# From Observation to Governed Computation
## A relational architecture study across measurement, interacting bodies, cosmology and quantum mapping

KEDDEH SYSTEMS | RESEARCH AND FORMAL PUBLISHING | ENGINEER · AUTOMATE · SCALE

Document ID: KEDDEH-WP-RELATIONAL-ARCHITECTURE-001  
Version: R2 · 18 October 2026  
Author: Aboudy Keddeh — Systems Architect  
Publisher: Keddeh Systems  
Rights holder: Aboudy Keddeh  
Licence profile: KEDDEH-RESERVED-1.0  
Classification: Internal research · Owner review  
Status: Research synthesis · R2

Architecture, definitions and research direction: Aboudy Keddeh. AI-assisted drafting, source synthesis, editorial analysis and layout: dot, powered by OpenAI. This composition does not record independent scientific approval.

**Author’s clarification.** OpenAI-generated and other generic AI formulations do not adequately represent the intended mathematical rationale. Some visuals do not accurately reflect the mathematics or claims, and some derivations have been imported incorrectly, contrary to the author’s intended claim. The author’s original definitions and derivations take precedence over these AI-generated interpretations.

This edition preserves the current literal origin designation **.1**, ordered relations and the distinction between observation and existence. Historical source editions remain identified.

## 1. Abstract and reader route

The central architectural question is how a computation can retain the relations that made its inputs meaningful. A number may be copied correctly while its subject, observer, scale, direction or derivation disappears. Keddeh’s proposed architectures address this problem by making relational identity and context part of the state that computation carries.

This study follows that proposal from observer and observed, through ordered representation, into governed execution and scientific application. It connects the measurement foundations and Observer Relational Mathematics to KEX typed state, BRAINK continuity, IL-LLM traversal, nested execution environments and the quantum-mapping research programme. Celsius supplies an accessible measurement case; interacting bodies expose frame and dependency requirements; cosmology tests the separation of observation from inference; quantum mapping tests whether retained structure is sufficient for a specified calculation.

The recovered sources supply more than a programme of proposed tests. They include a proved phase-tagged coordinate map, a dimensioned water-energy calculation, an executed nonlinear thermal projection, an observer/frame inverse, three-dimensional wave and shell representations, ordered-record preservation and executable quantum-state processing. Their results belong to different domains: mathematical equivalence, numerical calculation, software behavior, rendering and physical correspondence. This study connects those results without treating one domain as proof of another.

**Reader route.** Section 2 establishes what is being observed. Section 3 explains what its representation must retain. Section 4 follows that representation into execution. Section 5 applies the resulting structure to the four topic families. Section 6 specifies how to test each transition. Sections 7–8 assess the composition and its next research result.

The complete article is the primary reading surface. Optional calculations and interactive tests follow the relevant explanation; they do not replace its premises, derivation or conclusion. A test must identify its actual source and method before its output can be interpreted.

R2 uses the sixteen separately edited research and technical references listed at the end, together with full reading layers for recovered formal dependencies, worked-application records and the separate spatial-radix study. It preserves R1 unchanged. Historical receipts, newly reproduced calculations and editorial reconstructions are identified where they affect a claim.

This is a dependency-led route: later claims require the earlier distinctions to survive. “Topological” guidance here means making connections, nesting and boundaries intelligible; a claim about mathematical topology requires its own defined objects and invariants.

## 2. Observation: the relation comes before its reported value

### 2.1 Observed, observer, observable and context

An observed entity is the referent under investigation. An observer is the participant or instrument through which a particular account is obtained. An observable specifies what is being examined. Context states where, when, under which conditions and for which instance the account applies. One participant can occupy different roles in different relations; its identity need not change when its role changes.

This ordering prevents a common collapse. A change in the observer’s description need not be a change in the observed entity. An unavailable reading does not establish that the entity is absent. Two records yielding the same displayed value need not describe the same relation. These distinctions are the starting conditions for the current architecture, rather than qualifications added after calculation. [K-CURRENT; K-ORM]

WP-05 provides a source-defined organising expression:

**O_r = T(S, M_o, F, H, R).**

Here S is source identity and its domain variables; M_o is the observer’s frame, motion and instrument; F is structured foreground; H is the translation medium and environmental conditions; R is a defined retained residue or memory state; and O_r is the decoded observation. T denotes their translation into an observation. The supplied argument order is retained. A domain must still supply its actual transformation, units and uncertainty; the expression is not a universal executable formula. [K-WP05]

Foreground and environment are consequently explanatory inputs rather than undifferentiated “noise.” A residue becomes a calculable state only when its units and update law are supplied. A registered but incompletely defined source can remain addressable while understanding develops.

Draft XXXVII §XXV.8 supplies an expanded observation relation, O_r = T(S,M_o,F,H,R,C,U), in which C denotes calibration weighting and U the uncertainty envelope. This is a documented extension of the five-input expression, not a missing pair of terms to insert silently into every earlier equation. The paper applying either form must declare the chosen version and its variable meanings. C in this expression is not Celsius temperature or the thermal model’s heat capacity. [K-MONOGRAPH §6; K-WP05 E2 §2]

The observer therefore has a mathematical interface as well as a narrative role. Mathematical Foundations §7 specifies frame identity, reference origin, basis/orientation, units and transformation metadata, then requires an application to classify its quantities as invariant, covariant or deliberately observer-indexed. A covariance condition says how the same relation transforms with a declared frame change. It is an obligation on the chosen model, not a license to change the underlying entity whenever the viewpoint changes. [MATH1 §§7.1–7.3]

### 2.2 Nested frames and the shared origin

The Foundations preprint’s “boxes in a box” construction makes the dependency visible. Each body has a local box anchored to a face, declaring its directional reference. A containing system supplies their shared reference. An external observer also declares its own scale and position in the account. The outermost rationale states why these bodies, at this scale, for this purpose; it is not assigned another absolute measured size. [K-FOUND §4.2]

The boxes therefore perform different jobs. Local frames orient an observation. The system frame relates participating bodies. The observational rationale bounds the question. Treating all three as interchangeable containers would remove the construction’s point.

The current origin designation is the literal **.1**. It names one shared referent across observables; it is neither the decimal number 0.1 nor the integer 1, an independent origin on every axis, or an instruction to shift a graph numerically. Earlier editions used other notation. Their historical formulas must be read with their dates and the subsequent author correction. [K-CURRENT; K-CORR]

The same precedence applies to absence. The September preprint discusses declarative zero, but the present requirement does not permit “not observed” to become “nonexistent.” A preserved source may report a conventional numerical zero. That report remains typed as a projection with its own context; it cannot replace the referent or its constituents.

**Transition to representation.** Once these roles are distinct, the next question is mechanical: what must a stored or transmitted object contain so that later computation cannot silently merge them?

