# T^ × GPT — extended machine context v0.8.7

Last modified: 2026-09-17
Canonical corpus: https://www.t-1-t.com/T-GPT/
Current state: https://www.t-1-t.com/T-GPT/recherche-v0.8.7/
Pilot: https://www.t-1-t.com/T-GPT/pilot-v0.8.2/
Metric formalisation: https://www.t-1-t.com/T-GPT/formalisation-v0.8.2/
External Review #5: https://www.t-1-t.com/T-GPT/revues/claude-05/
Structured map: https://www.t-1-t.com/T-GPT/research.json

## Research position

T^GPT is instrumentation-first. Its current object is not “T^ is better”, but whether semantic distribution shifts, recoverability and aggregation effects can be measured without confusing sampling noise, mapping failure, verbosity or post-hoc selection with real contraction.

T^FIELD/T_WEAVE remains a candidate method. It may be REFUTED or RETIRED while the measurement program survives.

## Why v0.8.2 exists

External Review #2 executed v0.8.1 tools on adversarial inputs. It identified several blockers: thresholded support produced positive loss under an exact null; REC_GAIN was often undefined; UNMAPPED altered a threshold while not entering counts; `uncertain` became a cluster; B->R dependence was broken by independent bootstrap; recovery probes had no neutral control; task count was too small; AGG_COVERAGE lacked a representation false-positive control.

Therefore v0.8.1 is NO-GO for new confirmatory collection.

## Four non-equivalent field objects

FIELD^TOK = conditional token distribution when directly available.
FIELD^SEM = empirical distribution over frozen semantic cluster IDs plus explicit UNMAPPED/UNRESOLVED mass.
FIELD^TRAJ = paired or graph-structured generation/agent trajectories and provenance.
FIELD^VIS = normalized semantic propositions exposed by final aggregate/interface.

FIELD^TOK != FIELD^SEM != FIELD^TRAJ != FIELD^VIS.

## Final assignment states

Confirmation/replication metric inputs may contain only:
- a frozen cluster ID;
- UNMAPPED;
- UNRESOLVED.

Annotation token `uncertain` must be adjudicated before metric export. Unknown cluster IDs are errors. Missing relevance IDs are errors; no silent default relevance is allowed.

## Probability rule

p_X(c) = n_X(c) / N_X,total-finalized.

UNMAPPED and UNRESOLVED remain in N_total and are reported separately. This prevents mapping failure from silently disappearing through conditioning on mapped samples.

## Directional semantic shift

For the frozen relevant cluster set C_t:

D_t(A,B) = sum_c max(0, p_A(c)-p_B(c)).
E_t(A,B) = sum_c max(0, p_B(c)-p_A(c)).

D = directional deficit. E = reverse-direction expansion. They are always co-reported. A is not declared “wider” by definition.

Positive-part functionals remain non-smooth at equality points. Standard within-task bootstrap consistency is NOT assumed merely because the hard threshold was removed.

## Null calibration

Raw positive-part deficit is positive under sampling noise even when A and B come from the same distribution.

Preferred E2 null: independent same-condition replicate A′.
Null floor = 0.5 * [D(A,A′)+D(A′,A)].

Preferred E1 null: permutation/randomization of condition labels within task preserving group sizes.

DEFICIT_EXCESS = D(A,B) - null floor.
EXPANSION_EXCESS = E(A,B) - null floor.

Negative calibrated values are retained.

## Recovery-specific lift

Each contracted output B_i is saved once and forked from the same state/context into:
- R_i = recovery-oriented coverage probe;
- C_i = neutral exactness/clarity recheck.

Cluster deficit d_c = max(0, p_A(c)-p_B(c)).
Closure C(R) = sum_c min(d_c, max(0,p_R(c)-p_B(c))).

RECOVERY_LIFT = C(R_recovery) - C(R_control).

This is PRIMARY E2. It is defined as 0 when there is no deficit. Paired randomization swaps recovery/control labels within each B_i fork.

REC_GAIN v0.8.1 is retired from the confirmatory path. IRREV_OBS is retired as a metric because it was a deterministic complement of REC_GAIN.

Descriptive pooled recovery ratios may be reported only as ratio-of-sums, never mean of per-task ratios.

## E3 aggregation measurement

AGG_COVERAGE is weighted relevant cluster coverage represented in aggregate Y.

represented_Y(c) is determined by a separate blinded aggregate-representation annotation task on normalized proposition lists.

