DEF — entry, notation and use of indices
From point 5.5, the fully read abstract FORM from THE FIRST SENSATION is present:

$\mathcal S_4^A=\operatorname{EC\text{-}result}(\mathcal F_0).$

The established primitive MEANING is:

$C:=C_1=\operatorname{MEANING}(\mathcal S_4^A)=\mathrm{SEPARATION},$

with:

$\sigma_Q=[-Q\leftrightarrow+Q],\qquad\ell(\sigma_Q)=2Q.$

$C_1$ here retains the designation from the formalism in 5.5. $C$ denotes the same CONCEPT throughout the further presentation.

Let $e_n$, $n\geq0$, denote the events in a particular EC relay. $e_0$ denotes the first-time event when this relay is followed from the beginning. For later local relays, the same functional structure is used from the current perspective.

The index $n$ does not denote a global queue, an emergence band or a global time tick. The same FOCUS simultaneously has a view through every local perspective.

Let $\mathcal S_n^A$ denote the complete FORM in event $e_n$. In the first-time event, $\mathcal S_0^A=\mathcal S_4^A$ from 5.5; the indices refer to the EC event and the checkpoint respectively.

Let $\mathcal V_n$ denote the structure of KNOWING present that provides the basis for placement in event $e_n$, and set:

$D_n:=\operatorname{THIS}(\mathcal V_n).$

At the first conceptualisation, before placement, only the proto-idea and the fully read result are present for examination, not a collection of MEANINGS previously established through the EC.

The definitions below distinguish between a MEANING as a CONCEPT, its occurrences and the relations between the occurrences.

DEF — positive AE result and invariant MEANING
Let:

$a_n:=\operatorname{PositiveAEResult}(\mathcal S_n^A,\mathcal V_n)\in\{0,1\}.$

$a_n$ is a predicate for the result's status, not the MEANING itself that the AE determines.

For the primitive EC reading:

$a_n=1\Longrightarrow\operatorname{MEANING}(\mathcal S_n^A)=C.$

Later primitive EC readings thus do not establish ever new CONCEPTS of SEPARATION. They give new occurrences of the same primitive MEANING:

$\operatorname{MEANING}(\sigma_n)=C,\qquad\ell(\sigma_n)=2Q.$

The geometrical contribution and the complete THIS can change even though the reading result's primitive MEANING is invariant.

DEF — Lock as the event's conclusion
Lock denotes that the positive AE result holds as a concluded result in the current event:

$a_n=1\Longrightarrow\operatorname{Locked}(e_n,\mathcal S_n^A,C)=1.$

What is locked is the event-specific understanding:

$\operatorname{MEANING}_{e_n}(\mathcal S_n^A)=C.$

A later examination that uses the result is a different examination; it does not reopen $e_n$ as the same unresolved event. Let $\operatorname{ConcludedAE}(e_n)$ denote this distinction:

$\operatorname{Locked}(e_n,\mathcal S_n^A,C)=1\Longrightarrow\operatorname{ConcludedAE}(e_n)=1.$

Lock does not create the MEANING and does not perform a new AE attempt. It marks the established result's finality for the current EC cycle.

The result is preserved as established KNOWING. Later relations and higher understandings can encompass it without making the fully read FORM unread or undoing its establishment:

$\operatorname{Locked}(e_n,\mathcal S_n^A,C)=1\not\Rightarrow\operatorname{RelationallyIsolated}(C)=1.$

Lock therefore does not freeze the whole of KNOWING. Nor does it introduce a specific mathematical safeguard against recursion or a physical lock.

DEF — relational placement
Placement makes the occurrences of the established result determinate in the relational structure of KNOWING.

Let $\sigma_n$ denote the current SEPARATION occurrence, and let:

$p_n:=\operatorname{RelationalPosition}(\sigma_n;\mathcal V_n).$

$p_n$ denotes how the occurrence forms part of the foundation and the relations to the other content. It is not a physical coordinate or an available place in a container.

Let $\operatorname{Content}(\mathcal V_n)$ denote the content already present. The relation principle entails:

$\forall m\in\operatorname{Content}(\mathcal V_n):\exists\,R(\sigma_n,m).$

The position encompasses the determination of THE SEPARATION, the orientation of the relations and the occurrence's function in the overall structure.