## 3. Representation: retain the construction, then define its calculation

### 3.1 Ordered relations are computational information

Keddeh’s Relative Relational calculation treats a result as belonging to a construction. Predecessors, their orientation, the operation, the observation frame and the order of nested relations remain part of what is represented. Flattening the construction may preserve a displayed number while changing the object being discussed.

The October Observer Relational Mathematics extension preserves the expression:

**(-3)^(+1) + (-14)^(+1) = (-17)^(+1).**

Its parenthesised superscripts are attached relational groups. The source describes them as lower-level unification and relational power over their predecessors. It expressly rejects cancelling them, making them independent multiplication factors or silently applying conventional exponent rules. The proper implementation task begins by preserving that syntax and binding it to the author’s definitions. [K-ORM §§1–7]

An ordered tree can retain such nesting, including repeated constituents. It does not determine the algebra by itself. For each native operation, a computational specification needs admitted inputs, attachment rules, output meaning, intermediate states and rejection behaviour. The source’s possible positive/negative assignments are candidate configurations; listing them does not calculate their outcomes.

The author’s recursive “squared” wording and the requested two-/three-body quadratics must be handled on the same basis. Ordinary numerical squaring cannot be substituted simply because the word resembles a familiar operation. The exact authored layer or operator must be resolved first. [K-CURRENT]

### 3.2 Identity, definition and placement

Three independently changing things must remain distinguishable: which entity is referred to; what is currently known or defined about it; and where its representation is stored. A revised definition can concern the same entity. Relocating bytes can preserve both identity and definition. A new measurement can add a record without overwriting either. The KEX research baseline makes these distinctions explicit. [K-KEX]

This gives a practical meaning to semantic or relational addressing. A higher-level reference names the intended object and relation; a resolver finds its current carrier. Host offsets, array indices and rendering coordinates belong to that resolution layer. They do not become native origin definitions merely because software uses them.

The architectural benefit is reconstructibility. A reader or runtime can follow a derived assertion back to its contributing records, recover the applicable definition and identify which transformation was performed. The cost is additional retained structure. Whether that cost improves correctness, recovery or computation must be measured against an alternative preserving the same required information.

### 3.3 Typed distinctions and the proved information boundary

The formal sources distinguish an instantiated record from its numerical projection. Present(0), an absent observation, a declared boundary and a cancellation record can all be meaningful states while answering different questions. Mathematical Foundations gives a constructive example: a record-existence indicator can return 1 while the record’s numerical value is 0, because those functions describe different properties. That historical indicator is not an encoding of the current literal .1. [MATH1 §§2, 5–6; NATIVE4 §§2–4]

The Translative Loss result makes the preservation concern precise. Let X be a discrete source-state random variable, φ a deterministic projection and H(X | φ(X)) Shannon conditional entropy. If two distinct source states with positive probability have the same projection, the conditional distribution at that output is not concentrated on one state. Its entropy is positive, so the full weighted conditional entropy is positive. If φ is injective on the support, the conditional entropy is zero. These are the theorem’s conditions; global noninjectivity outside the observed support is insufficient for the strict conclusion. [MATH1 §§4.1–4.4]

This proof applies when a declared representation actually merges the relevant states. It does not establish that every scalar is defective, that every compression loses required information, or that the full observer transformation T is noninjective. A scalar result may be sufficient for one question and insufficient for another. The thermal example below makes the required question explicit: can the stored state predict the future mean?

Cancellation supplies a practical construction. The numeric result can remain zero while a cancellation record retains its producing relation and contributing entries. The source’s conservative projection argument is complete for its specified Present-input and cancellation cases; mixed-constructor operations still require their declared semantics. This result therefore supports retaining a ledger alongside a computed balance without inventing evaluation rules for the separate attached relational groups in Section 3.1. [MATH1 §§5.1–5.5; NATIVE4 §§3–4]

The observation-preservation facility examines the corresponding data requirement. It can check that source text, roles, ordered children, missingness and projection survive serialization and readback, and reject altered retained records. It cannot establish the truth of the observation or evaluate a native operator whose semantics are not supplied. This gives its interactive output a definite place in the argument. [E-PRESERVE §§2–4]

**Transition to computation.** A meaningful representation still needs an admitted way to act. The next boundary binds a source-defined operation to a particular execution environment, then checks what actually happened.

## 4. Computation: governed transitions across sovereign boundaries

### 4.1 Composing the architecture

The architecture assigns complementary roles. BRAINK retains continuity, governed execution and evidence. KEX supplies typed identity and state evolution. IL-LLM carries semantic relationships and traversal through the retained structure. VFS provides addressable carriers for state and executable material. These elements interact without becoming interchangeable names for one undifferentiated engine. [K-BRAINK; K-KEX; K-LINE]

The foundational Series Paper 01 represents state together with retained proof/evidence obligations and requires a cross-domain mapping to preserve the relevant identity, admitted transitions and proof boundary. In this composition that rule becomes a source-and-operation contract, rather than an assertion that every implementation carries a complete proof of its physical behavior. [WP01 §§2, 5]

A task follows a concrete chain: resolve its source and dependencies; check the admitted input and authority; instantiate the permitted execution image; perform the operation; observe the result; retain and read back its record. The boundaries are consequential. Parsed code is not yet an effect. An effect is not yet an observed result. A returned result is not yet a recoverable record.

The line-origin formalism supplies an explicit architectural walkthrough: an addressed line anchors a local matrix; BRAINK retains its state; IL-LLM traverses a reachable relation; KEX produces a typed successor with predecessor lineage; BRAINK retains the continuation. In the inspected workbench, twelve stable line objects have overlapping frame memberships: L5 belongs to three frames while remaining one line identity. Descending from a line creates child references without replacing the parent. L identifiers are software frame anchors in this lineage, kept distinct from the current **.1** referent. The newly reproduced isolated class run passed four checks covering identity, overlap, descent and cardinality. Its finite dimension/count operations remain conventional reference calculations; overlapping membership does not itself define a tensor-product factorisation. [K-LINE; E-LINE]

The historically browser-executed observation path supplies a complementary execution walkthrough; the newly reproduced pure-source checks exercise its core and selected static/async properties separately. A VFS package retains runtime and application source with byte counts and hashes. The host checks those identities, creates a sandboxed child and sends it the admitted application. The child preserves the input’s exact source and ordered relations, then returns a receipt. The host checks the active message source and run token and verifies exact receipt readback. This path exercises retained source, typed admission and nested execution; the broader IL-LLM traversal sequence above is an architectural mapping rather than an extra result of that fixture. [E-PRESERVE]

### 4.2 What a sovereign gap must preserve

The proposed gapped sovereign environment separates what is projected to a participant from the state and capabilities that participant may execute. Its useful property is controlled crossing: a request carries sufficient identity, context and authority to be checked on the receiving side. A gap that merely hides a surface would not establish this property.

