An external cognitive system can store information, recommend actions, or control a device without becoming part of a person's continuing cognitive process. This paper defines a stricter candidate architecture. An Extended Brain is a reciprocal, adaptive human-machine system in which inspectable human, artificial, and shared-workspace states repeatedly change one another during a task. The associated thought-density hypertime hypothesis proposes that such coupling could increase useful cognitive updates that a person accesses, uses, and later recovers per unit of physical time. It does not propose that world-clock time or biological lifespan changes. The historical program is separated from the scientific test. Contemporaneous 2012 Simplenote records separately document proposed brain-computer interface, extended-brain or artificial-cortex, and sentient-artificial-brain branches. Public 2017 Neural Lace sources develop a distributed path from artificial neocortex to expanded thought workspace, higher cognitive throughput, concurrent thought, and altered time experience. November 2021 notes consolidate the three-project recollection while separately identifying quantum-gravity work as a new fourth branch; 2022 Git records fix the clearest compact hypertime statement. This genealogy establishes development history, not scientific validity. Draft 2 froze five within-participant conditions: unaided baseline, ordinary tool, adaptive but nonreciprocal AI, reciprocal closed loop, and content- and latency-matched yoked replay. A human-integrated event must be novel, accessible, consequential, nonduplicative, timestamped, and provenance-labeled. Support requires three sequential gates: the lower confidence bound for reciprocal performance must exceed each strong control by 0.20 standard deviations; the lower bound for strict integrated-event rate must exceed each by 15 percent; calibration and agency must then remain within noninferiority margins. Time outcomes cannot rescue gate failure. Draft 3 adds a coupled-state model, task and latency contracts, agency, memory-provenance, identity-continuity and decoupling measures, Monte Carlo power sensitivity, and synthetic parameter recovery. The power analysis exposed a design defect. Under the frozen stringent confidence-bound rule, 270 completers yielded only 46.5 percent sequential success in 2,000 simulations even when the true reciprocal advantage was 0.35 standard deviations and the event-rate ratio was 1.30. A sample-size sweep first exceeded 80 percent at 540 completers under those assumptions. This is not a universal required sample size: pilot variance, attrition, coder uncertainty, task correlation, and observed event dispersion must inform the final lock. It does show that 270 cannot remain the unexamined confirmatory target. Draft 4 adds a source-bound empirical bridge and a stricter subjective-time preregistration. Human fMRI evidence shows that trial-by-trial duration-report biases during naturalistic viewing can be reconstructed from salient-event dynamics in stimulus-relevant visual cortex [13]. This supports measuring event structure and subjective duration together. It does not show that more thoughts per second universally slow felt time, that machine events become human thoughts, or that reciprocal coupling extends subjective lifespan. The study therefore retains performance and strict human-integrated event density as the sequential mechanistic gates and tests prospective duration, retrospective duration, felt passage, temporal resolution, and remembered boundaries as separate secondary outcomes. A separate correctly specified linear simulation recovered reciprocal human-to-artificial and artificial-to-human cross-lag parameters across five latency levels with maximum absolute error 0.0201. At 50 ms, reciprocal estimates were 0.2568 and 0.2785, whereas yoked replay recovered human-to-artificial coupling of 0.0028. Recovered reciprocal coupling declined monotonically as latency increased, and every local linearization remained stable. These are synthetic identifiability results, not evidence that an Extended Brain exists. A second robustness audit shows why the confirmatory analysis must address attrition and misspecification: observed-risk weighting corrected a generated missing-at-random bias, but it could not correct outcome-dependent missingness; omitting shared-workspace state created false reciprocal paths in a nonreciprocal fixture; lag mismatch and measurement error attenuated generated coupling. No participant data have been collected or opened. The current contribution is a reproducible methods correction and failure-detection framework. Draft 5 implements the pre-participant runner contract. It freezes 300 unique, hashed task instances across five conditions: 12 dynamic-planning, 8 evidence-integration, and 40 spatial-transformation instances per condition. Planning instances contain three deterministic hidden changes; evidence instances contain two planted conflict pairs; one quarter of spatial instances contain state-reconstruction probes with machine-checkable answers. A separate schedule contains 180 A/R/Y latency assignments with identical bin distributions and maximum standardized mean difference 0.0. The event-coder template exposes the five strict inclusion criteria and four provenance labels while withholding condition. Eleven validation checks pass. These are software-mechanics results only; no participant responses or outcomes were generated.