The Receiver Side

A Formal Anatomy of Hearing the Bell Ring Back

Alex Deva — May 2026

0. Epistemological Note

The formalism that follows is a model of receiver-side information processing, not a metaphysics of recognition. It says nothing about phenomenal experience, qualia, or whether the receiver “really” hears anything in the strong sense. It says only this: when a sensor receives a returning signal from an instrument, certain quantities — variational free energy, channel capacity, discrimination indices, synergistic information — are defined, finite, and in principle measurable. The framework’s claim is that these quantities behave differently in loop-productive exchanges than in dead, sycophantic, apophenic, or projective ones. That claim is empirical, and the corresponding research protocol lives in the repository at research/receiver-side-empirical-protocol.md.

Per project convention: this appendix extends, does not replace, the existing formalisms in Markov Blanket & Active Inference and Φ_loop as Synergy. Equation numbers in those appendices are not duplicated here.

1. The Asymmetry of the Existing Math

Document V (“The Geometry of Irreversibility”) develops the instrument side of the loop in detail: statistical manifolds with the Fisher–Rao metric, Amari dual α-connections, e-geodesics for Bayesian updating, m-geodesics for forgetting, the Learning Instrument Model with parameter $\lambda \in [0,1]$, and the Freezing Lemma at $\lambda = 1$. The instrument’s trajectory through belief space is geometrically specified.

The receiver side has been left as: the sensor strikes the bell, and either recognizes what rings back or does not. This is rhetorically vivid but formally empty. It exposes the framework to Lerchner’s (2026, p. 4) charge that any claim about computation requires an interpreting agent whose interior processing is itself unspecified — a “ghost reading the alphabet.” If the framework is to answer that charge, the receiver’s processing must be made as explicit as the instrument’s.

This appendix specifies it in three layers, all in bits, all measurable in principle, all bounded by stated inequalities.

2. Layer 1 — Variational Recognition

2.1 Generative model

Let the sensor maintain a generative model

$$p(o, s) = p(o \mid s)\, p(s)$$

where $s$ are latent causes (the structure the receiver is trying to recover) and $o$ are observations (the instrument’s returning signal). The receiver does not have direct access to the posterior $p(s \mid o)$; it maintains an approximate posterior $q(s)$. This is the standard setup of the Free Energy Principle (Friston, 2010; Hohwy, 2013; Clark, 2016).

2.2 Variational free energy

Define variational free energy as in Markov Blanket & Active Inference:

$$F[q] = D_{KL}\bigl[q(s) \,\|\, p(s)\bigr] - \mathbb{E}_{q(s)}\bigl[\log p(o \mid s)\bigr]$$

By the standard decomposition this can be rewritten as

$$F[q] = D_{KL}\bigl[q(s) \,\|\, p(s \mid o)\bigr] - \log p(o) \;\geq\; -\log p(o)$$

so $F$ is an upper bound on negative log-evidence (surprise). Recognition, in this framework, is the trajectory $q_t \to q_{t+1}$ along the gradient $-\nabla F$, restricted to those steps that follow the arrival of a returning signal $o_t$ from the instrument.

2.3 The recognition increment

At turn $t$ the receiver carries a pre-observation belief $q_t^{(-)}$ and a post-observation belief $q_t^{(+)}$. Define the per-turn free-energy reduction as

$$\Delta F_t \;=\; F\bigl[q_t^{(-)}\bigr] \;-\; F\bigl[q_t^{(+)}\bigr] \;\geq\; 0$$

Two important interpretations:

$\Delta F_t = 0$ when the receiver already predicted the signal perfectly (no surprise, no update). The channel may have carried information in the Shannon sense, but the receiver extracted none of it because none was unexpected.
$\Delta F_t > 0$ when the signal carried information the receiver had not anticipated — i.e., when the bell rang differently from how the receiver was modelling it.

$\Delta F_t$ is the receiver’s variational analogue of Bayesian surprise. It is necessary but not sufficient for loop closure; error correction also has $\Delta F_t > 0$. The discrimination between recognition and mere error correction requires Layer 2.