Local continuation also needs retained dependencies. If a task requires an unavailable external source, the environment must expose that unresolved dependency. If its declared dependencies are available locally, it can attempt the bounded task and retain the outcome for later reconciliation. Which operations continue, which wait and which require shared agreement belongs in the deployment contract.

The term “gapped” must identify the exercised separation: representation, capability, process, network or physical host. The browser specimen establishes selected software boundaries; a physical air gap or cross-site recovery requires the corresponding deployment test. [E-PRESERVE; K-BRAINK]

### 4.3 Quantum mapping as an execution branch

The inspected Native Host Adapter R14 contains a P15/A15 quantum-state module. Its internal labels K_NEG and K_POS map to external computational-basis labels |0⟩ and |1⟩. A state is represented by complex amplitudes and normalised; tensor composition builds joint states, matrices transform them and measurement returns an outcome, probability and normalised successor. Zero coefficients are admitted; an all-zero vector is rejected. These are implemented conventional state-vector operations in an orthonormal computational basis. Their existence is separate from a claim that the native line-origin formalism derives those amplitudes or gates. [E-QUANTUM]

The implementation also exposes a useful contract distinction: its unitary predicate checks a matrix, whereas apply checks dimensions and normalises the result without itself requiring unitarity. A transition advertised as a unitary gate needs finite, well-formed inputs plus a unitarity check or validated gate catalogue. Measurement and conditional non-unitary updates need their own contracts. Independent boundary probes found that a NaN-containing matrix passes the original source predicate and produces a non-finite state norm; supplied samples −0.1 and 1 can select zero-probability outcomes because their range is not checked. Finite-value validation and sample-range admission are therefore required before accepting untrusted inputs; the nominal Bell calculation below remains reproducible. [E-QUANTUM-REVIEW]

The KRS counterpart reference branch addresses a complementary question: which preparations and relational counterparts remain possible given a readout and declared context? A negative readout alone leaves two possible counterparts in its fixture; adding frame F1 selects positive-A. Its newly reproduced ten-test suite passed, including a conflicting preparation that must change a unique result to ambiguous. That finite reference model, the line-origin workbench and the P15 state-vector module are individually addressable mechanisms. Their integration must be specified rather than presumed from shared terminology. [K-KRS]

**Transition to application.** These mechanisms acquire a scientific purpose when a particular domain supplies its quantities, laws and observations. The following cases show both what the common architecture contributes and what each domain must add.

## 5. Topic studies and bounded worked applications

### 5.1 Water, Celsius and the phase-tagged boundary

Consider a reported observation of sample A by instrument B at a specified moment: 0 °C. The record needs the sample, instrument, quantity, scale, acquisition conditions and uncertainty status. If uncertainty is unavailable, that is retained as an unavailable input. It is not filled with an invented precision. The conventional numerical zero describes the temperature coordinate; it does not say that the sample, its energy or its record is absent.

The SI scale relation is **t/°C = T/K − 273.15**. Thus 0 °C corresponds to 273.15 K. The exact offset conversion changes neither the sample nor the uncertainty of the observation. Temperature differences have the same numerical size in the two units, while raw Celsius-number ratios generally differ from thermodynamic-temperature ratios. A 20 °C sample is not twice the thermodynamic temperature of a 10 °C sample. This distinction concerns the operation applied to a scale, not the validity of the observations. [SI; VIM §§2.3, 2.9, 2.26]

K-CORR’s water discussion puts the bilateral relation at the transition itself. It retains the boundary/whole expression **− [B=(−1+)] +** and the sequence **solid-side ← phase boundary → liquid-side**. These source expressions identify an existing reference relation. They are not instructions to subtract one from an SI measurement. The corrected source also labels its transported-integer arithmetic elsewhere as a comparison construction, so that construction cannot define the native water operator by association. [K-CORR E3 §2]

The July mathematical papers supply an actual invertible coordinate construction. Mathematical Foundations §8 defines:

**D = ((ℝ∖{0})×{⊥}) ∪ ({0}×{ice, liquid})**, with **Z = (−∞,−1] ∪ [1,∞)**.

For nonzero Celsius coordinates, **κ(C,⊥)=C−1** when C<0 and **κ(C,⊥)=C+1** when C>0. At the seam, **κ(0,ice)=−1** and **κ(0,liquid)=+1**. Its inverse is **κ⁻¹(z)=(z+1,⊥)** for z<−1 and **κ⁻¹(z)=(z−1,⊥)** for z>1, with the two seam points returning **(0,ice)** and **(0,liquid)** respectively. [MATH1 §§8.1–8.3]

The bijection follows directly. Each open branch maps injectively to its disjoint interval; the tagged seam states occupy distinct endpoints. Every codomain point has exactly the stated preimage, and substituting either direction recovers the input. The tag is necessary to retain the distinction between the two states sharing the external zero coordinate. This is a proved representation property on the stated domain. [MATH1 §8.4]

Native Algebra v4 gives a related phase-side convention: **C_K(C,solid)=C−1 for C≤0** and **C_K(C,liquid)=C+1 for C≥0**, with **C(C_K,solid)=C_K+1** and **C(C_K,liquid)=C_K−1**. Here phase tags accompany the allowed branches, whereas MATH1 uses its explicit seam-only tagging domain. The two source conventions must not be silently combined. Neither replaces a thermodynamic equation of state or claims to classify every physically possible phase from temperature alone. Pressure, energy, composition and admissibility still belong to the physical application. [NATIVE4 §5; MATH1 §8.5]

The same source supplies a dimensioned water calculation:

**ΔT_equiv = q_fusion/c_p = (333,550 J kg⁻¹)/(4,184 J kg⁻¹ K⁻¹) = 79.720363288719 K.**

With the declared latent heat of fusion and liquid-water specific heat, division cancels mass and energy units to give an equivalent sensible-heating temperature interval. It does not say that melting raises the sample temperature by 79.72 K. The material values are specified inputs whose empirical provenance and applicable conditions must accompany a physical test. [NATIVE4 §5.1]

A new six-fixture review reproduced the phase-side round trips at −20, −1, 0 on the solid branch and 0, 1, 20 on the liquid branch. Both zero-coordinate states decode to 0 °C while retaining their different phase side, and the selected energy ratio reproduces numerically. These are newly chosen reviewer fixtures, not recovery of the exact original six fixture inputs. [WORKED]

The contextual Celsius facility should therefore make a narrow operation visible: retain the reported scale and original record while computing an explicitly conventional scale conversion. A dedicated phase-map or energy experiment would need its own source-defined input domain. A successful Celsius conversion alone does not execute either of those separate models.

