*(Historical record, filed 14 July 2026, before the v2.0 rename: "resolution" herein is the framework term since renamed "cohering", and claim labels are as of v1.6. Preserved unedited.)*

# Study C Pre-Commitment Specification: Red-Team Constraint Document

**Referent:** `The_Container_Problem_v0.1.md` (working note v0.1, 14 July 2026), Study C: "Formalising 'cheapest model' (kill authority, mechanism)."
**Role of this document:** the adversarially fixed candidate encoding space and cost function the note itself requires ("candidate encoding space and cost function fixed adversarially before running (Fable as red team)"). This document must be hash-committed and frozen **before** any formalization, implementation, or pilot run of Study C. Any run that precedes the freeze, or deviates from it, has no kill or confirm authority and must be reported as exploratory.
**Discipline:** every threshold, test, and decision rule below is stated so that it can be executed by frozen code, not judged by eye. Where a criterion cannot yet be made executable, that fact is flagged as an open hole that must be closed *in this document, before running*, not in the analysis.
**Date:** 14 July 2026. **Status:** draft for freeze; becomes binding at hash-commit.

---

## 0. The claim under test, restated operationally

The note asserts: *for a system modelling its own selection process under stated compression constraints, the optimal encoding of the unpresentable remainder is medium-shaped, deriving all three signatures (homogeneous, surrounding, empty) rather than mere simplification.*

Decomposed, Study C must show:

1. **Existence of a remainder-modelling demand.** The optimum is not the null (no remainder representation at all). This is non-trivial: compression alone always favours the null.
2. **Medium over scalar.** The optimum is not a mere magnitude ("more available"). This is the "rather than mere simplification, which would just restate Graziano" clause. Note the structural problem stated in §5.2: a medium is strictly more expensive than a scalar under every cost function considered here, so *only task demands, never compression itself, can produce this result*. The note's phrase "under compression constraints" is therefore incomplete as stated and must be read as "under compression constraints *and a fixed task ensemble*" — and the task ensemble is the single largest rigging surface (§3, D6).
3. **All three signatures, independently operationalized.** Homogeneous, surrounding, empty must each pass a frozen executable test (§4.2). "Surrounding" is the expensive one; it is also the one most easily smuggled in via format (§3, D2).
4. **Victory over every live rival at matched capacity**, not merely over a strawman. The full candidate space of §1 must compete.

What Study C **cannot** show even in the best case: that the medium-shaped code is *read phenomenologically as* a container. The bridge from code properties to phenomenology is a posit external to the optimization (§5.3). C retains kill authority (a robustly non-medium optimum kills the mechanism, per the note's falsification conditions) but its confirm authority is capped at "necessary-condition support."

---

## 1. Encoding-space candidates

**Inclusion rule (binding):** the result counts only if all ten families below are implemented, at matched representational capacity (same bit/parameter budget per capacity point on the frozen sweep grid, §4.1) and matched optimization effort (§3, D8). The medium must beat *each* rival under the frozen decision rule, not just the null. Adding a candidate after the freeze restarts the study; removing one voids it.

Each family is specified by: definition (as an architectural/code-family constraint), why it is a live rival, and the phenomenology it predicts — because each rival, if optimal, is itself a candidate explanation of container reports, and the phenomenological predictions are what Studies B and D would then discriminate.

### E0 — Null model (remainder not represented)
**Definition.** The system encodes the figure (attended/selected content) only. No auxiliary code for the remainder; zero bits allocated.
**Why live.** Every cost function in §2 strictly prefers E0 unless the task ensemble penalizes it. E0 is the default winner; the burden of proof is on showing any remainder model earns its bits. Biological precedent: the visual blind spot and inattentional blindness show unmodelled absence can be phenomenologically silent.
**Predicted phenomenology.** No "more"; the figure exhausts the moment; no horizon, no felt periphery, no readiness for the unattended. Predicts naive reports contain no container structure at all — broadly consonant with the Sytsma-line "no problem" folk results the note already cites. If E0 wins, the container is not generated by remainder-modelling and the mechanism is dead.