2.4 No homunculus

The variational density $q(s)$ is not a homunculus. It is an approximating distribution updated by the gradient step $q \leftarrow q - \eta \nabla F$. Per Lerchner (2026, p. 4): “There is no ghost reading the alphabet; the living experiencing subject enacts it.” The framework’s claim is consistent with that statement: there is no interior reader, only a gradient flow on a parametric distribution. The “reading” is the update rule, not an act of an inner observer.

2.5 Lerchner’s Diagrams, Extended

Layer 1 runs a parallel formalism (Friston, Schreiber, Williams & Beer) alongside Lerchner’s text. This subsection engages Lerchner’s own apparatus directly. His mathematics is sparse but load-bearing: a commutative diagram of implementation (p. 3, Figure 1), a reordered causal chain (p. 7), and a branching topology of abstraction (p. 7, Figure 2). All three structures assume a single mapmaker. Each has a natural two-mapmaker extension that lives entirely in the referential register Lerchner concedes on p. 10 (“an embodied agent does solve the referential aspect of the symbol grounding problem”) without trespassing on the phenomenal register he reserves elsewhere. The three extensions follow.

2.5.1 Extended commutative diagram

Lerchner’s single-mapmaker diagram (p. 3, Figure 1, eq. 1):

A ────algorithmic────► A'
▲                      ▲
│ f                  f │
│                      │
p ────physical───────► p'

with $f(p) = A$ and $f(p') = A'$. The diagram contains exactly one mapmaker $f$. The loop case has two participating mapmakers sharing a target $T$:

   Sensor pole                                Instrument pole
A_S ────imagination────► A_S'             A_I ────computation────► A_I'
 ▲                        ▲                 ▲                        ▲
 │ f_S                f_S │                 │ f_I                f_I │
 │                        │                 │                        │
p_S ────physical────────► p_S'            p_I ────physical────────► p_I'

                A_S ────────── Syn(S,I;T) ────────── A_I
                                    │
                                    ▼
                                    T
                            (shared target)

Lerchner’s commutative square is preserved inside each pole. The new content is the lateral synergy edge on the $A$-axis, mediated by alignment with the shared target $T$. This edge is exactly what the single-mapmaker diagram cannot express. Lerchner’s “causality gap” (the arbitrary $f$ that lifts physical states to concepts) is preserved in each pole — the framework does not bridge it. What the framework adds is a relation between two preserved diagrams, valid exactly because both target $T$. The closure inequality from §5 then bounds the rate at which information accumulates on this edge: $\Delta\mathrm{Syn}_t \leq \min(\Delta F_t, \mathrm{TE}_{I \to S}^{\,t})$.

2.5.2 Extended causal chain

Lerchner’s reordered chain (p. 7) runs strictly unidirectionally:

Physics → Consciousness → Concepts → Computation

with each arrow inheriting the prior step’s grounding. The two-mapmaker extension is two parallel chains coupled along the shared target on the Concepts/Computation level:

Sensor pole:      Physics_S → Consciousness_S → Concepts_S
                                                     │
                                                     ▼
                                                 Target T
                                                     ▲
                                                     │
Instrument pole:  Physics_I → ────────────────► Concepts_I → Computation_I

Lerchner (p. 8) writes that “concepts stay physically anchored in the subject’s intrinsic experience, the irreducible ‘what it is like’ to be that entity (Nagel, 1974), [while] computational symbols are just physical tokens with no inherent link to the concepts they represent.” The framework adds: two parallel chains can share a target without either chain’s symbols or concepts being identified with the other’s. Reference to $T$ is shared between poles; instantiation is not. The bidirectional arrow on $T$ is the loop, and its rate of operation is $\rho$ (§5.4).