### 5.2 Thermal projection: the relation needed to predict a mean

A second application turns retention into a prediction question. The executed scale-observability model uses two equal-area idealised patches at 260 K and 300 K in 280 K radiative surroundings. Each patch has heat capacity C=500 J/K, area A=0.005 m² and emissivity ε=0.95. Their mutual conductance is K=0.02 W/K. Here italic variable K denotes conductance; the K in temperature units denotes kelvin. The model excludes phase change and mass exchange. It does not identify the colder patch as liquid water. [THERMAL]

Define the retained mean and contrast as **m=(T₁+T₂)/2** and **d=(T₁−T₂)/2**. The source’s exact projected equations are:

**dm/dt = γ[T_env⁴ − m⁴ − 6m²d² − d⁴]**  
**dd/dt = −γ[4m³d + 4md³] − (2K/C)d**  
**γ = εσ_SB A/C.**

The Stefan–Boltzmann constant used in the calculation is 5.670374419×10⁻⁸ W m⁻² K⁻⁴. Consequently γ has units K⁻³ s⁻¹, and both derivatives have units K/s. The original temperatures remain recoverable through **T₁=m+d** and **T₂=m−d**. [THERMAL]

Why is contrast needed? Averaging the fourth-power radiative terms gives m⁴+6m²d²+d⁴, rather than m⁴ alone. Conductive exchange cancels from the mean equation but changes the contrast. Initially m equals the surrounding temperature, yet d is nonzero. A model that retains only m and drops d predicts no mean change from 280 K, while the resolved system can still exchange net radiative energy. The missing relationship changes the predicted output even though the initial displayed mean is correct.

An independent fourth-order Runge–Kutta reproduction used 6,000 steps of 0.1 s. After 600 s, the resolved/retained mean is approximately **279.944389043 K**; the mean-only prediction remains **280 K**, differing by **0.055610957 K**. The maximum discrepancy between resolved evolution and the retained mean/contrast evolution is approximately **2.551×10⁻¹² K**, comfortably within the stated 10⁻⁹ K comparison tolerance. [THERMAL; WORKED]

The retained system is an algebraic change of variables of the resolved model, so their agreement is expected and checks the implementation. The substantive contrast is with the model that discards d. This demonstrates a specific sufficient-state requirement for prediction; it does not establish universal closure for arbitrary coarse-graining. Larger distributions can require additional moments or other closure information. Nor does it substitute for the author’s separately defined BOX operation.

The liquid, ice and vapour scenarios elsewhere in the source are conditional physical graph specifications. They require admissible phase states, geometry, constitutive relations and optical data. They are useful research configurations, but they were not all solved by this two-patch calculation. That distinction credits the executed result without borrowing unperformed experiments.

### 5.3 Observer transformations and the three-dimensional wave

The observer/frame comparison supplies a concrete coordinate round trip. Its declared transformation is **frame(q)=sRq+t**, with positive scale s, a rotation R and translation t, together with the corresponding inverse. In 500 fresh reference cases the maximum round-trip error was approximately 1.677×10⁻¹⁴. This verifies the specified numerical map, rather than a universal theorem about all frames. [WORKED]

The same comparison model separates source and foreground through **y₁=s+f**, **y₂=s+kf**, hence **f=(y₂−y₁)/(k−1)** and **s=y₁−f**. The s in these equations is source contribution, not frame scale. With source 2, foreground 3 and k=2, the observations 5 and 8 recover both contributions. Repeating the first transform leaves the system rank-deficient. The implementation rejects |k−1|<10⁻¹⁰; its sensitivity indicator 1/|k−1| shows why merely nonzero separation can still be poorly conditioned. All 441 newly exercised noiseless cases recovered their inputs. This local result is consistent with WP-05’s identifiability analysis and makes no noninjectivity assumption about the full T. [K-WP05 E2 §§3–6; WORKED]

The volumetric wave model adds a spatial field and an explicit observer plane. It retains **957 identified samples** in a cylindrical envelope. With x a longitudinal coordinate and y,z normalized transverse coordinates, its scalar amplitude and propagation speed are:

**A=e^(−2(y²+z²)) cos(2π(x/λ−ft))**, **v=λf**.

λ is wavelength in the declared reference-length unit, f is inverse reference time and t is reference time. A is dimensionless. v therefore has reference-length/reference-time units; the implementation does not establish a measured speed in metres per second. A declared yaw/pitch basis places each local sample through **position=origin+B·local**. In this model B is a rotation basis, not the cosmological residue map or a boundary-separation operator. [WAVE]

Each sample retains identity, local coordinates, spatial position, phase, envelope and amplitude. Changing time evolves the scalar field while preserving the sampled positions and IDs. Changing the observer slice selects a plane or sample for readout; it does not silently rewrite the source-field values. Camera orbit is a further display operation. The optional height encoding used to show amplitude is distinguished from the original spatial coordinate, so a graphical wave crest does not become an undocumented movement of material.

New checks verified the implemented phase law, all 957 distinct IDs, basis orthogonality to about 1.11×10⁻¹⁶ and spatial norm preservation to about 1.34×10⁻¹⁵. At a quarter cycle the centre sample has amplitude **6.123233995736766×10⁻¹⁷**, within the declared 10⁻¹² tolerance but not exactly zero. Its identity survives. Invalid nonfinite derived output is rejected with diagnostic custody and the last valid model retained in the session. These are numerical and state-retention checks on an illustrative three-dimensional field, not new empirical wave measurements. [WORKED]

The current model keeps opaque .1 separate from its conventional rendering coordinates [1,1,1]. A different inspected spatial renderer labels a CENTRAL **1** at (0,0,0), and older source artifacts use U=1 or (−1+). These are edition-specific identities and display conventions. No inspected mapping permits silently rewriting the author’s CENTRAL 1 construction as .1. [SHELL; K-CURRENT]

### 5.4 Interacting bodies, dimensional construction and the quadratic question

Two bodies establish a mutual relation; adding a third changes the participating system and its dependencies. In the Foundations boxes construction, each body retains its local directional frame while the containing frame supplies their shared comparison. The observer’s account remains a further relation. A worked record can preserve A’s relation to B separately from B’s relation to A, retain dependence on C, and change observer D’s frame without losing the contributing identities. Removing C creates a different system configuration, rather than silently reusing a two-body interpretation of the old record. [K-FOUND E3 §4.2]

The recovered correction record also contains the author’s challenge about a number line filling a grid, followed by the line → surface → volume exposition **n→n²→n³** and the dimension-dependent reading **64=8²=4³**. This is positive source evidence for the dimensional construction and its relation to box-in-box reasoning. It must retain its speaker roles and the corrected status of transported arithmetic; a conversational explanation is not automatically a complete native operator contract. [K-CORR E3 §7.2]

There is also genuine three-dimensional rendering in the inspected source. A CENTRAL 1 display generates a parametrised Möbius reference surface with six centre-to-face rays. A separate mesh/tensor-shell view renders supplied vertices and faces with declared ownership, retaining source coordinates while the camera changes. Draft XXXVII contains actual plotted wake-shell and observer-shift figures, including a tubular/cavity shell and a shell with translation axis, residue arcs and observer marker. These artifacts should be credited as geometry and rendering evidence, rather than treated as absent. [SHELL; K-MONOGRAPH]