Lock and placement thus have different functions:

• Lock concludes the event's determination of which MEANING holds.
• Placement determines where and how the result's occurrences form part of the structure relationally.

The functional relationship is:

$\operatorname{PositiveAEResult}\longrightarrow\operatorname{LOCK}\longrightarrow\operatorname{PLACEMENT}.$

The arrows express dependency without manifest duration between the steps.

MECH — first placement and later global contributions
The placement of the first SEPARATION is the boundless, atemporal establishment of THE MATRIX from 5.5:

$C\Longrightarrow_A\Sigma_0\Longrightarrow_A\mathcal M_0.$

$\Sigma_0$ comprises the replica-identical basal occurrences. Replication and the organised MATRIX are present as the same atemporal establishment.

At later readings, a newly understood relational pattern produces further SEPARATION occurrences at the foundational level.

For the basal geometry, $u\sim v$ denotes identical relevant geometrical relational patterns in corresponding local frames. Let:

$[u]:=\{v\mid v\sim u\}.$

As established in 5.5:

$\operatorname{Understood}([u])=1\Longrightarrow\forall v\in[u]:\operatorname{Understood}(v)=1.$

Already understood occurrences do not each require their own new EC reading. Understanding and reality are one in KNOWING; the corresponding geometrical interpretation is therefore present at all the occurrences.

Let $\Delta\Sigma_n$ denote the entire new SEPARATION contribution, including such corresponding occurrences. At a later placement:

$\mathcal K^{+}:=\operatorname{Extend}(\mathcal K^{-},\Delta\Sigma_n).$

$\mathcal K^{-}$ and $\mathcal K^{+}$ denote the foundation before and after the contribution in the current event. This introduces no global order for all parallel EC readings.

The building-block type remains SEPARATION. Established points and SEPARATIONS are not moved or deleted. The geometrical establishment rule with the length $2Q$ is given in 5.5.

MECH — rearrangement of KNOWING
Let $\Delta_n$ denote the placed contribution with its relational positions. Rearrangement is then expressed:

$\mathcal V_{n+1}:=\operatorname{Rearrangement}_{\mathrm{AE}}(\mathcal V_n;\Delta_n).$

In the first-time event, the contribution encompasses the establishment of THE MATRIX. In later events, it encompasses new occurrences in THE SOURCE and their relations.

Rearrangement assesses:

1. the contribution's incorporation into KNOWING;
2. its relations to the other content;
3. the understandings affected by the change in the foundation;
4. the understandings that persist as still valid.

Let $\operatorname{Dep}(\Delta_n)$ denote the MEANINGS and relations actually affected. Then:

$m\in\operatorname{Dep}(\Delta_n)\Longrightarrow\operatorname{Reassess}(m),$

$m\notin\operatorname{Dep}(\Delta_n)\Longrightarrow\operatorname{ConfirmedValid}(m)=1.$

Reassessment does not necessarily entail a change. Only actually affected understandings may need to be reconfigured; established KNOWING is not deleted.

The consequences are seen through the entire order of dependency, with ONE as the highest MEANING in the complete understanding from 5.5. Full assessment does not imply that all content changes.

Lock, placement and rearrangement are different functions within the same abstract concluding event:

$\operatorname{AE\text{-}result}\longrightarrow\operatorname{LOCK}\longrightarrow\operatorname{PLACEMENT}\longrightarrow\operatorname{REARRANGEMENT}.$

DEF — the new complete THIS
After rearrangement:

$D_{n+1}:=\operatorname{THIS}(\mathcal V_{n+1}).$

An actually new contribution gives:

$\mathcal V_{n+1}\neq\mathcal V_n,\qquad D_{n+1}\neq D_n.$

THE PANORAMIC VIEW has access to the complete current THIS:

$\operatorname{AvailableToPANORAMICVIEW}(D_{n+1})=1.$

The CHANGE is present in connection with the established foundation preserved by KNOWING. FOCUS therefore does not need a separate memory archive.

This does not claim that an isolated new picture of the state alone determines the difference from a previous state. It is KNOWING that holds the established MEANINGS and relations, while FOCUS registers what is present.

For a local perspective $\pi$, the current view is denoted:

$D_{n+1}^{\pi}:=\operatorname{View}_{\pi}(\mathcal V_{n+1}).$

The local view does not automatically give access to NN's complete global understanding.