### E1 — Scalar sufficiency signal ("more available")
**Definition.** One bounded scalar per moment: an estimate of how much task-relevant content is currently unattended-but-available. No structure, no location, no content.
**Why live.** Cheapest non-null code; exactly what metacognition literature already posits (feeling-of-knowing, availability estimates). This is the "mere simplification" that would restate Graziano: an attention schema needs roughly this and no more.
**Predicted phenomenology.** An undifferentiated *fringe* in William James's sense: a non-spatial feeling of moreness, familiarity, or pregnancy without any where. Predicts container reports are post-hoc verbal elaborations of a non-spatial feeling — vocabulary, not structure — collapsing C's result into Lakoff's territory.

### E2 — Bounded-confidence scalar
**Definition.** E1 plus a precision/confidence term: (magnitude, uncertainty), or equivalently a two-parameter distribution over availability.
**Why live.** Standard in bounded-rational and Bayesian metacognition models; nearly as cheap as E1; strictly dominates E1 whenever the task rewards knowing how much to trust the availability estimate.
**Predicted phenomenology.** Graded feeling-of-knowing; tip-of-the-tongue-like states; a moreness that can feel firm or flimsy — still non-spatial. Same deflationary consequence as E1, with the added prediction that container-adjacent reports should covary with metacognitive confidence measures.

### E3 — Edge/boundary gradient at the attention margin
**Definition.** Representation allocated only at the boundary of the selected region: a gradient of decreasing precision/resolution outward from the figure's edge, truncated at small depth. A rim, not a field.
**Why live.** Matches the actual physiology of foveated vision and the psychophysics of peripheral degradation; it is what "horizon" means when read minimally (a local fringe of the figure, which is arguably all Husserl's descriptions strictly require). It buys partial "surrounding" at a fraction of a full medium's cost.
**Predicted phenomenology.** A halo or penumbra: fading margins around whatever is attended, but no closed enclosing space and specifically no "behind me," no omnidirectional envelope. Predicts container reports reduce to peripheral fading plus metaphor. Discriminable from E6 in Study B by items probing enclosure *behind and outside the perceptual field*.

### E4 — Indexical pointer set (addresses of retrievable-but-unretrieved content)
**Definition.** A sparse set of handles: {(address_i, retrieval-cost_i)} for unattended items that could be brought to the figure. Content-free but structure-rich; heterogeneous by construction.
**Why live.** This is the horizon as *accessibility affordances* — the natural formalization of Husserl's determinable indeterminacy and of sensorimotor accounts. In any environment with recurring objects, pointers pay for themselves via retrieval speed-ups. It is the medium's strongest rival at moderate capacity.
**Predicted phenomenology.** The remainder as a set of specific absences: "the door behind me, the rest of the room, the thing I just set down" — structured, itemized potentiality, not an empty medium. Predicts container language decomposes on probing into lists of retrievables. If E4 wins, the container is a misdescription of an affordance inventory.

### E5 — Probability distribution over unattended content
**Definition.** A generative prior: compressed sufficient statistics of the expected unattended scene (gist, scene grammar, amortized posterior). Content-*full* at low resolution.
**Why live.** This is the predictive-processing default and therefore the reigning paradigm's answer; any Study C that omits it will be dismissed on arrival. Amodal completion and boundary extension are empirical evidence that brains actually do something E5-like.
**Predicted phenomenology.** A *furnished* periphery: the remainder experienced as determinate-but-vague expected content (the room continues, the wall is behind me), not as emptiness. Predicts container reports should be scene-dependent and contentful under probing. If E5 wins, "empty" fails and the third signature dies.

### E6 — Homogeneous-medium encoding (the hypothesis's champion)
**Definition.** A field-type code: an index set enclosing the figure's own index set in the code's *learned* geometry (not the format's given geometry — see D2), carrying a constant (permutation-invariant) value asserting existence-without-content at every remainder index.
**Why live.** It is the claim under test. Its honest cost profile must be stated up front: E6 pays for an index set (unlike E1/E2), pays for enclosure topology (unlike E3), and refuses to pay for content (unlike E4/E5). It can only be optimal where omnidirectional availability matters but specific content does not.
**Predicted phenomenology.** The container: a homogeneous, surrounding, empty medium in which contents are presented — the note's target structure, and derivationally, the Space Immanence container error.