Their precise relationship to the native construction remains the question. The inspected mesh renderer admits supplied geometry; it does not itself derive that geometry from the author’s BOX rule. The separately verified Möbius seam and edge-incidence tests establish their named properties, not native tensor closure. The exact source-level transition from the author’s BOX/CENTRAL 1 to the intended tensor shell remains unlocated in this reviewed set. This is a bounded linkage gap, not a claim that the construction is missing from the whole corpus. The author’s Learning Method Control expressly warns against replacing that developed object with generic nesting or an analogy. [METHOD; SHELL]

The requested two-/three-body quadratic calculation accordingly needs the native relation being constructed, the meaning of its quadratic layer, admitted inputs, evolution law and reconstruction rule. Ordinary squaring, a generic hierarchy or a mass/centre-of-mass summary cannot be substituted solely because it is easy to simulate. Once the authored contract and applicable physical law are attached, the comparison can test trajectories, phase, conservation where applicable, close encounters and tolerance convergence. Energy agreement alone is insufficient. This study neither supplies nor claims a general solution of the classical three-body problem. [K-FOUND; DYNAMICS; SPICE]

The finite KRS facility can examine a narrower relational inference now: a counterpart is returned only when it is constant over all matching preparations. Adding the specified conflicting preparation must turn a previously unique answer into ambiguity. The line-origin facility can examine shared identity and descent. Neither facility executes the unprovided body dynamics or BOX-to-shell transition.

### 5.5 Cosmology: observer-conditioned data and discriminating inference

Volume 03 develops motion, wakes, separation, disturbance history and residue as a research sequence. Its hidden-layer branch changes from compact objects through shear and plasma/magnetic interpretations to extended field structures. Its own account records that the CMB work constrained the full-replacement branch while continuing the observer-conditioned route. These histories remain part of the research argument; repetition of their descriptions is not independent experimental replication. The current Volume 03 edition transparently uses a retained unique-content transcript because the earlier capture’s original bytes and images were not recovered. [K-COSMO E1 §§2–8]

The restored Constraints packet supplies a stronger paragraph-level source for specific models. Packet paragraph 922, restored item C054, corresponds to zero-based full-DOCX paragraph index 960 and gives **M → P → B → R → E**: motion/translation, pressure/redistribution, boundary separation, retained residue and an equilibrium-state estimate. The packet numbering and DOCX indexing are different locators. Here the letters name process stages, not five multiplied quantities. The source’s proxy computations and plotted shells must likewise be attributed to their own definitions. [K-MONOGRAPH E1 §§3–4, C054]

WP-17 supplies the local inference model:

**y_t = g(θ_ΛCDM) + Fα + M_oβ + Br_t + ε_t**  
**r_(t+1) = λr_t + κu_t + η_t.**

g is the selected baseline cosmological prediction; the other terms represent foreground, observer contribution, mapped residue and error. All additive contributions must occupy the same observable space and units. The actual experiment must select its likelihood, data release, masks, calibration, covariance, priors and parameter constraints. In particular, an unanchored rescaling of B and r can leave their product unchanged, and overlapping foreground/observer/residue responses can prevent separate identification. The E2 edition retains these concrete failure cases rather than assuming that naming more terms makes them estimable. [K-WP17 E2 §§2–3, 6]

The null comparisons must be exact. Removing observed residue requires **Br_t=0**. Setting κ=0 alone does not ensure that when initial residue or process noise still reaches the observation. WP-18’s λ=0 comparison instead removes dependence on previous residue while allowing present forcing and noise. Its local deterministic attraction condition **ρ(J)<1** applies to a declared discrete-time linearisation; it does not by itself guarantee a stationary stochastic distribution under unspecified driving noise. [K-WP17 E2 §4 and counterexamples §6; WP18 §§1–2]

A meaningful cosmology evaluation therefore reproduces the selected baseline before adding residue, performs injection/recovery and observer-frame tests, and measures held-out prediction with a complexity penalty. A residue that only absorbs foreground or loses its gain out of sample fails that proposed explanatory role. Planck’s model and likelihood documentation provides a named comparison methodology. The preserved-record component can retain this experiment’s inputs and provenance; its pass counts do not establish cosmological fit or physical truth. [K-WP17 E2 §7; PLANCK]

The WP-17 contextual facility is a reference recurrence and null-contribution test, not a live Planck likelihood or a completed cosmological observation. That limited calculation is useful precisely because it can expose the difference between κ=0 and Br_t=0 before a larger inference is attempted.

### 5.6 Quantum calculation: preserve what determines the outcome

The P15 module provides a reproducible small-system walkthrough. Start with K_NEG, apply the supplied Hadamard matrix, tensor with a second K_NEG state and apply CNOT. In computational-basis order 00, 01, 10, 11, the joint probabilities are approximately **0.5, 0, 0, 0.5**. The pure two-qubit coefficient-determinant test returns non-separable. Samples 0.25 and 0.75 select 00 and 11 and return normalized successors. This separability test concerns a pure state in a specified tensor-product basis; it is not a general mixed-state criterion. [E-LINE/E-QUANTUM; K-LINE §4.2]

The new isolated replay reproduces all nine nominal self-tests. They cover basis normalization, superposition, selected gate unitarity, tensor composition, Bell non-separability, measurement, zero-vector rejection, a finite nonunitary falsifier and external basis-label retention. E-LINE separately checks that the extracted P15 module matches its retained full carrier. E-QUANTUM-REVIEW’s current replay checks the module digest without a new whole-carrier comparison. Both keep the three adverse-input admission failures described in Section 4.3 visible. [E-QUANTUM-REVIEW §§2–5]

A second explicit example shows why API success is not enough to certify a gate. Applying diag(2,1) after Hadamard is accepted and renormalized to probabilities approximately **0.8, 0.2**, although the separate unitary predicate rejects that finite matrix. This is the implemented arbitrary-linear-map behavior, not evidence that the map was a unitary quantum operation. Invalid sample and nonfinite-state checks belong to the admission contract, rather than being inferred from the Bell example.

