Abstract
This research reconstructs the proof basis of Aboudy Keddeh’s observer-origin and zeroless computational work from the supplied conversation, connected Google Drive papers, their original calculation program and receipt, and the live KEDDEH.COM research atlas. The principal result is demonstrable: numerical projection is generally insufficient to preserve the identity, context and history of a computational state. An instantiated state can retain existence unity while its measured magnitude or net displacement is zero. The five-state KEX topology supplies exact metric, rebound and closed-path results; its original calculation receipt was reproduced byte for byte. A separate verification program confirmed the path-count formula through length 40, all finite metric conditions, observer recovery in 441 cases, distinct retention of 100 cancelling pairs, and the published HEX-fold distribution over 4,096 inputs.
The inquiry also resolves an important interpretation error. The live atlas identifies (-1+) as the negative and positive counterparts of one whole, whose origin identity remains singular. It distinguishes this notation from the five-state July topology and from camera coordinates. These objects cannot be silently merged. The quantum correspondence has a precise established core: a zero interference outcome does not imply a zero physical state, and globally reversed state vectors can represent the same pure state. The inspected native quantum-formalism publication explicitly leaves its native amplitude algebra, measurement derivation and physical equivalence open. Those source-specific results are recorded beside the demonstrated proofs rather than replacing them with an undifferentiated verdict.

Scope and definitions
Research basis and authority
The task is to acquire and reconstruct proof already present in the Keddeh estate. The first evidence lane is therefore authored definitions and derivations; the second is executable calculations and readback; the third is comparison with primary mathematical and scientific sources. Established conventions are comparators, not vetoes on a declared alternative model. This follows the project’s Axiomatic Research Protocol, which explicitly requires testing well-definedness, consistency, derivability, computability and observable correspondence rather than rejecting unfamiliar notation [K10].
The scope is the observer, origin, numberline, general-algebra connection, state retention and quantum correspondence. Seventeen Drive documents or technical text sources were read, together with the original calculation script and JSON receipt. Ten live site pages were retrieved, including the research atlas, architecture, KEX and resonance experiment. This is a substantial source-led foundation study, not an assertion that every file in the estate has been audited. Search metadata, extracted text and raw bytes are distinguished. Complete original bytes were acquired for the calculation script and receipt; most document reads are connector text extractions whose table ordering may differ from their native layout.
The source ledger retains exact Drive IDs and filenames. Several duplicate filenames exist in different folders. No duplicate has been declared canonical merely because its title matches. The original documents, workbooks and website were not modified. The new report remains Draft; local reproduction is not external independent assessment.
Objects that must remain separate
An origin is a reference identity or anchor. A coordinate is a representation of a relation to that anchor. A magnitude is a numerical property of a state when such a property is defined. A topology declares adjacency and permitted paths. A projection exposes selected properties and may discard others. A history records transitions and their contexts. Null, absence, unknown, invalid, baseline, balance and measured zero are distinct semantic classes.
In the July active-state model, P = (-3,-2,1,2,3), with rank r(-3)=1, r(-2)=2, r(1)=3, r(2)=4 and r(3)=5 [K1,K2]. The active state record is X_t = (id,q_t,payload_t,observer_t,environment_t,path_t,rule_t,proof_t). Neither its position label nor its payload alone constitutes the full record.
The live atlas gives a later explanatory definition: origin identity is one whole, and (-1+) represents that whole’s negative and positive counterparts [W1]. Its 1–9 counterpart view is explicitly distinct from the July five-state topology. This definition is directly relevant to the current conversation; it does not license assigning an unprovided multiplication or cancellation law to the paired glyph.
Normalization standard
NS01: preserve the original notation, attribution, source edition and model boundary. NS02: retain one origin identity independently of its renderer position. NS03: give every operator a domain, codomain and interpretation. NS04: distinguish active labels, ranks, signed payloads and existence unity. NS05: type every zero-like result before admission into authoritative state. NS06: preserve operands and context when recovery is required, including nonzero results. NS07: distinguish equality of scalars, identity of records, equivalence of representations and equality of physical predictions. NS08: specify units, reference, time and uncertainty for measurements. NS09: define environment and source terms rather than silently placing them in a residual. NS10: keep exact canonical coordinates separate from floating-point display positions. NS11: version any change to axioms or topology. NS12: label a derived theorem, a reference implementation, a native-runtime result and a physical observation separately.