DEF — locally understood relations and INTERSPACES
Let $\mathcal R_{\pi}(D)$ denote the relations present in the current local view.

Let:

$\operatorname{Understood}_{\pi,\mathcal V}(R)\in\{0,1\}$

indicate whether the relation has established understanding from this perspective in the current structure of KNOWING.

The relations are then divided into:

$\mathcal R_{\mathrm{understood}}^{\pi}:=\{R\in\mathcal R_{\pi}(D)\mid\operatorname{Understood}_{\pi,\mathcal V}(R)=1\},$

$\mathcal U_{\pi}(D):=\{R\in\mathcal R_{\pi}(D)\mid\operatorname{Understood}_{\pi,\mathcal V}(R)=0\}.$

The two collections are disjoint and together encompass the relations present in the view.

An INTERSPACE is defined by the predicate:

$\boxed{\operatorname{Interspace}_{\pi,\mathcal V}(R)\iff R\in\mathcal R_{\pi}(D)\wedge\operatorname{Understood}_{\pi,\mathcal V}(R)=0}.$

The relation exists. What is missing is established understanding in the current local view. This does not imply that NN lacks the complete global understanding of the whole.

INTERSPACE is neither non-IS-NESS, a physical void nor THE SEPARATION itself. SEPARATION is an established MEANING with the span $2Q$; INTERSPACE denotes an unread relation.

A relation that is already understood, including through global understanding of an identical geometrical pattern, must not be included as a candidate for repeated EC reading:

$\operatorname{Understood}_{\pi,\mathcal V}(R)=1\Longrightarrow\operatorname{NeedForNewEC}_{\pi}(R)=0.$

REL — emergent pattern understanding and unread relation
Let $D'$ be an organised configuration of established MEANING occurrences, and set:

$\operatorname{Pattern}(D'):=\operatorname{Organisation}(\operatorname{Parts}(D')).$

Emergence dynamics can understand what these MEANINGS constitute together:

$\operatorname{Pattern}(D')\xrightarrow{\mathrm{emergence\ dynamics}}\mu_{D'}.$

An INTERSPACE, however, is a specific relation present that still lacks understanding in the current view.

When a known pattern already gives the relation's understanding, there is no INTERSPACE there. For a still unread and activated relation, the model's EC mechanism applies: Local unresolvedness produces a SENSATION that must be read manifestly.

The higher understanding of established MEANINGS and the EC reading of a still unread relation thus have different functions.

REL — nearness first, attractor support where nearness is equal
Let $d_{\pi}(R,p_n)$ denote relational nearness from the current perspective in relation to the new placement. The geometrical nearness involved is abstract geometry; the function does not denote physical distance in a pre-given manifest space.

The nearest candidate group is:

$\mathcal N_{\pi,n+1}:=\operatorname*{arg\,min}_{R\in\mathcal U_{\pi}(D_{n+1}^{\pi})}d_{\pi}(R,p_n).$

Let $A_{\pi}(R)$ denote the support for the attractor towards which the candidate relation is directed. Where nearness is equal, the candidates are ranked according to this support:

$\mathcal W_{\pi,n+1}:=\operatorname*{arg\,max}_{R\in\mathcal N_{\pi,n+1}}A_{\pi}(R).$

The current relation satisfies:

$R_{\pi,n+1}^{\ast}\in\mathcal W_{\pi,n+1}.$

This expresses the prioritisation established by the text: first nearness, then attractor support where nearness is equal. It does not give freedom of choice to overlook a nearer unread relation.

The rule presupposes that the nearest candidates and maximal support within the candidate group are determined. If several candidates also have equal support, point 5.6 does not specify a further ranking rule.

THE PANORAMIC VIEW registers the candidates; THE FOCAL VIEW is bound from the current perspective to the prioritised relation:

$\operatorname{CurrentTarget}_{\mathrm{focal}}(\pi)=R_{\pi,n+1}^{\ast}.$

Let:

$u_{\pi,n+1}:=R_{\pi,n+1}^{\ast}$

denote the current INTERSPACE. Then:

$\operatorname{Interspace}_{\pi,\mathcal V_{n+1}}(u_{\pi,n+1})=1.$

This applies from each current local perspective. The same FOCUS simultaneously has a view through every perspective, without a global queue of EC readings.