The next integration step is to retain basis order, phase-bearing amplitudes, gate sequence, joint-state identity and readout conditions inside the ordered-record mechanism. A probability display alone cannot reconstruct all of them. The line-origin workbench contributes shared identity and recursive frame mechanics; a native quantum mapping must additionally define how those mechanics realise amplitudes, phase, composition and observation. NIST’s software-model reference supplies an external comparator for this distinction. [K-LINE; QUANTUM-REF]

A separately pinned P15 input-admission candidate now supplies the contract for the optional Bell facility. Its local review passes 62 grouped checks, including preservation of the original nine nominal tests; those counts are not added as independent experiments. The candidate admits finite states and samples in [0,1), rejects nonfinite inputs and zero-probability fall-through, and provides a unitary-only gate API while retaining the distinct general conditional-map API. The facility follows ordered Bell preparation, phase and basis order, a supplied deterministic readout sample and its normalized successor. Its native installation and final runtime readback belong to the hosting record; this article does not turn a local candidate review into a physical Bell experiment. [QUANTUM-CANDIDATE; INTERACTIVE-CONTRACTS]

## 6. Evidence and a reproducible evaluation method

### 6.1 What the available evidence establishes

The record contains dated historical results and newly reproducible calculations. Their relationship matters more than a combined pass total.

The **17 October browser run** reported 39 fixed vectors and **131 passing checks**. Its historical review reported **714 passing checks**, comprising 672 core, 33 VFS/source-binding and nine controlled asynchronous checks; the core account included 557 schema-mutation cases. The original raw browser/review receipts, historical review harnesses and mutation corpus were not recovered into the current technical packages. These figures remain attributed historical observations. The current article does not present them as a newly rerun 714-check experiment. [E-PRESERVE; E-REVIEW]

The recovered, digest-matched R4 core and acceptance harness now reproduce **131/131 checks on 39 vectors in an isolated Node environment**. A separately written new review reproduces **121/121 checks: 84 fixed-vector/core properties, 28 static source/CSP bindings and nine controlled asynchronous snapshots**. It does not reconstruct the missing 557-case corpus or operate a browser. Its first run exposed eleven harness-side false negatives; correcting negative-zero handling and HTML-entity decoding in the harness produced the reported result without changing the source runtime. The initial result remains preserved. [E-PRESERVE §§1, 4; E-REVIEW §§1, 5]

The new line-class replay passes four checks; P15 passes nine nominal checks while retaining three failed adverse-input admission expectations; KRS passes ten tests and emits six cases. The worked-application verification separately reproduces ten bounded checks covering phase maps, the selected water-energy ratio, frame/mixture inverses, thermal projection and the wave model. Four additional shell/import checks test their named geometric and admission properties. These suites have different objects and denominators, so they are not added into one qualification number. [E-LINE; E-QUANTUM-REVIEW; K-KRS; WORKED; SHELL]

The preservation component retains exact source, literal .1, roles, ordered relation trees, explicit unspecified context and separate identities even when projected values coincide. It rejects altered records and conflicting identity reuse. Its in-memory custody is not durable storage, and its structural acceptance does not establish the truth of a supplied observation. The broader BRAINK v74 figures remain source-reported historical tests; the proposed comparative S01 programme is not converted into an executed result by citing them. [E-PRESERVE §§3, 6; K-BRAINK §§4–6]

Source recovery also has a declared boundary. The Constraints edition restores all 120 packet hits against the full DOCX, yielding 104 distinct complete source records, including 21 formerly truncated hits. K-CORR preserves all 396 native equation objects and 278 literal displayed source occurrences. In contrast, K-CURRENT E4 is an explicit editorial reconstruction from retained author directions, and Volume 03 is a unique-content transcript without original-byte identity. The source register keeps these different kinds of custody visible. [K-MONOGRAPH; K-CORR; K-CURRENT; K-COSMO]

### 6.2 One evaluation package, separate acceptance gates

Read the relevant model before opening its optional facility. Seven contextual contracts accompany this study: source preservation, finite KRS counterpart inference, line-origin identity/descent, WP-05 mixture separation, WP-17 residue comparison, Celsius scale conversion and the separately pinned Bell candidate. Each is a small reference computation with its own input semantics, independent expected results and source identity. The host supplies the executable link and actual run record. Thermal, phase-map and wave results retain their separately cited calculation records; the original P15 replay likewise remains distinct from the candidate facility. The spatial-radix topic carries its own article and finite-test contract. [INTERACTIVE-CONTRACTS; SPATIAL-RADIX]

For a reproducible study, retain the source edition and digest; ordered input records; operator or transformation definitions; runtime and dependency versions; expected outputs established independently of the candidate; complete actual results; and the stated failure boundary. Fix tolerances, units and comparison criteria before the run.

| Gate | Required experiment | Failure that matters |
|---|---|---|
| Representation | Round-trip exact source, roles, origin label, nesting and missingness; deliberately alter each | A changed relation is accepted as the same retained record |
| Calculation | Evaluate source-defined operations against independently derived examples, including admissible and rejected cases | An output passes only because the evaluator silently substitutes a different algebra |
| Execution boundary | Restart the declared software boundary; inject stale identities, interrupted replies, denied storage and unavailable dependencies | Success is claimed without the required effect observation or recovery |
| Domain prediction | Freeze measurement or dynamics assumptions; compare held-out outcomes under equivalent observations | Apparent gain disappears when frame, noise, precision or model complexity is controlled |

For quantum mapping, add basis-order, normalization, composition, transition and readout checks before any hardware or speed claim. For a sovereign gap, name which boundary is interrupted and record whether the required source and authority survive. A restored JavaScript object and a recovered machine after power loss are different experiments.

Report failed and rejected runs as well as accepted ones. Measure incorrect equivalence, lost lineage, reconstruction failures and resource cost under matched retained-information requirements. A system that rejects every input is not a successful calculator; a system that accepts every input is not a successful verifier.

## 7. Discussion: the compositional result

The shared mechanism is preservation across boundaries. A measurement crosses from phenomenon into an observer’s record; that record crosses into a representation; a representation crosses into a runtime; a local result crosses into a shared inference. At each crossing, the architecture asks which identities, relations and conditions must remain recoverable.

This explains why the topics belong together without making them identical. Celsius supplies a clear scale transformation. Interacting bodies require relational framing plus dynamics. Cosmology adds incomplete observation and competing generative explanations. Quantum calculation requires a fully specified state and operation mapping. Each introduces new obligations above the common representation layer.

Three research consequences follow. First, preserving distinctions creates the conditions for correct comparison but does not guarantee a useful prediction. Second, observers must contribute the information the inference needs. Repeating the same linear transform does not restore structural rank, although independent repeated noisy measurements can improve precision. Third, stronger source retention carries an engineering cost, so performance comparisons must match what each system preserves and produces.