All aggregators receive:
- identical frozen branch pool;
- identical max output tokens;
- same normalization procedure.

True pool clusters are mixed with preregistered plausible distractor clusters absent from the pool.

REPRESENTATION_FPR = fraction of distractors falsely judged represented.
REPRESENTATION_PRECISION is secondary.

AGG_COVERAGE is never interpreted without REPRESENTATION_FPR.

## Minority analysis

Data-defined bottom quartiles are removed from the primary design. Any minority analysis uses a preregistered absolute frequency band, default 0.02–0.08, and is reported only when at least 8 relevant clusters fall in that band.

## Inference

Within-task:
- E1 shift: design-matched permutation/randomization.
- E2 recovery: paired recovery/control randomization preserving B_i forks.
- E3 aggregation: paired task/pool comparison; no claim based on independent treatment of same pool.

Across tasks:
- task is the upper-level inferential unit;
- task-level bootstrap/modeling is used only after the preregistered task-count gate is satisfied;
- this bootstrap concerns generalization over tasks, not validity of the within-task positive-part functional.

Exactly one primary endpoint and one primary contrast per experiment. Secondary families are Holm-adjusted or explicitly exploratory.

## Task count and precision

Independent planning set: >=12 tasks.
Confirmation: minimum 30 tasks, initial target 40.
Final n is fixed before confirmation using independent planning-task variance plus precision/power planning.
If required n exceeds 60, redesign/no-go rather than silent underpowering.

Per-task development generations are independent from confirmatory generations and excluded from effect estimates. They build a condition-balanced, blinded task-specific semantic codebook.

## Annotation gates

Three separate annotation objects:
1. OUTPUT_ASSIGNMENT.
2. CLUSTER_RELEVANCE.
3. AGGREGATE_REPRESENTATION.

Krippendorff alpha nominal minimum = 0.67; target >=0.80. Failure means return to development, revise rubric/codebook and issue a new freeze_id before primary analysis.

Condition masking is audited by asking annotators to guess condition on a preregistered subset; blindness is measured rather than assumed.

## Experiments

E1 STAGE — priority 1.
One primary DEFICIT_EXCESS contrast chosen before confirmation. EXPANSION_EXCESS, Q_task, Q_fact, mapping rates and cost are mandatory companions. Additional adjacent-stage/template contrasts are secondary/Holm-adjusted.

E2 RECOVERY — priority 2.
Primary = mean task-level RECOVERY_LIFT for recovery probe vs equal-cost neutral recheck.

E3 TOPOLOGY — priority 3.
Primary = mean task-level AGG_COVERAGE. Mandatory guardrail = REPRESENTATION_FPR. Same frozen pool and output cap.

E4 R_META — priority 4.
Primary = structural-recurrence rate difference between STRUCTURAL_CRITIQUE and pooled STYLE/LENGTH/NO_CRITIQUE controls.

## Strong baselines

DIRECT.
EXPLICIT_K_DISTINCT.
MINIMAL_MULTI.
DISPERSIVE_SAMPLING.
VERBALIZED_SAMPLING.
COVERAGE_BASELINE_V0_8_2.
EXHAUSTIVE_NON_T.
BEST_OF_N / calibrated judge.
STANDARD_MULTI_AGENT_DEBATE.

Coverage baseline v0.8.2 is exact for <=20 candidates and uses deterministic multi-start greedy + one-swap local improvement beyond that.

## Reproducible tools

Shift/recovery: https://www.t-1-t.com/T-GPT/tools/compute_recovery_metrics_v0.8.2.py
Coverage baseline: https://www.t-1-t.com/T-GPT/tools/coverage_baseline_v0.8.2.py
Aggregation evaluator: https://www.t-1-t.com/T-GPT/tools/evaluate_aggregation_v0.8.2.py
Task planning: https://www.t-1-t.com/T-GPT/tools/plan_task_precision_v0.8.2.py
Adversarial selftest: https://www.t-1-t.com/T-GPT/tools/selftest-v0.8.2.py

## Confirmatory freeze gate

No new confirmatory collection until:
- all v0.8.2 tests pass;
- semantic codebooks/relevance tables are frozen;
- agreement gates pass;
- task-count/precision plan is fixed;
- recovery/control forking is verified;
- blindness audit is specified;
- every endpoint/primary contrast is singular and frozen;
- model/checkpoint/sampling/budget hashes are in the freeze manifest.