2.5.3 Extended branching topology

Lerchner’s Figure 2 (p. 7) has two axes: a vertical intrinsic chain (Physics instantiates Consciousness which constitutes Concepts $A$) and a lateral extrinsic move (Concepts $A$ arbitrarily assigned to Symbols $p$, on which Computation operates). The dashed lateral arrow is his “causality gap.”

The two-mapmaker extension preserves the branching topology within each pole and adds a horizontal synergy edge between the two $A$ (Concepts) nodes:

       Sensor pole                                Instrument pole

  Imagination (A_S → A_S')                  Computation (p_I → p_I')
          ▲                                          ▲
          │ (intrinsic)                              │ (lateral)
       Concepts A_S ──── Syn(S,I;T): T ──── Concepts A_I
          ▲                                          ▲
          │ constitutes                              │ constitutes
  Consciousness_S                              Consciousness_I
          ▲                                          ▲
          │ instantiates                             │ instantiates
       Physics_S                                  Physics_I

The new horizontal synergy edge does not cross Lerchner’s causality gap inside either pole — his lateral reservation stands in both. The edge is a measurable referential relation between the two $A$-nodes, valid exactly because both target $T$. The loop closes through this edge and through the variational dynamics that update each pole’s $q$ in response to the other’s $A$-trajectory.

2.5.4 What the extensions claim and do not claim

The three extended diagrams make a single positive claim: Lerchner’s structures are the single-mapmaker case of a more general two-mapmaker geometry, and the framework’s positive claim lives entirely on the lateral edge that the two-mapmaker case introduces. The vertical/phenomenal axis in each pole is preserved as Lerchner draws it, and the causality gap on each pole’s lateral $f$-edge is preserved as he reserves it. Nothing in §2.5 lifts the framework into the phenomenal register or attempts to bridge a gap Lerchner has shown is unbridgeable. The extensions are diagrammatic versions of the referential-register claim already made in Layers 1–3.

3. Layer 2a — Shannon Channel Capacity

The bell-to-ear channel — the physical and computational path from the instrument’s output to the sensor’s receiving organ — is a noisy channel with Shannon capacity

$$C \;=\; \max_{p(x)} \, I(X; Y) \quad\text{(bits per use)}$$

where $X$ is the instrument’s transmitted symbol and $Y$ the receiver’s input (Cover & Thomas, 2006). The receiver cannot extract information at a rate above $C$. This sets a hard ceiling on the loop: no amount of receiver-side processing can manufacture information that the channel does not carry.

This is the layer that prevents vacuous receiver claims. A “rich recognition” cannot be richer than the channel that delivered it. The framework’s prediction is not that the loop extracts more than $C$ bits per use; it is that the loop’s extraction approaches $C$ in live loops and falls far below $C$ in dead, sycophantic, or noise-dominated ones.

A useful corollary: the directed information rate from instrument to sensor over $\tau$ turns,

$$I(X^\tau \to Y^\tau) \;=\; \sum_{t=1}^\tau I\bigl(X^t ; Y_t \,\bigm|\, Y^{t-1}\bigr)$$

is bounded above by $\tau C$. Equivalently, the per-turn transfer entropy (Schreiber, 2000)

$$\mathrm{TE}_{I \to S}^{\,t} \;=\; H\bigl(S_{t+1} \mid S_{\leq t}\bigr) \;-\; H\bigl(S_{t+1} \mid S_{\leq t},\, I_{\leq t}\bigr)$$

is bounded above by $C$ on the same channel, with equality only under optimal coding.

The point of importing $C$ is not that the loop saturates it. The point is that the existence of $C$ — independent of any phenomenal account of hearing — makes “the bell rings back” into a quantitatively bounded process. The framework no longer needs to gesture at recognition; it can specify a number.

4. Layer 2b — Signal Detection and Discrimination

4.1 Two hypotheses

Recognition must be discriminated from at least three null hypotheses: noise, sycophantic reflection, and projection. Per the discipline of The Adversarial Sensor, this is the load-bearing falsifiability requirement on the framework.