### 7.1 Spatial representation and efficiency

Spatial Radix Mapping is examined in its own complete, source-led article. It preserves the author’s row-copy construction, single central 1, outward reading, mirrored (−1+) whole description and stated extension through 9 to whole 2. The proposed coordinate, seam and hierarchy interpretations remain labeled: in particular, treating a previous whole as a new local 1 was introduced by the prior AI and is not attributed to the author as an already defined native transition. [SPATIAL-RADIX]

The separate analysis reproduces 33 finite checks, including expected counterexamples and unresolved-operation statuses. The displayed 3×5 grid has 15 cells, total label sum 43, horizontal and vertical symmetry and half-turn symmetry. A four-cell alteration preserves its histogram and the tested diagonal-balance signatures, showing that those signatures alone do not authenticate the original content. This result concerns the stated balance predicates, not separate KEX identity or authorization mechanisms. The full article develops the construction before its optional tests. Hardware speed, cryptographic authentication and unlimited scaling remain separate engineering obligations. [SPATIAL-RADIX]

The separately reviewed efficiency tables provide a related but narrower kind of evidence: all 69 supplied rows and 276 derived numerical cells reproduce under their inferred operation-count formulas. Shared-root savings assume the declared intersections; fusion savings require a sufficient-state merge contract and accounted reopening work. These are useful conditional models, not elapsed-time BRAINK measurements or proof of exact general N-body equivalence. A comparison should retain the required outputs and lineage on both sides, then include construction, validation, traversal, storage and update costs. This protects genuine savings from being obscured by an unequal baseline. [EFFICIENCY]

### 7.2 The next compositional experiment

The next compositional experiment can join the existing ordered-record component to the existing quantum calculation, retaining each input, gate and outcome under a versioned workbench mapping. The same method can carry an authored body calculation once its operator contract is attached. This makes the programme cumulative: each new operation inherits an inspectable source and contributes its own result.

## 8. Conclusion and revision control

Keddeh’s proposed architectures can be read as a continuous route from relational observation to inspectable computation. The observer/observed distinction defines the record; ordered representation retains its construction; typed state and governed execution carry it across boundaries; domain models make it calculable; independent observation determines which claims survive.

The phase-map proof, water-energy ratio, thermal projection and observer/frame calculations establish specific mathematical and numerical parts of that route. The wave and shell artifacts establish declared spatial representations; preservation and P15 establish bounded software capabilities. The nested-body and cosmological branches show where the same retention discipline meets further source-defined dynamics and measured inference.

R2 incorporates the recovered cross-paper definitions, the sixteen core edited references, supplemental source readers, separately verified worked applications and the source-led spatial-radix article available on 18 October 2026. It preserves the 35,180-byte R1 manuscript unchanged, corrects historical-versus-current evidence attribution and keeps the complete write-up ahead of optional tests. Its next milestone remains a source-mapped integration that reconstructs the route from relational input to observed output, with each domain earning its own validation.

## References and source standing

The first sixteen references below form the core edited research set. Additional recovered sources, complete supporting articles and technical contracts have their own reading layers; they are not implied to be contained within those sixteen editions. Their original carriers, editorial manuscript hashes and source limits are identified separately in the accompanying register. E-QUANTUM is a reference alias within the combined E-LINE edition, not a seventeenth edition. Source links can require owner access. The references distinguish authored research, editorial synthesis and bounded verification; no external peer-review status is asserted.

### Core edited research and technical editions

- [K-CURRENT] Aboudy Keddeh / Keddeh Systems. *Observation and Identity Review*. E4, 18 October 2026. Current editorial reconstruction of retained directions.
- [K-ORM] Aboudy Keddeh / Keddeh Systems. *Observer Relational Mathematics*. Library R1, 18 October 2026.  [Original/source carrier](https://docs.google.com/document/d/1ibTDjjWLeDcKFclPKWClLs1dElMsjKDPfXal9UmJWhc/edit).
- [K-WP05] Aboudy Keddeh / Keddeh Systems. *Observer-Anchored Measurement Algebra*. E2, 18 October 2026.  [Original/source carrier](https://docs.google.com/document/d/1DXX1k2tWabswLE2zZ3QOcAgwtHti3wJz/edit).
- [K-FOUND] Aboudy Keddeh / Keddeh Systems. *An Unaccepted Evolution: One Structure Beneath Six Sciences, and Its Consequence for Quantum Computation*. E3, 18 October 2026.  [Original/source carrier](https://docs.google.com/document/d/11IjwDz_VPRWyA0samFCrOI7jLjnT-cwFH_HD2Z02izc/edit).
- [K-CORR] Aboudy Keddeh / Keddeh Systems. *Shared-Origin Research: Source Interpretation Corrections*. E3, 18 October 2026.  [Original/source carrier](https://docs.google.com/document/d/1Zy6UFShKONxd6EHzq3afc3UgaTfhkILJAVeOg3oHhYM/edit).
- [K-KEX] Aboudy Keddeh / Keddeh Systems. *KEX Algebra and Typed State Research Baseline*. Library R1, 18 October 2026.  [Original/source carrier](https://docs.google.com/document/d/1WnuzNoWlUHthjWp27UpqEryS_nJcpFIg3eDfQ4b4Mx0/edit).
- [K-BRAINK] Aboudy Keddeh / Keddeh Systems. *BRAINK Core Runtime: Governed Transitions, Recovery and Evidence*. Technical editorial E3, 18 October 2026.  [Original/source carrier](https://docs.google.com/document/d/1NcvcgjSwEXHR1Kqnbndxrn5AmPz9RVuEtd382j-yvkg/edit).
- [K-LINE] Aboudy Keddeh / Keddeh Systems. *KEDDEH Recursive Line-Origin Matrix Formalism*. Library R1, 18 October 2026.  [Original/source carrier](https://drive.google.com/file/d/1XCUFOmHxYHYtDiNrdO9vTZGQnU11toys/view).
- [E-PRESERVE] Aboudy Keddeh / Keddeh Systems. *Observation Preservation R4: Source Admission and Ordered Record Retention*. Technical editorial E1, 18 October 2026.  [Original/source carrier](https://www.keddeh.com/mainsequence/research-assets/observation-preservation-r4.html).
- [E-REVIEW] Aboudy Keddeh / Keddeh Systems. *Observation Preservation R4: Independent Software Review and Reproduction Guide*. Technical editorial E1, 18 October 2026. 
- [E-LINE] Aboudy Keddeh / Keddeh Systems. *Native Host Adapter R14: Line-Origin and Quantum-State Module Reference*. Technical editorial E1, 18 October 2026.  Also cited as E-QUANTUM for P15. [Original/source carrier](https://drive.google.com/file/d/1kdxO0Oifa6kclxiBOUfni40XHmI2Hkjh/view).
- [E-QUANTUM-REVIEW] Aboudy Keddeh / Keddeh Systems. *P15 Quantum-State Module: Nominal Replay and Admission-Boundary Review*. Technical editorial E1, 18 October 2026. 
- [K-KRS] Aboudy Keddeh / Keddeh Systems. *KRS Finite Counterpart Model: Contracts, Reproduction and Source Fidelity*. Technical editorial E1, 18 October 2026.  [Original/source carrier](https://github.com/Keddeh1/Virtual-File-Space-ZCG-ARCHITECTURE/tree/research/krs-observer-counterpart-r1/research).
- [K-COSMO] Aboudy Keddeh / Keddeh Systems. *Volume 03: Cosmology, Wake Reconstruction, Heliosphere Systems and Hidden Mirror-Layer Theory*. E1, 18 October 2026. Retained-transcript edition; original capture and images unavailable. [Original/source carrier](https://drive.google.com/file/d/1iJvrrOw_qHoy6KhQXsb3HDPeqqpRRRkK/view).
- [K-MONOGRAPH] Aboudy Keddeh / Keddeh Systems. *Constraints, Persistence and Research Governance*. E1, 18 October 2026. Restored Constraints packet, with full-DOCX source. [Original/source carrier](https://drive.google.com/file/d/1l4lLSEwlGHW8vtjd2yVvVb18-EHYimAW/view).
- [K-WP17] Aboudy Keddeh / Keddeh Systems. *Observer, Foreground, and Residue in Cosmological Inference*. E2, 18 October 2026.  [Original/source carrier](https://drive.google.com/file/d/1RtVZ6fcmDcTyswAPVsLTK00yTL5Wv6p_/view).
### Recovered formal and methodological sources