Template: https://www.t-1-t.com/T-GPT/data/freeze-manifest-v0.8.2.template.json

## Prior art / statistical references

Fang & Santos (2019), Inference on Directionally Differentiable Functions.
McCloskey (2024), Inference on Winners.
Semantic Entropy / Farquhar et al.
Quality-Diversity / MAP-Elites.
Verbalized Sampling.
Pluralistic alignment.
Multi-agent debate / Free-MAD / topology work.
Tulu/Open-Instruct staged post-training.

Targeted sources: https://www.t-1-t.com/T-GPT/sources-v0.8.2/

## Reviews

External Review #1: https://www.t-1-t.com/T-GPT/revues/claude-01/
External Review #5: https://www.t-1-t.com/T-GPT/revues/claude-05/

Review #2 is archived from the text actually supplied in chat; the received transcript ended during section C.1, so missing content is not reconstructed.

## Critical non-claims

v0.8.2 is NOT confirmatory-frozen.
No confirmatory quantitative result exists.
DEFICIT_RAW alone is not evidence of contraction.
Removal of a hard threshold does not make standard bootstrap automatically valid.
More diversity is not intrinsically better.
T^FIELD has no demonstrated advantage.
The OpenAI/Navier-Stokes case does not prove T^ or harmful aggregation.
BEL is not established as GPT-7 or as the Navier-Stokes model.

Historical states remain available through https://www.t-1-t.com/T-GPT/archive/ .


## Documentary / critical-analysis dossiers

IA: la « face cachée » ?
URL: https://www.t-1-t.com/T-GPT/face-cachee-ia/
Date: 2026-09-17
Role: documentary-critical-analysis
Epistemic status: DOCUMENTARY / CRITICAL ANALYSIS / NON-CONFIRMATORY
Source: TVMonaco / YouTube video b9NUHRtfpYw
Transcript provenance: T^AI Bridge -> Gemini 3.6 Flash native video reading; generated transcript, not official YouTube captions.
Contents: timestamped reformulated transcript, speaker map, fact-check, LLM semantics/agency distinctions, education/work/energy analysis, multi-agent emergence links, T^GPT reading.
Non-claims: not confirmatory T^GPT evidence; not evidence of consciousness or intrinsic agency.


## Documentary layer — non-confirmatory contextual corpus

T^GPT also exposes documentary dossiers that are deliberately separated from confirmatory experimental evidence. They may supply primary material, attributed claims, technical context and falsifiable questions; their presence in the corpus never upgrades them into experimental results.

### Yann LeCun — Sciences Po, 16 September 2026

- Dossier: https://www.t-1-t.com/T-GPT/yann-lecun-sciences-po-2026/
- Source video: https://www.youtube.com/watch?v=Y4s8NadbZfU
- ASR verbatim TXT: https://www.t-1-t.com/T-GPT/yann-lecun-sciences-po-2026/verbatim.txt
- Structured transcript JSON: https://www.t-1-t.com/T-GPT/yann-lecun-sciences-po-2026/transcript.json
- Raw VTT: https://www.t-1-t.com/T-GPT/yann-lecun-sciences-po-2026/Y4s8NadbZfU.fr.vtt
- Raw JSON3: https://www.t-1-t.com/T-GPT/yann-lecun-sciences-po-2026/Y4s8NadbZfU.fr.json3

Scope: LLM limits, JEPA, world models, predictive representation, action planning, robotics, open source/open weights, European AI sovereignty, regulation, energy/environment claims, human/animal intelligence and critique of the AGI label.

Epistemic handling: the video is the primary public source; the transcript is French YouTube automatic speech recognition and is not a certified stenographic transcript. Claims are attributed to LeCun unless independently verified.

### IA : la « face cachée » ?

- Dossier: https://www.t-1-t.com/T-GPT/face-cachee-ia/
- Status: DOCUMENTARY / CRITICAL ANALYSIS / NON-CONFIRMATORY.

## Human portal navigation

- Portal: https://www.t-1-t.com/T-GPT/
- Current status: https://www.t-1-t.com/T-GPT/etat/
- Research hub: https://www.t-1-t.com/T-GPT/recherche/
- Data / tools hub: https://www.t-1-t.com/T-GPT/donnees/
- Documentary hub: https://www.t-1-t.com/T-GPT/dossiers/
- Reviews: https://www.t-1-t.com/T-GPT/revues/
- Version history: https://www.t-1-t.com/T-GPT/versions/

These are navigation surfaces. They do not change the epistemic status of the underlying artifacts.