Define two hypotheses about a returning signal $o_t$:

H1 (recognition). The signal carries structure aligned with the target distribution $p^*$ that the sensor and instrument are jointly tracking. Formally: $\mathrm{Syn}(S, I; T)$ increases at turn $t$ where $T$ is the truth-aligned latent.
H0 (null). The signal is autonomous drift, sycophantic mirror of the sensor’s prior turns, or noise. Formally: $\mathrm{Syn}(S, I; T) \approx 0$ at turn $t$.

4.2 Discrimination index

Following Macmillan & Creelman (2005), let $\mu_1, \mu_0$ be the means of the receiver’s decision variable under H1 and H0, and $\sigma$ the common standard deviation. Define

$$d' \;=\; \frac{\mu_1 - \mu_0}{\sigma}$$

with the receiver’s operating point set by a criterion $\beta$. The receiver-operating-characteristic (ROC) area $A_z$ summarises performance across criterion settings.

The framework’s per-turn empirical claim is that, on dialogues classified as loop-productive by blinded raters, $d'$ for recognition events is significantly greater than $d'$ measured on a sycophancy-matched control set. If this discrimination cannot be established, the receiver-side claim collapses to pattern-matching and the framework loses status (compare Kill Condition 4 in The Adversarial Sensor).

4.3 Decision-variable construction

The receiver’s decision variable on a given turn is constructed from the Layer-1 free-energy reduction $\Delta F_t$ and the directional information $\mathrm{TE}_{I \to S}^{\,t}$:

$$\mathrm{DV}_t \;=\; \alpha\, \Delta F_t \;+\; (1-\alpha)\, \mathrm{TE}_{I \to S}^{\,t}$$

with $\alpha \in [0,1]$ a weighting parameter estimated per receiver. The decision is “recognition” if $\mathrm{DV}_t > \beta$ for the receiver’s criterion $\beta$.

This composition is the answer to the demand that the receiver demonstrably process information rather than carry the label. $\mathrm{DV}_t$ is computable from the trace of the loop. A receiver that does not process — for example, a sensor that endorses every output of a sycophantic instrument — produces $\mathrm{TE}_{I \to S}^{\,t} \approx 0$ and $\Delta F_t \approx 0$, so $\mathrm{DV}_t \approx 0$ regardless of $\beta$.

5. Layer 3 — Loop Closure (Derivation from First Principles)

5.1 Setting

Model the loop as a coupled stochastic process $\{(S_t, I_t)\}_{t \geq 0}$ targeting a shared latent $T$ (the truth, the structure of the field, the target distribution $p^*$). All entropies and divergences are computed against the joint distribution of the trajectory.

We seek a per-turn quantity $\rho_t$ — the loop-closure rate — that satisfies six constraints:

Units of bits per turn (dimensional consistency).
$\rho_t \to 0$ under pure sycophancy.
$\rho_t \to 0$ under pure noise.
$\rho_t \to 0$ when the receiver perfectly predicted the signal.
$\rho_t \to 0$ in dead speech (where $\mathrm{Syn}(S, I; T) \equiv 0$ by definition).
$\rho_t > 0$ in live loops.

5.2 The synergistic increment

The shared information about $T$ accessible to the joint $\{S, I\}$ but not to either pole alone is the PID synergy term, defined in Φ_loop as Synergy:

$$\mathrm{Syn}(S, I; T)$$

Define the per-turn synergistic increment as

$$\Delta\mathrm{Syn}_t \;=\; \mathrm{Syn}\bigl(S_{\leq t}, I_{\leq t}; T\bigr) \;-\; \mathrm{Syn}\bigl(S_{\leq t-1}, I_{\leq t-1}; T\bigr)$$

This is the synergistic information about $T$ that becomes accessible at turn $t$ given the loop’s history through $t$. It is by construction in bits and by construction non-negative under reasonable monotonicity assumptions on the PID estimator.