### E7 — Procedural/sensorimotor encoding (no declarative remainder code)
**Definition.** The remainder is encoded nowhere as a data structure; it is implicit in the policy — the system's trained dispositions about what attention shifts would yield ("the world as its own model," O'Regan & Noë's outside memory).
**Why live.** It is the deep rival because it breaks the note's inference at its first step: "the system must model this remainder somehow" is false if skillful access substitutes for representation. E7 predicts container phenomenology with *zero* remainder encoding, which would make Study C's entire framing (an optimal *encoding*) a category error.
**Predicted phenomenology.** Presence-in-absence proportional to sensorimotor mastery; container reports tracking skill and environmental stability, not introspective training. Discriminable in B/D: E7 predicts container destabilisation under motor/contingency disruption, not under Ganzfeld figure-ground dissolution.
**Implementation note (binding).** E7 is implemented as the no-side-channel architecture with the policy network free to absorb the equivalent capacity. It is *not* the same as E0: E0 caps total capacity at figure-only; E7 reallocates the remainder budget into procedure.

### E8 — Egocentric point-index
**Definition.** A deictic origin: a single located self-point plus radial availability referenced to it ("more, relative to *here*"). A pointer to the observer, not to the contents.
**Why live.** The note's own Step-0 finding says this is the measured naive default (Starmans & Bloom; Bertossa; Cartesian Folk Theater). If the encoding space cannot represent the point stage, Study C cannot even in principle connect to the trajectory claim (point → container → collapse), which the note calls the discriminating signature. E8 must be present so that the predicted *transition* E8 → E6 under increasing introspective demand is testable (Appendix A).
**Predicted phenomenology.** The located egocenter: experience organized around a point at or near the sensors; no felt enclosing medium. Exactly the untrained-population result.

### E9 — Structured slot/category code
**Definition.** A small fixed set of discrete, labelled background registers (e.g., body, peripersonal space, room, world), each with its own scalar or low-dimensional summary. Heterogeneous, nested, cheap.
**Why live.** Matches the spatial-cognition literature's actual decomposition (peripersonal/extrapersonal systems); a plausible evolutionary layering; costs little more than E2 while capturing most task-relevant structure of the remainder.
**Predicted phenomenology.** Nested, qualitatively distinct background zones rather than one homogeneous medium. Predicts container reports decompose into named strata under careful probing — a direct attack on the "homogeneous" signature.

### Admissible extension (must be decided at freeze, not after)
A relational-graph code (remainder as relations among figure and unattended items, no geometry) was considered and is **folded into E4/E9** as parameter regimes rather than a separate family. If the freeze committee disagrees, it must be added as E10 *now*; adding it after a pilot run voids the study (D-catalogue, §3).

---

## 2. Cost-function candidates and the operational meaning of "compression constraints"

**Binding definition of "compression constraints."** A compression constraint is a numeric budget on the remainder side-channel specifically — bits per timestep (information-theoretic settings) or parameters × precision (learned settings) — swept over a frozen grid (§4.1), applied identically to every candidate family. It is *not* a vague simplicity preference, and it is *not* a budget on the whole system (a whole-system budget lets candidates hide remainder information in the figure code, which contaminates the comparison; a leakage audit is part of the frozen test suite). The freeze must state whether the budget binds (a) the code, (b) the decoder, or (c) both — each choice biases (see F-notes) — and the main analysis must run under at least two of these regimes.

The study must run under **all four** cost-function families below. The hypothesis is confirmed-eligible only if E6 wins under at least two of the four in overlapping capacity bands (decision rule, §4.3). For each family: definition, and the two-sided bias analysis — how it could hand E6 an unearned win, and how it could unfairly kill E6.

### F1 — Minimum description length (MDL)
**Definition.** Two-part code: L(encoding scheme) + L(remainder data | scheme), evaluated over the frozen environment ensemble.
**Rigging risk toward E6.** MDL is relative to a description language. A language with a `fill(region, value)` or run-length primitive makes homogeneous fields nearly free; convolutional weight-sharing does the same silently. This is D1 (§3) in cost-function form.
**Rigging risk against E6.** A pointer-native language (LISP-like, content-addressable) makes E4 nearly free instead. Also: if MDL is computed over raw sensory history rather than over the remainder model, the null wins trivially, because unattended data need never be encoded at all.
**Mitigation (binding).** At least two description languages, adversarially chosen — one field-friendly, one pointer-friendly — both frozen. E6's win counts under F1 only if it holds in both.

