# Conventions and principal distinctions

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<a id="chapter:conventions-and-principal-distinctions"></a>  ${\mathsf{U}}$ denotes reality prior to the operational source/readout distinction. The different typeface distinguishes this ontological notation from locally defined evolution operators such as $U_t$ in the mathematics. $S$ is the working source or structure-side cut; $T$ is the readout or record-side cut. The schematic map is $p:S\to T$. The descent theorems use $X$ for that readout codomain; this is a local notation convention, not another ontological level. Symbols such as $T$ for a time horizon or $T_u$ for a transition kernel retain their expressly defined mathematical meanings.

The older ontological notation ${\Omega_{\mathrm{src}}}$ is interpreted here through ${\mathsf{U}}$, not through a source state in $S$. Neither symbol names the closure operator $\mathcal O$ in $L=\mathcal O\Delta\partial[L]$. No theorem in this book treats ${\mathsf{U}}$ as a set, a Hilbert space, a field, or an argument of a computable transition law.

For probability laws $P,Q$ on the same measurable space, 

$$

{d_{\mathrm{TV}}}(P,Q)=\sup_A|P(A)-Q(A)|.

$$

 For density operators $\rho,\sigma$, $D(\rho,\sigma)=\tfrac12{\lVert \rho-\sigma\rVert}_1$. Complete-path distance, endpoint distance, quantum-state distance, and faithfulness to a past event are different claims. A bound in one space is transferred to another only through a specified common channel or map.

An *exact theorem* is a mathematical implication on a declared domain. A *physical model* supplies laws of motion, preparation, and interaction. A *psychophysical constitutive law* assigns experiential significance to a physical structure. A *phenomenological report* describes what a subject reports as experienced; its metaphysical interpretation is a separate claim. In particular, a mathematically complete assignment need not be an empirically correct assignment.

The phrase *candidate internal resolution* has one controlled meaning in this monograph: all maps and laws required for the nominated finite constitutive model are specified, and its conclusions follow under their hypotheses. It does not mean that the actual-vessel realization problem, empirical adequacy, universal source selection, or external verification has already been settled.  

<a id="paragraph-1"></a>

## Terminology

<a id="sec:reader-terminology"></a> 

| Term | Meaning in this monograph |
| --- | --- |
| Term | Meaning in this monograph (continued) |
| ${\mathsf{U}}$ | Unsplit ontological prior: reality before an operational source/readout distinction. Not a countable individual or a mathematical state space. |
| $S$ | Working source, the structure-side description complete relative to the nominated problem. |
| $T$ | Readout, the restricted record-side description in which physical histories, archives and vessels are represented. Called $X$ in the descent theorem. |
| Awareness | The proposed knowing aspect of ${\mathsf{U}}$; not a person, a scene, a report, or an extra force. |
| Localized subject | An experiential perspective instantiated only during qualification under A1, with a lived scene under A2. A3 relates qualifying occurrences into episodes; a genuine gap ends the episode. |
| Lived scene | What it is like now: the current phenomenal presentation. Scene does not require vision, spatial imagery, reflective attention, or a narrative self. |
| Unconscious/ generative organization | Processes contributing to an awareness-bearing vessel without appearing as separately presented contents or possessing a second scene. |
| Self-model/person | Bodily, practical and autobiographical organization; biological and person-level continuity can persist without a current scene or experiential subject. |
| Memory of a scene | Retained or reconstructed representation of prior experience; distinct from its occurrence and the continuing organism. Failed recall does not establish that no scene occurred. |
| Reportability | Availability to an actual reporting channel. It depends on access, memory, motor or linguistic resources, and channel conditions. |
| Agency | Capacity for organized selection and action; not a synonym for experiential presence. |
| Metacognition | Representation or assessment of one's cognitive processes; not required for every admitted perspective. |
| Vessel / $R^\ast$ | A physically realized organization / its certified specification of components, native instruments, boundaries, resources and process provenance. |