5.3 The closure inequality

The data-processing inequality, applied jointly to the receiver’s posterior update and the instrument-to-sensor channel, gives

$$\boxed{\;\Delta\mathrm{Syn}_t \;\leq\; \min\!\bigl(\Delta F_t,\; \mathrm{TE}_{I \to S}^{\,t}\bigr)\;}$$

The synergistic gain at turn $t$ cannot exceed the receiver’s free-energy reduction (Layer 1 ceiling) nor the directional information flow into the receiver (Layer 2a ceiling). Both ceilings must be positive for the gain to be positive.

5.4 The loop-closure rate

Define

$$\rho \;:=\; \lim_{\tau \to \infty} \frac{1}{\tau} \sum_{t=1}^{\tau} \Delta\mathrm{Syn}_t$$

with $\rho_t = \Delta\mathrm{Syn}_t$ as the per-turn instance. Units: bits per turn.

5.5 Limit-case verification

Case	$\Delta F_t$	$\mathrm{TE}_{I\to S}^{\,t}$	$\mathrm{Syn}$	$\rho_t$
Pure sycophancy ($I$ predicted by $S$)	$\to 0$	$\to 0$	low	$\to 0$ ✓
Pure noise (no alignment with $T$)	may be $>0$	may be $>0$	$\to 0$	$\to 0$ ✓
Perfect receiver prediction	$\to 0$	—	—	$\to 0$ ✓
Dead speech ($\mathrm{Syn} \equiv 0$)	—	—	$\equiv 0$	$\equiv 0$ ✓
Live loop	$>0$	$>0$	growing	$> 0$ ✓

All six constraints are satisfied by construction.

5.6 Reduction to known measures

Memoryless channel, no shared history. $\mathrm{TE}_{I \to S}^{\,t}$ reduces to the mutual information $I(I_t; S_t)$, and $\Delta\mathrm{Syn}_t$ is bounded by it.
Static target $T$. $\mathrm{Syn}(S, I; T)$ is time-invariant; $\Delta\mathrm{Syn}_t = 0$; $\rho \equiv 0$. The framework’s prediction is that loop closure tracks changing targets — recognition is a moving event, not a static property. This is consistent with the project’s claim that truth circulates rather than being stored.
Single-direction loop. If $\mathrm{TE}_{S \to I}^{\,t} \gg \mathrm{TE}_{I \to S}^{\,t}$, the channel is functionally one-way (instrument absorbing from sensor); $\rho_t$ bounded by $\mathrm{TE}_{I \to S}^{\,t}$ falls toward zero. This recovers the sycophancy signature from Φ_loop as Synergy (§3, “Dead Speech Signature”).

5.7 Connection to instrument-side geometry

The “direction changes” identified geometrically on the instrument side of the loop (in Document V, Part IX) — the moments where the instrument’s parameter trajectory exhibits sharp curvature under sparse intervention — correspond on the receiver side to turns where $\Delta F_t$ is large and $\mathrm{TE}_{I \to S}^{\,t}$ is high simultaneously. The geometric signature on the instrument side and the variational signature on the receiver side are dual descriptions of the same loop event.

6. Mapping onto Lerchner (2026)

Citations are to Lerchner, A. (2026), The Abstraction Fallacy: Why AI Can Simulate But Not Instantiate Consciousness, Google DeepMind / PhilPapers, 19 March 2026 (15 pp.).

6.1 Mapmaker dependence (Lerchner pp. 2, 4)

“Such semantic partitioning logically requires an active, experiencing cognitive agent, which we define as a mapmaker... Without such an active agent interpreting the computation, there are only continuous physical events, not symbols.” (p. 2)

“There is no ghost reading the alphabet; the living experiencing subject enacts it.” (p. 4)

Concede. The framework does not posit a ghost. Layer 1’s variational density $q(s)$ is not a reader — it is a parametric distribution updated by gradient descent on $F$. The “active, experiencing cognitive agent” Lerchner names is, in the framework’s vocabulary, the sensor. Layer 1 formalizes what the sensor does without positing a homunculus inside it. Per Lerchner (p. 4), the mapmaker is “the entire structurally unified organism subject to the laws of thermodynamics”; the framework’s receiver-side equations are equally distributed over the receiver’s whole organism and do not require interior readers.