### F2 — Rate-distortion with a named distortion metric
**Definition.** Minimize rate of the remainder channel subject to distortion ≤ D, for a *named, frozen* distortion metric.
**Rigging risk toward E6 (severe — flagged as the classic trap).** Under squared-error distortion on content space, the low-rate optimal reconstruction is the conditional mean — a smoothed, homogenized field *by mathematical necessity*. An L2-on-pixels rate-distortion setup "derives" homogeneity vacuously: blurring toward the mean is just what lossy compression does to images. **Binding rule:** homogeneity obtained under L2-on-content distortion is assigned to the null explanation ("mere simplification") and cannot count toward S1.
**Rigging risk against E6.** Hamming/0-1 distortion on discrete content favours E4/E9 (identity-preserving codes); task-irrelevant distortion metrics can make any candidate look arbitrary.
**Mitigation (binding).** The primary distortion metric is *task-referenced*: distortion = expected downstream decision regret on the frozen task ensemble. This moves the rigging surface into the task ensemble — which is where it honestly lives (D6) — instead of hiding it in the metric. Perceptual metrics (LPIPS, SSIM) are **excluded**: they import human visual-system priors and are contamination in the same sense as LLM probing (D5).

### F3 — Predictive loss plus compute budget
**Definition.** Variational/free-energy style: minimize prediction error on the (partially attended) stream plus a compute/amortization cost at inference.
**Rigging risk toward E6.** Two-fold. (a) Max-entropy logic: the cheapest usable prior over unattended content is flat, and a flat prior is "homogeneous" — but a flat prior over content is *not* an encoding of the remainder as an empty medium; conflating them hands E6 a spurious win. The frozen S-tests (§4.2) must distinguish "code that asserts existence at enclosing indices" from "absence of contentful prior." (b) Amortization favours constant, reusable codes — constants are homogeneous for free.
**Rigging risk against E6.** Prediction-error objectives intrinsically reward content (E5): any predictable structure in the unattended stream pulls the optimum toward the furnished periphery. If the frozen environments are highly predictable, E5 wins by construction; if white-noise, E0/E1 win by construction. Environment statistics are therefore part of the freeze (D6).

### F4 — Bounded-rational / rational-inattention variants
**Definition.** Information-cost-constrained decision making (Sims-style rational inattention; KL-regularized control with a fixed default policy; policy compression).
**Rigging risk toward E6.** In KL-control, the *default policy* acts as a prior; choosing a uniform default rigs toward homogeneity exactly as in F3(a). The default policy must be frozen and varied (at least uniform and empirical-marginal defaults).
**Rigging risk against E6.** The information cost prices content-bearing channels (E4, E5) directly but is nearly indifferent among content-free codes (E0, E1, E2, E6) — F4 alone cannot separate medium from scalar and will report false ties. F4 results are therefore interpretable only jointly with the task ensemble's structure demands.

### Compute-cost rider (applies to all four)
Bit-cost and inference-time cost dissociate: media support O(1) "is there more in direction θ?" queries; pointer sets cost O(log n) dereferences; distributions cost sampling. Whether compute is priced, and at what exchange rate to bits, changes the winner. **Binding:** the bits-compute exchange rate is a frozen parameter with a frozen small grid (including zero), and results must be reported across the grid, not at a chosen point.

---

## 3. Experimenter-degrees-of-freedom catalogue

Each entry: the move, why it decides the outcome, detection, and the binding mitigation. Violations detected after running convert the study to exploratory (no kill or confirm authority) and must be reported as such.

**D1 — Basis rigging: representational bases where media are cheap by construction.**
Fourier/DCT bases (a constant field = one DC coefficient), convolutional weight sharing, `fill` primitives, low-rank factorizations — all make homogeneous fields nearly free, so "the medium is cheapest" becomes an artifact of the alphabet. *Detection:* compute each candidate's cost under a basis permutation audit (random unitary re-basing should not reorder candidates if the result is basis-honest). *Mitigation:* two frozen bases, one field-friendly, one pointer-friendly (see F1); win must survive both.

