What a temporal construction must distinguish

4. Information, construction and conditional sufficiency

4.1 Order must survive the operative code

Proposition: 1. Order-invariant code

Let $a$ map input histories to all information available to a nominated order interpretation. If $a(C,E)=a(E,C)$, no fixed deterministic or stochastic readout of $a$ can discriminate these two orientations.

Proof. Equal arguments give equal outputs to a deterministic readout and equal response distributions to a fixed stochastic kernel. That code alone therefore cannot supply orientation-dependent discrimination.

The result constrains the particular order distinction. It neither makes timestamps or language necessary nor denies experience when order is unresolved. A listener can experience features, fusion or uncertainty.

Three distinct pitch categories yield six ordered pairs and only three unordered pairs when repetitions are excluded. A lossless code separating all six requires at least six states. Under equiprobable pairs the entropy is $\log_2 6=2.58496$ bits; a fixed-length binary implementation needs three bits. Once an unordered pair is known, its orientation requires one binary distinction.

Let $Y$ denote orientation, balanced within each unordered pair $Q$, and let $X$ be the operative code. If the optimal decision from $(X,Q)$ has error $\epsilon\leq1/2$, then

$$I(Y;X\mid Q)\geq1-h_2(\epsilon). \tag{5}$$

Here $h_2$ is binary entropy. Given $(X,Q)$, the decision and its error bit determine $Y$, so $H(Y\mid X,Q)\leq h_2(\epsilon)$; subtracting from balanced orientation entropy proves the bound. At 10% error, at least 0.5310 bits are required. This is an order-discrimination constraint, not a consciousness measure.

4.2 Why the actual transition is sufficient within the framework

Proposition: 2. Enacted ordered transition

Take the qualifying human unit with an admissible formative assignment. Its actual activity receives distinguishable contributions, retains a predecessor, interprets and consolidates a directed relation to current input, and preserves that construction sufficiently for actual uptake. Suppose grounded interpretation differentiates live and retained roles. Under equation (1) and Constitutive premise 1, this enactment constitutes an experience of the ordered transition, including its felt character.

Proof. Reception supplies $D$; grounded discrimination and relating supply $I$; operative binding supplies $C$; retention through that relating supplies $M$; actual interpretive use supplies $U$. The nominated unit and preserved history supply the remaining admission conditions. Predecessor, successor and directed change belong to the interpreted organization in their respective modes. Under complete-enactment identity they belong to experience itself.

The role labels alone would not determine which transition occurs. The specified construction distinguishes $C$-before-$E$, reversal and fusion. A feature bag or sealed archive does not substitute for these relations. Later addressed retrieval remains possible but is unnecessary to the proof.

Proposition: 3. No additional constitutive flow

For an actual enactment meeting Proposition 2, the specified local reception, retention, directed integration and uptake are sufficient within the framework for temporal experience. An advancing-present variable, outside observer or further conversion into experience is not an additional constitutive requirement.

Proof. Proposition 2 supplies qualification and the interpreted transition. Constitutive premise 1 identifies complete qualifying enactment with experience. The differentiated temporal roles are already realized within the activity: incoming contribution, retained predecessor, directed binding and uptake. No omitted conjunct remains for a separate observer or moving present to perform.

The finite implementation in the next chapter gives this argument physical content. It specifies realizable component functions and discriminating countermodels. Applying them to a human listener still requires their actual integration into that person's activity. A representation or detached circuit alone does not establish that integration.

4.3 Preservation of complete organization

Proposition: 4. Constitutive invariance

Let actual qualifying enactments $K,K'$ preserve the complete relevant interpreted organization, uptake, implementation, and causal, source and formative embedding. Within this framework, an added property $F$ changing none of those constitutive facts cannot change experiential admission or character.

Proof. Preserving the right-hand side of equation (1) preserves admission. Constitutive premise 1 places character within complete qualifying organization, so preserving that organization preserves character. The occurrences can nevertheless remain numerically different tokens.

This premise is stronger than an equal report, neural snapshot or temporal projection $\mathcal T(K)$. Changing appraisal, calibration, bodily organization or uptake can alter experience without contradicting it. A rival claiming changed character at fixed complete enactment rejects the constitutive identity. A missing variable in a partial model instead motivates improving that model. The two objections have different targets.