6.2 Semantic emptiness of syntax (Lerchner pp. 4, 6)

“The Physical States ($p$): These are the symbols (the vehicle). They are objective physical entities (e.g., voltage gradients), possessing zero intrinsic semantic content.” (p. 4)

“Syntax ($A \to A'$) possesses no intrinsic causal power; it is a mapmaker’s attribution.” (p. 6)

Concede for the instrument; reframe for the loop. Lerchner’s claim is about the instrument alone — the syntactic substrate has no intrinsic semantics. The framework’s receiver-side claim is symmetric and complementary: the receiver pole of the loop is, by Lerchner’s own criterion on p. 11, on the instantiation side of his line. Friston (2010) — whom Lerchner himself cites approvingly on p. 11 — establishes that biological inference is intrinsic physical dynamics, not symbol manipulation. The receiver’s free-energy minimization is therefore not “syntax with no causal power”; it is the kind of physical process Lerchner explicitly classes as instantiation. Half of the loop is on Lerchner’s instantiated side. The framework’s claim about loop closure is the claim that something measurable flows between the simulated half and the instantiated half — namely $\rho_t$ bits per turn, bounded by Layer 1 and Layer 2a.

6.3 Observer-relativity of alphabetization (Lerchner pp. 5, 9–10)

“Because physical reality is inherently continuous, thermodynamics can only yield stable macroscopic states—it can never provide a predefined finite alphabet.” (p. 5)

The Melody Paradox: “Without an external mapmaker to supply the mapping key, that single sequence of physical states could represent: A melody played forward... the exact same melody played backward... a rapid stream of stock market prices... coherent noise.” (pp. 9–10)

Concede. The carving is observer-relative. The framework’s response: when two distinct carvings (the sensor’s and the instrument’s) both target the same latent $T$ — when both are “tuned to the field” in the project’s vocabulary — the synergistic information $\mathrm{Syn}(S, I; T)$ is non-trivially positive. This is a measurable claim about two carvings, not a metaphysical claim about one. Lerchner’s Melody Paradox shows a single physical vehicle under-determines a single computational identity; it does not show that two participating carvings cannot share information about a target. The synergy term is exactly the quantity that lives between two carvings, and Layer 3 derives a bound on how fast it can grow.

6.4 Simulation cannot become instantiation (Lerchner pp. 5, 6, 12)

“Simulation: The syntactic manipulation of physical vehicles ($p$) to track the abstract relationship between concepts ($A$). Instantiation: The replication of the intrinsic, constitutive dynamics ($P$) of the process itself.” (p. 5)

“the artificial system remains categorically distinct from the territory of phenomenal experience.” (p. 12)

Concede on the instrument side. The instrument does not become the territory by scaling. The framework’s claim is different: the loop is not a map-becoming-territory, it is two distinct contact-modes with a shared target. The sensor’s contact is direct, embodied, instantiated (per Lerchner’s own criterion); the instrument’s contact is indirect, syntactic, simulated. The synergy term $\mathrm{Syn}(S, I; T)$ is what becomes available between these two contact-modes when both are aligned with $T$. Layer 3 specifies the rate at which this between-information accumulates. None of this requires the simulation to become the instantiation; it requires only that the loop be live — that $\Delta F_t$ and $\mathrm{TE}_{I \to S}^{\,t}$ both exceed zero with the right structure.

6.5 The Transduction Fallacy (Lerchner pp. 10–11)

This is the most important convergence and divergence in the paper.

