2 * events` bytes |
| `max_posterior_error` | Maximum absolute posterior-coordinate discrepancy across 16 replacements |
| `max_centered_logscore_error` | Maximum error after subtracting each implementation's first hypothesis logscore; distinguishes accumulated relative-logscore error from posterior saturation |

Tree compositions and forward steps are different work units, with additional hypothesis/state arithmetic factors. The depth reduction is not an equal-unit FLOP comparison. The tree payload is 160 times the minimal raw two-sign payload on these fixtures, excluding overhead; do not describe it as a compression result.

`local_revision_trials.csv` has **48 rows**, keyed by `(events, revision)`. It contains `index` (replaced event position), `posterior_max_error`, `centered_logscore_error`, `tree_compositions`, and `forward_steps` for each replacement. Replacements within one archive are sequentially related and are not 48 independent archives.

`runtime_telemetry.json` is a list of **3 entries**. Fields are `events`, `build_seconds`, `tree_16_revisions_seconds`, `replay_16_revisions_seconds`, and `measured_revision_speed_ratio` (replay update time divided by tree update time). Durations use wall-clock seconds. The ratio excludes tree construction and measures a single local execution. This file is intentionally excluded from deterministic reference hashing. Original reference telemetry and fresh audit telemetry are distinct retained observations.

## Future-query memory

`memory_graphs.csv` has **7 exact finite cases** for record lengths 1 through 4 bits. `queried_coordinates` is either the first coordinate alone or every coordinate; the one-bit case appears once.

| Fields | Meaning |
|---|---|
| `record_bits` | Length n of a binary historical record |
| `queried_coordinates` | Number of prefix coordinates that a future query may request |
| `records` | Number of possible input records, `2 ** record_bits` |
| `minimum_memory_states` | Exact chromatic number of the constructed confusability graph |
| `minimum_fixed_bits` | Ceiling of log2 of that state count; fixed-length exact-storage requirement in bits |

`retrospective_memory.csv` has **6 aggregate rows** for retained prefixes of 0, 8, 32, 64, 128, and 256 bits from a 256-bit synthetic history. Each storage condition is evaluated on the same 16,000 generated histories/coordinate queries; conditions are paired, not six unrelated datasets. The implemented strategy stores a prefix and guesses outside it.

Fields: `history_bits`, `retained_prefix_bits`, `trials`, `correct`, `accuracy`, `ci_low`, `ci_high`, `analytic_accuracy`, and `evidential_coverage`. The latter two equal `0.5 + 0.5 * retained_prefix_bits / history_bits` and `retained_prefix_bits / history_bits`, respectively. This is a disclosed prefix-retention baseline, not a claim of optimal approximate coding at every bit budget.

`lossy_memory_bound.json` contains `history_bits` and a `bounds` list with `average_error` and `minimum_bits_lower_bound`. The lower bound is `n * (1 - h2(error))`, measured in bits, under the declared random-access setting. It is an information-theoretic lower bound, not an implemented encoder size or compression benchmark.

## Semantic-law policy improvement

The arena has six ground states, six ground actions, two semantic posture labels, and two semantic tactic labels, with discount factor gamma = 0.9. Each tactic has three motor realizations. Rewards in `FiniteMDP` are expected per-decision rewards; the demo environment samples Bernoulli rewards from them.

| `method` | Delivered controller |
|---|---|
| `source_anchor` | Original interior tactic/motor-mixture policy |
| `path_shield_LP` | Exact finite policy iteration using LP-constrained joint next-tactic/next-posture signatures |
| `conditional_class_only` | Policy iteration preserving current-state tactic probabilities, with no full semantic-path contract |
| `unconstrained` | Policy iteration without those semantic constraints |
| `nullspace_24_updates` | 24 feasible projected-Q updates from the source anchor |

`shield_arena.csv` has **80 rows**: five methods across 16 seeded arenas. `seed` is the replicate index 0–15; the generator receives `4100 + seed`, with synthetic source type alternating by parity.