**D2 — Spatial topology smuggled into the format, so "surrounding" comes free.**
If observations arrive as a 2D/3D grid with the figure at the interior, the complement of the attended mask is *already* enclosing — signature S2 is true by format before optimization begins. Egocentric coordinate frames do the same ("around me" is the coordinate system). *Detection:* run the S2 test on an untrained/random code; if it passes above chance, the format leaks topology. *Mitigation (binding):* the primary observation format is permutation-invariant (set/token-based with learned position codes); "surrounding" must be exhibited in the code's *learned* similarity geometry (§4.2, S2), never in the input indexing. Grid-format runs are permitted only as secondary analyses, labelled format-contaminated.

**D3 — Defining "remainder" so that only field-like objects can encode it.**
If the remainder is *defined* as the complement of a spatial mask, it is spatially indexed by fiat, and E1/E2/E4 are handicapped at the definition stage. *Mitigation (binding):* the frozen definition is format-neutral: the remainder is the set of currently-unmodelled causes of future prediction error / retrievable-but-unselected content, individuated by task consequence, not by location. Any spatial structure in the optimum must be *earned* by the code.

**D4 — Soft scoring of "homogeneous / surrounding / empty" after seeing the optimum.**
Verbal, post-hoc judgments ("this looks field-like") are unfalsifiable and were the note's own worry ("'cheapest' in C is rigging-prone"). *Mitigation (binding):* the three signature tests are executable scripts with numeric thresholds, frozen and hash-committed before any run (§4.2). No re-thresholding, no "the test missed the spirit of it."

**D5 — The LLM-probing route, and its subtle variants.**
The note already excludes probing LLMs for container talk as contamination (human container metaphors saturate training data; convergence proves inheritance, not mechanism). **Extension (binding):** the exclusion covers all human-phenomenology-laden components — pretrained vision or language encoders anywhere in the pipeline, perceptual similarity metrics, human-annotated datasets, and human raters scoring code properties. Study C's system must be trained from scratch on synthetic ensembles.

**D6 — Task-ensemble selection (the master degree of freedom).**
Because every cost function prefers cheaper codes, and the medium is strictly costlier than the scalar, *compression can never select the medium; only task demands can* (§5.2). Whoever chooses the tasks therefore chooses the winner: omnidirectional-availability tasks force "surrounding"; pure-detection tasks force the scalar; predictable-content tasks force E5; retrieval tasks force E4. *Mitigation (binding, partial — this DOF cannot be eliminated, only disciplined):* (i) the task ensemble is frozen with a written ecological justification composed before any results exist, arguing each task's presence from the biology/economics of selective systems, not from the hypothesis; (ii) a mandatory *task-sensitivity report*: the win map over task-subsets is a required output, and if E6 wins only on task subsets whose justification presupposes container-like demands, the honest conclusion is "the container is optimal for systems that need containers," which is failure; (iii) at least one task must be non-spatial by construction (D10).

**D7 — Capacity-band cherry-picking.**
Scanning the rate axis until a band where E6 wins, then reporting that band. *Mitigation (binding):* the capacity grid is frozen, and — stronger — the hypothesis must pre-register *which band* it predicts (the note's own logic implies an ordering: high rate → E5/E4, mid rate → E6, low rate → E1/E2, floor → E0). A win in an unpredicted band is a surprise to investigate, not a confirmation.

**D8 — Asymmetric optimization effort.**
More seeds, more hyperparameter search, or better architecture engineering for the favored family. *Mitigation (binding):* per-family tuning protocol and compute budget frozen and equal; all seeds reported; red team implements (or holds line-item veto over) the rival families E4, E5, E7, since a hypothesis-holder's strawman implementation of rivals is the quietest way to rig.

**D9 — The interpreter degree of freedom (bridge scoring).**
Mapping code properties to phenomenological predicates ("this code would be read as emptiness") post-hoc. *Mitigation:* the bridge principles are stated in this document (§1, per-candidate phenomenology) and in §4.2, before results; they are acknowledged as posits, and C's confirm authority is capped accordingly (§0).