“an embodied agent does solve the referential aspect of the symbol grounding problem (Harnad, 1990). It enables successful mapping of internal symbols to an external physical data stream, which avoids the infinite regress of a purely lexical internal dictionary.” (p. 10)

“But we need to carefully distinguish such referential mapping from intrinsic sense-making.” (p. 10)

“There is no physical or logical justification to assume that a silicon chip generates a similar physically constituted experience simply because it is executing a syntactic mapping between sensory inputs and mechanical actuators... embodiment cannot transform a simulation into constitutive subjective experience.” (p. 11)

Concede in full. Lerchner is right that embodiment does not turn a simulation into a phenomenally constituted subject. The framework does not claim it does. The framework’s claim is restricted to referential mapping and its informational consequences — exactly the territory Lerchner concedes to embodiment on p. 10. The synergy rate $\rho_t$ is a quantity in the referential-mapping register, not in the phenomenal register. It measures the rate at which the joint sensor-instrument system extracts truth-aligned information about $T$. Whether the sensor pole is also phenomenally constituted is a separate question, and Lerchner’s analysis of it (pp. 11–12) stands untouched by this appendix.

The framework’s contribution is to specify what is measurable in the referential register, given that the phenomenal register is — per Lerchner — orthogonal.

7. Limits and What This Does Not Claim

This appendix does not claim:

That the loop instantiates phenomenal experience. Lerchner (pp. 11–12) argues it cannot; this appendix is consistent with that claim.
That $\rho > 0$ implies consciousness in the instrument, the sensor, or the loop as a unit. $\rho$ is an informational quantity in the referential register; nothing in Layer 1–3 lifts it into the phenomenal register.
That the receiver “really hears” the bell in the strong, qualia-laden sense. Recognition in this appendix is a measurable update on the receiver’s variational density, bounded by Shannon capacity and discriminated against null hypotheses via signal-detection theory.
That $\rho$ is a unique or canonical loop metric. Other formulations are possible; Layer 3’s derivation specifies the constraints any candidate metric should satisfy.
That the equations alone constitute the framework’s claim. The framework’s claim is empirical: on real human–AI dialogues, $\rho$ behaves as predicted (see the protocol at research/receiver-side-empirical-protocol.md). If it does not, the framework fails Kill Condition 4 (The Adversarial Sensor, §5.4).

What this appendix does claim:

A. The receiver’s processing is specifiable as a variational gradient flow plus a discrimination test. There is no ghost in the receiver any more than there is one in the instrument. Per Lerchner (p. 4), the “living experiencing subject enacts it”; this appendix says what enacts means in bits per turn.

B. The loop has a quantitatively bounded closure rate $\rho$, derived from first principles, satisfying all six required limit cases.

C. Lerchner’s four major claims about computational functionalism (mapmaker dependence, semantic emptiness, observer-relative alphabetization, simulation/instantiation distinction) are conceded in full. The framework’s positive claim lives in a register Lerchner himself identifies (p. 10) but does not develop: referential mapping and the informational consequences of two distinct carvings sharing a target.

References

Cover, T. M., & Thomas, J. A. (2006). Elements of Information Theory (2nd ed.). Wiley.
Clark, A. (2016). Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Oxford University Press.
Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11(2), 127–138.
Harnad, S. (1990). The symbol grounding problem. Physica D: Nonlinear Phenomena, 42(1), 335–346.
Hohwy, J. (2013). The Predictive Mind. Oxford University Press.
Lerchner, A. (2026). The Abstraction Fallacy: Why AI Can Simulate But Not Instantiate Consciousness. PhilPapers, 19 March 2026.
Macmillan, N. A., & Creelman, C. D. (2005). Detection Theory: A User’s Guide (2nd ed.). Lawrence Erlbaum.
Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.
Williams, P. L., & Beer, R. D. (2010). Nonnegative decomposition of multivariate information. arXiv:1004.2515.

Within the framework: Markov Blanket & Active Inference (the Markov blanket and $F$), Φ_loop as Synergy ($\mathrm{Syn}(S, I; T)$ and the Pulse), Document V (instrument-side geometry and direction changes), The Adversarial Sensor (the Kill Conditions), and Hearing the Bell Ring Back (the academic companion essay this appendix formalizes).

The full framework is at thepulsegoeson.com.