Does the source extend beyond physical history?

Locate the obstruction on the right map

Local loss does not establish a lossy source-to-history map

A specified physical model may have a restricted presentation. Independent observations may then require distinctions beyond that presentation. The stronger claim that physical reality itself is readout of a particular richer source requires another argument. The source-to-use programme establishes the first result and supports a conditional empirical route to the second.

Proposition 9.1: composition and the identity countermodel. Let $F:S\to H$ be onto, $q:H\to Z$ a record and $f:H\to A$ a target. If $q(h_0)=q(h_1)$ but $f(h_0)\ne f(h_1)$, then $f$ does not descend through $q$ and $f\circ F$ does not descend through $q\circ F$. This implies neither noninjective $F$ nor a necessary source beyond $H$.

Proof. A common function of equal records cannot give different targets. Surjectivity provides source antecedents and lifts the same obstruction. Set $S=H,F=\mathrm{id}$ for the countermodel: local loss remains while the history map is injective.

Explicitly, $H=\{0,1\}^2$, $q(a,b)=a$, $f(a,b)=b$ suffice. The entire history is an adequate working source. Appending a silent coordinate creates a richer mathematical representation but provides no evidence of an additional physical bearer.

The integration remains useful without that inference: relativity constrains the access map and completion specifies what it must preserve. A deeper history realization can be established where independently warranted. No jump from $q$-loss to $F$-loss is licensed or needed.

A complete passive path can still miss intervention laws

Take qubits $E,S$ initially $|\lambda,0\rangle$, $\lambda\in\{0,1\}$. During dwell $T\gt0$ use

$$H_{ES}=\frac\pi T|11\rangle\langle11|,\qquad U_{ES}(T)=|0\rangle\langle0|_E\otimes I_S+|1\rangle\langle1|_E\otimes Z_S.$$

The entire passive reduced trajectory is $\rho_S^\lambda(t)=|0\rangle\langle0|$ for both preparations, because $|\lambda,0\rangle$ has zero energy. Apply Hadamard $W$ to $S$, dwell, then apply $W$ again. Since $WZW=X$ and $W^2=I$,

$$(I\otimes W)U_{ES}(T)(I\otimes W)|\lambda,0\rangle=|\lambda,\lambda\rangle.$$

The same final $Z$ measurement distinguishes perfectly. A predictor given only the identical passive path must issue one Bernoulli parameter $m$, with conditional TV errors $m,1-m$ and minimax $1/2$. Final-law calibration errors $\eta_0,\eta_1$ reduce the bound to $[1-\eta_0-\eta_1]_+/2$ if passive equality stays exact. This applies the established half-TV obstruction [29,34], not a new universal inequality.

The preparation archive and $E$ are inaccessible before decision. Isolate coupling during finite pulses, counting pulse time, control strength, timing and protected storage. The positive involution generator $\pi(I-W)/(2\tau_g)$ realizes each pulse. Its norm is $\pi/\tau_g$; the sequence takes $T+2\tau_g$ with dwell norm $\pi/T$. The schedule is common and independent of $\lambda$. Joint interface/switching calibration remains required. The missing distinction is an ordinary environment state with a prescribed coupling, not an appended stochastic seed.

Thus an entire passive local path need not determine an active response. A process tensor or equivalent intervention-sensitive specification supplies the missing law [5,19]. This is an elementary physical illustration of an established distinction. Complete histories include $E$ and differ in $\lambda$, so $F=\mathrm{id}$ survives. The diagnostic does not prove a nonspatiotemporal source.

Compare the strongest existing source results

The regular-branch global record theorem assumes a selector carried by source/preparation structure, nonmeasurability in the preceding Tier-1 filtration, conditional full support, measurement independence and reduction preserving distinctions that yield different objective records [23]. These support the pathwise witness. A nontrivial Born kernel alone gives a conditional law. Representing it by a uniform randomizer independently establishes no extra physical substrate. Distributional closure can coexist with failure to select a realized continuation from the present.

Its full-history theorem is separate: a lawful nonisomorphic inactive extension can preserve the entire Tier-1 history law, showing architecture non-identifiability in that class. Isomorphic active apertures suffice for equal laws; the converse needs another identifiability theorem. The warranted conclusion is operational/readout equivalence, not an inferred unique aperture isomorphism class or physical necessity of a silent sector.

What would strengthen the physical inference

Let $\Xi(s)=(\mu_{e,s})_e$ collect record laws under all admitted experiments, including adaptive interventions. A description $r(s)$ supports the family exactly only when

$$r(s)=r(s')\Rightarrow\Xi(s)=\Xi(s').$$

Enlarged access can enlarge $\Xi$ and split previous equivalence classes, as the control and pooled-record protocols do. Yet canonical protocol equivalence and the complete-law surrogate result permit a history/process model reproducing the enlarged family [30,34]. Reconstructing causal history kernels does not evade that ceiling.

A stronger inference needs independently justified restrictions: a closed causal cut, finite coherent memory, locality/factorization, incompatible preparations or a specified dynamical law. The readiness/completion theorem provides one such inference without requiring source-level outcome determinism. A universal source-beyond-history claim would need a reason that every adequate whole-history realization fails a warranted condition, or evidence selecting one deeper physical model. Neither local experience nor a block interpretation supplies that reason here.

The advance is exact realization and explanation. A source-accurate temporal relation needs attainable completion when used; experiential significance follows under a separate constitution. The stronger source question remains precise, without confusing these achievements.