**D10 — Building the selection process itself as a spatial spotlight.**
If "attention" in the model is a spatial window, the geometry of the conclusion is imported in the mechanism specification. *Mitigation (binding):* at least two selection-process types must be run — one spatial (windowed glimpse) and one non-spatial (feature-based or memory-retrieval selection over an unordered store). If E6 wins only under spatial selection, the result is about spatial attention, not about modelling-one's-own-selection as such, and must be reported at that reduced strength.

**D11 — Stopping rules and run selection.**
Running until a win appears; excluding "failed" runs as buggy. *Mitigation (binding):* number of runs, seeds, and inclusion criteria frozen; every run reported; a bug-exclusion requires red-team sign-off with the bug identified in code, not in outcome.

**D12 — Threshold placement on the signature tests.**
Choosing the emptiness threshold ε so E6 passes and E5 fails; choosing the homogeneity threshold so E9's slots blur together. *Mitigation (binding):* all thresholds in §4.2 frozen numerically at commit time, with a sensitivity appendix (results across a small frozen threshold grid) mandatory in the report.

---

## 4. Pre-commitment protocol

### 4.1 What is frozen, exactly
The freeze artifact is a single tagged commit (plus OSF registration of its hash) containing:

1. Formal definitions of E0–E9 as code-family constraints, with capacity accounting rules (how bits/parameters are counted per family, including E7's reallocation rule).
2. All four cost functions F1–F4 with exact formulas; the two MDL description languages; the task-referenced distortion metric; the default-policy set for F4; the bits-compute exchange-rate grid.
3. The environment/task ensemble generator, seeds included, with the written ecological justification (D6) as a dated document.
4. The capacity sweep grid and the predicted win-band (D7).
5. The observation format specification (permutation-invariant primary; grid secondary, labelled) (D2).
6. The two selection-process implementations (D10).
7. Per-family optimization budgets and tuning protocols (D8); run counts and seeds (D11).
8. The three signature test scripts with numeric thresholds (§4.2) and the leakage audit script (§2, preamble).
9. The decision rule (§4.3), verbatim.
10. The failure-reporting conditions (§4.4), verbatim.

### 4.2 Hard operational criteria for the three signatures
All tests are executable scripts operating on the trained/derived optimum; thresholds (ε, δ, α, τ) are placeholders that must be replaced by frozen numbers at commit, after pilot calibration on *synthetic reference codes* (hand-built exemplars of each family E0–E9), never on study runs.

**S1 — Homogeneous.** Partition the remainder (under the format-neutral definition, D3) into K task-consequence-matched parts. Requirement: the code's part-wise components (or its Jacobian with respect to part perturbations) are statistically exchangeable across parts — distance between part-responses indistinguishable from the encoding noise floor at frozen level α. E9 (slots) must fail this test on reference implementations, or the test is miscalibrated and must be fixed before freeze.

**S2 — Surrounding.** Only valid under the permutation-invariant format (D2). Recover the code's latent geometry from its own similarity structure (frozen embedding procedure applied to code responses under localized perturbations). Requirement: an *enclosure statistic* — along random directions in the recovered geometry from the figure-code centroid, a remainder-coded region is encountered before the boundary of the coded manifold in at least (1 − τ) of directions — passes at frozen τ, **and** the same statistic on an untrained/random control code fails (format-leak control, D2). E3 (rim) reference implementations must score intermediate; E1/E2 must fail; if not, recalibrate before freeze.

**S3 — Empty.** Two-sided information criterion: I(code; remainder content identity) < ε **and** I(code; remainder existence/volume) > δ. The first clause separates E6 from E5 (furnished) and E4 (indexed); the second separates E6 from E0 (null) and from a degenerate constant. Mutual information estimated by the frozen estimator named in the registry (estimator choice is itself a DOF; freeze it).

**Joint requirement.** The optimum must pass S1 ∧ S2 ∧ S3. Passing two of three is failure, not near-success; the note demands the derivation of *all three* signatures explicitly.