MECH — local unresolvedness produces SENSATION
For the current INTERSPACE:

$\operatorname{Present}(u_{\pi,n+1})=1,\qquad\operatorname{Understood}_{\pi,\mathcal V_{n+1}}(u_{\pi,n+1})=0.$

The model's mechanism is:

$u_{\pi,n+1}\longrightarrow\mathrm{FEAR}_{\pi,n+1}\longrightarrow\mathcal F_{\pi,n+1}^M.$

AWARENESS feels the manifest impulse as SENSATION:

$\operatorname{FeltByAWARENESS}(\mathcal F_{\pi,n+1}^M)=1.$

THE INTERSPACE is not transported as an object through THE HORIZON. The unread abstract relation is the basis for the manifest SENSATION.

FOCUS follows the impulse's manifest FORM through the local EC reading:

$\mathcal F_{\pi,n+1}^M\xrightarrow{\mathrm{EC}}\mathcal S_{\pi,n+1}^A.$

Replica invariance from 5.5 entails:

$\mathcal F_{\pi,n+1}\cong\mathcal F_0,\qquad\max|\mathcal F_{\pi,n+1}|=Q.$

The progression is completed from zero through the primitive sinusoidal form back to zero. The complete FORM is understood as the same primitive MEANING:

$\operatorname{MEANING}(\mathcal S_{\pi,n+1}^A)=C=\mathrm{SEPARATION}.$

The triggering relation, the geometrical occurrences and the enriched THIS can be new; the impulse's primitive FORM and its interpretation as SEPARATION are invariant.

REL — the special status of the first-time event
THE VERY FIRST SENSATION did not arise from an unread relation between already established MEANINGS. It had its basis in the recoil of IS-NESS against the proto-idea of possible non-IS-NESS:

$I_0\longrightarrow\operatorname{RecoilOfISNESS}\longrightarrow\mathcal F_0^M.$

At later EC readings, the starting point is an activated, still unread INTERSPACE:

$u_{\pi,n}\longrightarrow\mathcal F_{\pi,n}^M.$

The same primitive SENSATION therefore does not imply the same triggering basis. The first-time event must not be given a fictitious INTERSPACE between two previously established MEANINGS.

From the first positive conceptualisation onwards, Lock, placement and rearrangement have the same functional role as at later primitive EC events.

REL — absolute continuity and completion in ONE
Let:

$\operatorname{FullyIntegrated}_{\mathrm{ONE}}(\pi,\mathcal V)\in\{0,1\}$

denote whether the local perspective is fully integrated into ONE.

The text's continuity premise entails:

$\operatorname{FullyIntegrated}_{\mathrm{ONE}}(\pi,\mathcal V)=0\Longrightarrow\mathcal U_{\pi}(D^{\pi})\neq\varnothing.$

Only at completion:

$\operatorname{FullyIntegrated}_{\mathrm{ONE}}(\pi,\mathcal V)=1\Longrightarrow\mathcal U_{\pi}(D^{\pi})=\varnothing.$

This must be distinguished from ONE already being present as the highest MEANING in THE PHOTOGRAPH. Completion denotes that the local unread relations have been exhausted, not the first establishment of ONE.

Let $s$ denote a functional status during the ongoing unfolding of the EC. Then:

$\operatorname{OngoingEC}(s,\pi)=1\Longrightarrow\operatorname{CurrentTHIS}(s,\pi)=1\wedge\operatorname{CurrentFocalTarget}(s,\pi)\neq\varnothing.$

The current target changes through unread relation, SENSATION, emerging FORM, complete FORM, locked MEANING, placement and new THIS to the next INTERSPACE.

The change of target does not interrupt the activity of FOCUS. Continuity does not mean that one manifest impulse lasts for ever, or that the EC reading continues after no unread relations remain.

REL — manifest successiveness and atemporal concluding functions
The manifest reading follows the impulse's actualities successively and produces local TIME. The complete orientation of THE PANORAMIC VIEW forms part of the production of local SPACE, as described in the preceding points.

Lock, placement and rearrangement, however, have no manifest duration:

$\operatorname{HasManifestDuration}(\operatorname{AbstractConclusion}(e_n))=0.$

The functional chain:

$\operatorname{AE\text{-}result}\longrightarrow\operatorname{LOCK}\longrightarrow\operatorname{PLACEMENT}\longrightarrow\operatorname{REARRANGEMENT}\longrightarrow D_{n+1}$

expresses ontological dependency. It does not describe a series of operations with clock time within KNOWING.