| Fields | Definition |
|---|---|
| `discounted_value` | Mean of exact infinite-horizon discounted state values over all six initial ground states, equally weighted |
| `normalized_value` | `(1 - gamma) * discounted_value`; comparable per-decision reward scale |
| `normalized_gain` | Mean normalized state-value improvement relative to the same seed's anchor |
| `minimum_state_value_gain` | Minimum unnormalized discounted-value gain over the six ground states |
| `class_probability_error` | Maximum absolute departure from target current-state tactic probabilities |
| `signature_error` | Maximum absolute departure from the full target joint semantic-action/next-semantic-state kernel |
| `semantic_path_TV_h6` | Half the L1 difference between exact enumerated six-step semantic-word laws, starting specifically at ground state zero |

**Initial conditions differ across metrics:** the value metric averages all six starting ground states; path TV starts at state zero. They must not be described as the same trajectory-return measurement. `semantic_law` enumerates sequences of `(semantic action, next semantic state)` pairs; it does not enumerate motor actions or require ground-state distributions to match.

`shield_summary.csv` has **5 rows**, one per controller. `normalized_value`, `normalized_gain`, and `semantic_path_TV_h6` are means over 16 seeds. `paired_gain_ci_low` and `paired_gain_ci_high` are the mean gain plus/minus a Student-t standard-error interval with 15 degrees of freedom. `max_signature_error` is the maximum over seeds, not the mean. `seeds` records the replicate count.

`nullspace_updates.csv` has **384 rows**, keyed by `(seed, iteration)`:

| Fields | Meaning |
|---|---|
| `mean_value` | Mean **unnormalized discounted value** after this update, over six ground states |
| `minimum_value_gain` | Minimum state-value change relative to the immediately previous update, in unnormalized discounted-value units |
| `signature_residual` | Maximum absolute signature-constraint residual after this update |

Its sequential iterations are not independent trials. Compare normalized values only after applying the explicit `(1 - gamma)` factor.

`semantic_horizons.csv` has **32 rows**: four methods (`source_anchor`, `path_shield_LP`, `conditional_class_only`, `unconstrained`) at horizons 1–8, for arena seed index zero only. `semantic_path_TV` uses exact law enumeration from ground state zero. This file is neither a 16-seed average nor a sample-size/accuracy curve; the projected-update method is not included in it.

`policy_examples.json` contains **15 entries**: the five controller policies for seed indices 0, 1, and 2. Each has `seed`, `method`, a 6-by-6 row-stochastic `policy` matrix, and `audit` where applicable. LP audit objects report iteration count, Bellman residual, and per-state primal residual, dual violation, and duality gap. Source-anchor/projected examples may have null audit fields. Tiny negative zeros are floating serialization artifacts, not negative probability claims.

`calibration_unlock.json` contains:

- `calibration`: three named entries, `before_calibration_robust`, `true_world_0`, and `true_world_1`. Each contains a three-action `policy`, expected one-decision `reward`, constraint `rank`, `nullity`, and numerical LP `audit` with primal/dual residuals and duality gap. This small fixture is separate from the six-state averaged arena.
- `no_headroom_max_absolute_gain`: maximum absolute discounted state-value difference between optimized and anchor policies in the separate constant-reward no-headroom arena.

The positive world control's reward 0.85 and negative world's 0.4 are finite constructed controls. They are not human player returns or a general empirical calibration effect.

## Approximate operator circuits

`approximation_trials.csv` has **1,000 rows**, one per positive-circuit perturbation trial. Each trial uses eight factors, four hypotheses, and two hidden states.

| Fields | Meaning |
|---|---|
| `trial` | Perturbation-trial index |
| `log_error_budget` | Sum of entrywise multiplicative log-error allowances over factors; natural-log scale |
| `posterior_TV` | Total variation between exact and perturbed posterior distributions |
| `uniform_bound` | `tanh(log_error_budget / 2)` bound used by this declared positive-operator construction |

`approximation_summary.json` records `trials`, `violations`, `maximum_posterior_TV`, and `maximum_error_bound_ratio`, the largest observed `posterior_TV / uniform_bound`. Zero violations in these simulations supports the implemented fixture check; the mathematical theorem and its assumptions must be assessed separately.