### 4.3 Decision rule and adjudication
E6 is declared the winner if and only if:
(i) at some point(s) of the frozen capacity grid *within the pre-registered band*, E6 achieves strictly lowest cost among all ten families under at least two of F1–F4;
(ii) the E6 optimum at those points passes S1 ∧ S2 ∧ S3;
(iii) every rival at those points either has strictly higher cost or fails at least one signature (i.e., no rival matches both cost and signatures);
(iv) (i)–(iii) replicate across both representational bases (D1), both selection-process types (D10), and all frozen seeds, with the task-sensitivity report (D6) showing the win is not confined to container-presupposing task subsets.
All ties, borderline threshold cases, and estimator ambiguities resolve **against** the hypothesis.

**Adjudication.** The frozen scripts are the adjudicator; humans adjudicate only *conformance to the freeze*, and that role belongs to the red team (Fable), which additionally: implements or holds veto over rival-family implementations (D8), signs off on any bug exclusion (D11), and countersigns the final report. The hypothesis author does not run the final sweep; an executor who did not write the hypothesis note does. Any deviation from the registry — however reasonable it looks mid-study — is recorded, and its existence converts the run to exploratory.

### 4.4 Honest reporting: conditions under which Study C must be reported as FAILED
Study C is reported as failed (not "promising," not "suggestive") if **any** of the following hold:

1. A non-medium family wins robustly under the decision rule's conditions — this is the note's own falsification condition ("a non-medium-shaped optimum in C under adversarially fixed constraints") and triggers the drawer.
2. E6 wins but only under one cost function, only in one basis, only under spatial selection, or only outside the pre-registered capacity band.
3. E6 wins but the task-sensitivity report shows the win confined to tasks whose ecological justification is found (by the red team) to presuppose container-like demands.
4. Any signature test, threshold, candidate definition, or ensemble parameter was modified after the freeze.
5. The encoding space is discovered mid-study to have omitted a live rival: the fix is a new freeze and a full restart, and the original run is reported as failed-by-incompleteness.
6. **Formalization failure:** "a system modelling its own selection process" cannot be specified without violating D2/D3/D10 — i.e., without smuggling in the spatial structure to be derived. This outcome must be published as a result ("the mechanism claim is not currently formalizable"), not silently absorbed into redesign. Per §5, this is a live possibility, not a formality.
7. The E6-favourable result depends on the L2-distortion homogenization artifact (F2 binding rule) or the flat-prior conflation (F3 binding rule).

A failed C does not by itself kill the container-problem programme (B carries the existence question independently), but it kills the *mechanism* claim's current formulation, and the note must be revised to say so.

---

## 5. Feasibility verdict

### 5.1 The strongest case that C is not formalizable as posed
Three arguments, in descending order of severity.

**The reflexivity/regress problem.** "A system modelling its own selection process" requires the model of selection to be itself a product of selection. Formalizing this forks: (a) *break the loop* — treat the selection process as an external object the system estimates, like any partially observed variable. But then the "unpresentable remainder" is ordinary POMDP hidden state, its unpresentability is garden-variety partial observability, and nothing distinguishes the container hypothesis from routine state estimation — the phenomenological specialness the note needs has been defined away. Or (b) *keep the loop* — demand a fixed point where the selection process selects its own model. There is no assurance the fixed point is well-posed, and the degenerate fixed point (model nothing about your own selection: E0) is always available and always cheapest. Either fork is bad: (a) trivializes, (b) may be vacuous. Deeper still: "unpresentable" is doing philosophical work no optimization target can capture — any formally specified remainder is, by that specification, presented to the formalism. The formal study can only ever concern the *system's* code for what *it* does not present, specified from a God's-eye view the system lacks; whether that captures "the ground that funds the figure" is not decidable inside C.

**The scalar-dominance problem.** As established in §2 and D6: every compression principle strictly prefers E1 to E6, because a medium is a scalar plus an index set plus enclosure topology. Therefore the note's core sentence — "under compression constraints the default encoding of a more-that-cannot-be-shown is a homogeneous, surrounding, empty medium" — is, as literally stated, false: under compression constraints alone the default is the null, then the scalar. The claim is only coherent as a *conditional*: there exists a task-and-rate regime, ecologically plausible for introspecting systems, in which the medium is uniquely optimal. That is a weaker, honest, testable claim — but the task ensemble that defines the regime is chosen by the experimenter, and no freeze protocol fully launders that choice (D6 disciplines it; nothing eliminates it). The note should be amended to state the conditional form before C is attempted.