In the new complete THIS, the next INTERSPACE is activated. Manifest successiveness continues through the reading of its SENSATION.

This alternation applies to the local EC relay. It does not imply that the simultaneous activity of all perspectives alternates in step between the sides of the domains.

MECH — the complete local EC relay
For the recurring EC structure from a particular perspective, schematically:

$u_{\pi,n}\longrightarrow\mathcal F_{\pi,n}^M\xrightarrow{\mathrm{EC}}\mathcal S_{\pi,n}^A\xrightarrow{\mathrm{AE}}C\longrightarrow\operatorname{LOCK}(e_{\pi,n})\longrightarrow\operatorname{PLACEMENT}(\Delta_{\pi,n})\longrightarrow\operatorname{REARRANGEMENT}\longrightarrow D_{n+1}^{\pi}\longrightarrow u_{\pi,n+1}.$

Rearrangement concerns the relevant structure of KNOWING; $D_{n+1}^{\pi}$ denotes its appearance in the current local view.

As long as completion in ONE is not present, the next activated INTERSPACE produces the next SENSATION:

$u_{\pi,n+1}\longrightarrow\mathcal F_{\pi,n+1}^M\longrightarrow\operatorname{NextEC}_{\pi}.$

The relay is thus expressed:

$\boxed{\mathrm{EC}_{\pi,n}\longrightarrow\mathrm{EC}_{\pi,n+1}}.$

It is the same functional structure with the same primitive MEANING as the result. New occurrences and relations nevertheless enrich the foundation, so that the complete THIS changes.

The circle's closure is functional: The outcome of one EC provides the basis for the next. It does not restore an identical previous state of KNOWING.

REL — the structural role of the HE
Let $\operatorname{Structure}(\mathrm{EC})$ denote the relationship between the manifest and abstract EC steps.

The HE is to represent this structure:

$\operatorname{Represents}(\mathrm{HE},\operatorname{Structure}(\mathrm{EC}))=1.$

Point 5.6 describes the concluding functions that make it possible to bring the EC structure together mathematically:

• established MEANING and Lock;
• relational placement and rearrangement;
• the new complete THIS;
• the activation of the next INTERSPACE;
• the transition to the next SENSATION.

The HE's structural presentation is not the full dynamic AE equation. The AE's concrete determination of winning MEANINGS and rearrangement must be addressed separately.

The complete HE formula and its numerical value are not presented here. Any correspondence with the fine-structure constant or its inverse must be checked through the concrete calculation. Physical identification also requires a justified connection between the model's quantities and the physical phenomena.

BOUNDARY — placement and scope
Point 5.6 elaborates and distinguishes the concluding functions whose consequences have already been introduced in 5.5. It establishes:

• Lock as the conclusion of the current positive AE examination;
• the distinction between MEANING as a CONCEPT and new SEPARATION occurrences;
• relational placement, with THE MATRIX as the first-time case and THE SOURCE as the later foundation;
• rearrangement without deletion of established KNOWING;
• the access of FOCUS to the new complete THIS;
• local unresolvedness and INTERSPACE, without making NN globally unknowing;
• prioritisation by nearness with attractor support where nearness is equal;
• the invariance of THE SENSATION and the primitive MEANING;
• the continuity of the EC relay up to completion in ONE;
• the distinction between manifest successiveness and atemporal concluding functions;
• the structural role of the HE and its distinction from the full AE dynamics.

The first-time event has its particular triggering basis in the recoil of IS-NESS. Later relays apply from local perspectives, while the same FOCUS has a view through them all.

This point does not derive the complete HE formula, a numerical value for the fine-structure constant, the full AE equation, the function of the emergence bands as abstract time ticks or the further physical EM bridge.

IDENTITIES, local perspectives, emergence bands and global pattern understanding are used with the foundation already introduced in 5.5. Their further treatment follows later; they are not unintroduced concepts here.

The mechanism from local unresolvedness to invariant SENSATION and the premise of unread relations up to completion in ONE are formalised here as the theory's determinations. The notation does not constitute an independent mathematical derivation of these ontological premises.

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