## Lifetime promotion audit

`lifetime_audit.csv` has **2 aggregate rows**, for true mean session gains 0 and 0.3. Each condition simulates 10,000 histories, 40 candidate versions, and 256 bounded audit observations per version. Gains are synthetic independent signs with the declared mean. The version budget is `lifetime_budget / (version * (version + 1))` for one-based versions.

| Fields | Meaning |
|---|---|
| `true_gain` | Generating expected bounded session-level gain |
| `trials` | Simulated lifetime histories, not individual session observations |
| `versions` | Number of candidate versions tested per history |
| `audit_sessions_per_version` | Audit sample count used by each version's decision rule |
| `lifetime_budget` | Total nominal error allocation, 0.05 |
| `any_promotion_count`, `any_promotion_rate` | Number and fraction of histories with at least one accepted promotion |
| `ci_low`, `ci_high` | Wilson interval for that any-promotion fraction |
| `mean_promotions` | Mean count of accepted versions per history |

This is a statistical acceptance-rule fixture. It does not simulate a learning system discovering 40 successively improved algorithms, and is not evidence of sustained recursive self-improvement.

## Exact audits, combined JSON, and retained reports

`exact_audits.json` records separate finite checks under `lag`, `operator`, `memory`, `shield`, and `composition`, plus `status`. It includes exact rational quantities as strings, enumerated-case counts, and selected floating discrepancies. Cases include 2,550 lag atoms, 16 hidden operator paths, 276 deterministic encoders, 2,046 semantic words, and 72 posterior/horizon composition cases. These are internal exact-arithmetic implementations, not external proof review.

`config.json` records design counts, sizes, seed, and the synthetic-study scope. `summary.json` collects the outputs of the seven study functions. Some entries are nested pairs, such as `[sequence_aggregate_rows, sequence_audit]` and `[shield_aggregate_rows, calibration_report]`; the JSON is a study report, not a tabular split. Values already present in CSVs are duplicated summaries, not additional observations.

`v3_source_reproduction.json` and `final_zip_reproduction.json` are retained original execution reports. Their `comparisons` entries contain `file`, expected/actual SHA-256 digests, and `match`; top-level fields count the declared deterministic files and matches. `legacy_v2_reproduction.json` and `final_zip_legacy_reproduction.json` similarly retain the original v2 execution evidence. Original test logs (`tests.txt`, `v3_reproduced_tests.txt`, and `legacy_v2_run.txt`) are text diagnostics, not study data. The legacy archive is omitted from this curated edition; see [REPRODUCIBILITY.md](REPRODUCIBILITY.md) for restoration instructions.

Fresh release-preparation outcomes are separately identified under `validation/`. The original report descriptions, source paths, and timestamps are provenance and must not be interpreted as a fresh run performed by every downloader.

## Demonstration artifacts

The three files under `examples/demo/` are known synthetic fixtures rather than dataset splits:

| File | Structure and meaning |
|---|---|
| `synthetic_recording.jsonl` | 32 source events. Fields: nonempty `event_id`, integer simulation `tick`, signs `action_signal` and `context_signal`, asserted `source_kind = synthetic_fixture`, `clock_domain = shared_simulation_tick`, and `source_epoch`. The exact contract is in `schemas/fixture_event.schema.json`. |
| `descendant_trace.jsonl` | 1,000 execution decisions with `tick`, ground `state`, chosen ground `action`, `semantic_action`, sampled 0/1 `reward`, and `next_state`. A single stochastic continuation trace, not 1,000 independent agent evaluations. |
| `player_capsule.json` | Source digest/epoch and event count, finite hypothesis catalog, coupled pre/post-calibration posterior, persistent sampled type branch, anchor/descendant policies, declared protected semantic kernel, exclusions, numerical optimizer audit, and evaluation summary. |

The capsule's normalized analytic values average the finite state-value vectors; its path TV uses the default state-zero initial law; its `sampled_reward_mean` is the arithmetic mean of one 1,000-step sampled trace. They have different estimands. Source-kind labels and event identifiers are caller assertions, not cryptographic proof of human origin or observation independence. Distinct IDs do not by themselves establish independent observations.