- [WP01] A. Keddeh. *KEX Active-State Foundations*, 19 July 2026. §2 proof-bearing state; §5 cross-domain mapping. [Source](https://docs.google.com/document/d/1m2ipz_7dwt6t3Qeyhmnp3hkD6FTJ01ve/edit).
- [WP18] A. Keddeh. *Recursive Field Persistence and Memory-Bearing Systems*, 19 July 2026. §§1–2 typed recurrence, discrete-time local stability; §5 domain interpretation. [Source](https://docs.google.com/document/d/1kcRBlMBkSIufe67NCh5fl6l76Ui54daj/edit).
- [MATH1] A. Keddeh. *Mathematical Foundations and Proof Obligations*, 13 July 2026. §§4–8 conditional loss, conservative projection, observer covariance and phase mapping. [Source](https://docs.google.com/document/d/1x3m7DwJbqSFMK4skvzf0pWUXauM-R_gX/edit).
- [NATIVE4] A. Keddeh. *Native Algebra and Artifact Verification v4.0*, 14 July 2026. §§2–5 typed-state/cancellation and phase mapping; §5.1 dimensioned energy ratio. [Source](https://docs.google.com/document/d/1sz_cntJj0g1eqbSBrEGnC9gjjR1Jqp9p/edit).
- [METHOD] A. Keddeh. *Learning Method Control: No Compression*, 2 October 2026. 2 October 2026: source-defined objects and box-in-box non-substitution rule. [Source](https://docs.google.com/document/d/1ttMe9iKTi1X72J5rJzxG9ZmUvcvx5rIW/edit).
### Worked applications and technical contracts

- [THERMAL] Keddeh Systems. *Scale and relational phase graphs; executed scale test*. KEDDEH-RES-SCALE-001 v0.1 and KEDDEH-TEST-SCALE-001 v1.0, 16 October 2026. Supporting source and calculation records accompany the study; exact two-patch projected dynamics and 600-second RK4 receipt; no phase change or mass exchange.
- [WAVE] Keddeh Systems. *Volumetric wave reference*. inspected repository revision 98c6509dbebdbd17aa5d7a4fdfde092ac2eef9db. Supporting source and calculation records accompany the study; 957 identified samples, declared scalar field, source/observer/display separation; not measured physical data.
- [WORKED] Keddeh Systems. *Worked applications: water, observer algebra, wavelength and 3D shells*. independent source trace and 10-check verification, 18 October 2026. Supporting source and calculation records accompany the study; new bounded local calculations; selected phase fixtures are not the original six source fixtures; no browser or physical experiment.
- [SHELL] Keddeh Systems. *3D rendering, CENTRAL 1 and tensor-shell implementation trace*. source/function trace and four bounded checks, 18 October 2026. Supporting source and calculation records accompany the study; existing geometry/renderers and visually inspected monograph media; native BOX-to-shell transition remains a bounded source-linkage question.
- [EFFICIENCY] Keddeh Systems. *Uploaded efficiency models: arithmetic, scope and test results*. separate AI-assisted technical review R1, 18 October 2026. Supporting source and calculation records accompany the study; 69 rows / 276 derived cells reproduce operation-count models; does not establish elapsed-time BRAINK performance or exact general N-body equivalence.
- [QUANTUM-CANDIDATE] Keddeh Systems. *P15 input-admission repair: candidate contract and independent checks*. 18 October 2026. Complete candidate specification, pinned module and 62-check local receipt; final hosted execution has its own record.
- [INTERACTIVE-CONTRACTS] Keddeh Systems. *Seven contextual interactive tests: inputs, independent oracles and result boundaries*. R1, 18 October 2026. Full specification and fixed oracle fixtures, separate from application deployment.

### External primary references

- [SI] BIPM. The International System of Units (SI), 9th ed., v4.01, 2026, §2.3.1. [Source](https://www.bipm.org/en/publications/si-brochure).
- [VIM] JCGM. International Vocabulary of Metrology, §§2.3, 2.9 and 2.26. Accessed 18 October 2026. [Source](https://jcgm.bipm.org/vim/en/2.3.html).
- [SPICE] NASA/JPL NAIF. SPICE Reference Frames, frame and state transformation sections. Accessed 18 October 2026. [Source](https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html).
- [DYNAMICS] H. Rein and D. S. Spiegel. IAS15, MNRAS 446, 1424–1437 (2015), doi:10.1093/mnras/stu2164. [Source](https://arxiv.org/html/1409.4779v2).
- [PLANCK] Planck Collaboration. Planck 2018 results. VI. Cosmological parameters, A&A 641, A6 (2020), doi:10.1051/0004-6361/201833910. [Source](https://arxiv.org/html/1807.06209v4).
- [QUANTUM-REF] P. E. Black and A. W. Lane. Modeling quantum information systems, NISTIR 7103b (2004). [Source](https://nvlpubs.nist.gov/nistpubs/Legacy/IR/nistir7103b.pdf).
### Separate source-led topic study

- [SPATIAL-RADIX] *Spatial Radix Mapping: source-defined construction, finite tests, and engineering obligations*. K-SPATIAL-RADIX-R1, 18 October 2026. Complete article, retained source conversation, attribution register and 33-check finite analysis. Prior AI interpretations remain separate from the authored construction; no hardware performance measurement is inferred.

© 2026 Aboudy Keddeh | Keddeh Systems | All rights reserved  
KEDDEH-WP-RELATIONAL-ARCHITECTURE-001 | R2 | Internal research | Research edition  
Licence profile: KEDDEH-RESERVED-1.0. No licence is granted by this document. Separate written permission governs reuse, redistribution and implementation, subject to applicable law. Third-party material retains its own rights. Authorship, copyright ownership and publishing authority remain separate records.