**The bridge problem.** Even a maximal positive result exhibits a data structure with three formal properties. "Read phenomenologically as a container" — the step that connects C to the hard-problem territory the programme cares about — is a posit no optimization can test. C is therefore constitutionally asymmetric: it can kill the mechanism (non-medium optimum → drawer) but can at best supply necessary-condition support for it. The pre-registration must state this asymmetry so a positive result cannot be inflated later.

### 5.2 Verdict
**C as posed — deriving the container from modelling-one's-own-selection as such, under compression alone — is not formalizable without presupposing part of the conclusion.** The honest reformulation is: *"there exists a non-rigged (independently justified) task/rate regime in which the medium encoding is uniquely optimal against all live rivals and exhibits all three signatures under frozen tests."* This is an existence claim, not a universality claim; it retains full kill authority and capped confirm authority. The note's authors should either accept this downgrade explicitly in v0.2 or strike C's mechanism-confirmation role.

### 5.3 Minimum viable toy model that is still informative
Two tiers, the first of which should be attempted before any code is written.

**Tier 1 (analytic, weeks not months).** An exchangeable-source problem: a source of N content elements, an attention mask revealing k of them, an auxiliary channel of R bits about the N−k unattended elements, and a downstream objective family spanning (a) reorientation (choose where to attend next), (b) unattended-change detection, (c) availability estimation. Derive, as a function of (R, objective mix), the form of the optimal auxiliary code, and check which regions of the plane are occupied by codes isomorphic to E0/E1/E4/E5/E6 (E6 defined here as: exchangeable across unattended elements ∧ existence-affirming ∧ boundary-indexed in the induced geometry). **Kill power:** if no (R, objective) region yields an E6-isomorphic optimum even in this maximally clean setting, the mechanism is dead without a single training run. **Limit:** exchangeability partially begs S1's question; the Tier-1 write-up must say so.

**Tier 2 (computational).** A glimpse-based agent on a synthetic partially-observable environment; permutation-invariant observation format (D2); explicit bottlenecked side-channel for the remainder code; the ten families as architectural constraints; the four cost functions; frozen tasks T1 (where-to-look-next efficiency), T2 (unattended-change detection), T3 (availability estimation), T4 (a non-spatial selection task: retrieval over an unordered memory store — the D10 control). Everything per §4.

**What the minimal result would mean.** A Tier-2 win under the decision rule is an existence proof that medium-shaped remainder codes occupy a non-rigged optimum region — enough to promote "darkening" from placeholder toward formal object, not enough to establish it as *the* default of selective systems. A loss is a clean kill under the note's own falsification conditions. Either outcome is informative; that is the standard C must meet, and under this document's constraints, it can.

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## Appendix A — Secondary pre-committed prediction: the trajectory transition (no kill authority unless separately frozen)
The note's discriminating signature is the sequence point → container → collapse. Study C can add a cheap secondary test: introduce an *introspective demand* parameter λ (weight on tasks that require modelling the selection process itself — e.g., predicting one's own next attention shift — rather than merely modelling unattended content). Pre-committed prediction: as λ rises at fixed capacity, the optimum should transition E8-like → E6-like, and at high λ with tight capacity, degenerate (collapse toward E0/E1 — the code stops maintaining enclosure when the ground itself is figured). If frozen alongside the registry with its own thresholds, this becomes the only part of C that touches the trajectory claim; if not frozen, it is exploratory garnish and must be labelled as such.

## Appendix B — Source notes
Standard results relied on above and citable from the general literature: rate-distortion optimum under squared error is the conditional mean (Shannon/Berger, standard); rational inattention (Sims); KL-control default-policy priors (Todorov; Kappen); MDL language-dependence (Rissanen; Grünwald); the "fringe" (James, *Principles*, ch. IX); outside-memory/sensorimotor account (O'Regan & Noë 2001); peripersonal/extrapersonal dissociations (standard spatial-cognition literature). No web verification was performed for this document; none of these attributions is load-bearing for the constraints themselves, which stand on the arguments as written. Any citation used in the eventual C report must be verified at that time.