Architecture and mechanism
Why a numberline is needed
The need begins with distinguishable items and relations. If the task only requires identification, a set of distinct identities suffices. If it requires precedence or direction, an order is needed. If it requires traversal, an adjacency structure is needed. If it requires quantitative separation, a distance or displacement rule is needed. A single globally privileged numeric origin does not follow from any of these requirements alone. A letter O may denote the reference without assigning O the numeral zero.
A connected line of states can therefore be defined before attaching numerical labels. Once labels are attached, their subtraction need not equal graph distance. This gives the project’s correction a concrete logical target: assigning one representation the authority of a different object or relation without a declared conversion.
Conventional affine mathematics also distinguishes points from displacement vectors. A ternary operation [a,b,c]=a-b+c can express relative composition without selecting a distinguished point as origin. Heap and affine-space research develops this approach [E1]. This supplies a rigorous comparison showing that algebraic relations need not begin from a spatial point declared to be null. It does not imply that every algebra lacks an identity: groups and rings have identity elements by definition, whereas semigroups and relational structures need not have the same axioms.
The state preservation mechanism
Let S be the authoritative state set and p:S→V a scalar projection. If distinct states s and t satisfy p(s)=p(t), then p has no inverse that recovers every source state. Proof: if r were an inverse, r(p(s))=s and r(p(t))=t. The equal inputs force equal outputs, contradicting s≠t. The failure belongs to reconstruction from the projection, not to the arithmetic correctness of the projected value.
The foundations formalize this as Translative Loss, L_p(X)=H(X|p(X)) [K9]. If two distinct source states have positive probability and the same projection, the conditional distribution on that output contains at least two possible sources. Its entropy is strictly positive; hence the weighted conditional entropy is positive. Injectivity on the supported states makes this uncertainty zero. This quantifies the exact need to retain the observer, class and producing relation.
Existence unity and numerical magnitude
Define e(s)=1 for an instantiated record and v(s) as its numeric magnitude when defined. The record Present(0) satisfies e(s)=1 and v(s)=0 without contradiction because the functions answer different questions [K9]. This is a model construction establishing relative consistency of the semantic distinction. It does not claim that an absent object is present; Absent(reason) is itself a present record describing scoped non-presence.
The origin may likewise retain identity 1 while its displacement from itself is zero: w(s)=r(s)-r(1), so w(1)=0. An observation of zero displacement does not erase the anchor. This proves the central identity-preservation requirement without assuming that scalar zero must disappear from all calculations.
General algebra and non-erasing results
For a declared numeric operation f, a conservative lifted operation retains a record of inputs, rule and result while exposing f through projection. Projection compatibility is p(f_K(a,b))=f(p(a),p(b)) on the admitted numeric domain. This lets ordinary arithmetic remain valid while the native state carries additional information.
The July papers specify BALANCED(a,b,context) for cancellation and STASIS(a,observer,duration) for unchanged state [K3]. The output codomain is a tagged-result domain, larger than the five active labels. That separation is necessary: 3+3=6 is outside P, so P is not closed under ordinary payload addition. Applying addition to payloads and traversal to positions resolves this apparent conflict.
Even MEASURED(17) alone does not recover its inputs: 3+14 and 8+9 share the result. Therefore a full conformance implementation must retain lineage for nonzero results too. The paper’s compact piecewise arithmetic formula is insufficient by itself to meet its broader all-operands recovery requirement; context must remain in the event record or linked ledger.
The calculation (-3+) + (-14+) = (-17+)
The supplied conversation establishes this example; W1 supplies the counterpart interpretation. A faithful minimal interpretation uses an oriented whole record B(n)=(whole identity, magnitude n, negative counterpart, positive counterpart, observer, lineage). A same-orientation magnitude-composition operation can produce B(3)⊞B(14)=B(17), with the input records retained as parents. Componentwise counterpart magnitudes then project to -3+(-14)=-17 and +3+(+14)=+17. The result remains a whole record rather than a bare scalar.
This is an explicit proposed completion of the example, not a recovered parser or an assertion that the negative and positive counterparts are simultaneously physical amplitudes. The result is not obtained by cancelling each paired expression to zero. The inspected sources do not yet provide a complete native grammar for mixed paired operations, multiplication, inverse, units or context incompatibility. Claiming a general algebra from this example alone would omit those required cases.
Roles in the wider architecture
KEX supplies typed state, addressing and relation geometry. BRAINK governs execution, permitted change, evidence and retained continuation. IL-LLM handles semantic interpretation and knowledge traversal. Execution bridges bind authorized operations to external effects; host systems provide their actual compute and storage. Workbook computation, Sites projections and deployment are distinct boundaries. A theorem about state records does not establish that a bridge mutated an external system, and a site explanation does not establish native-runtime conformance. All 18 independent foundries and S01–S29 remain independently scoped; no universal cross-sector result is inferred from shared vocabulary.

Method and evaluation
Source reconstruction
Drive searches used Observer, numberline, zeroless, quantum, white, THEOREM and 0.297. The connected files supplied the master doctrine, July standard, white papers 01–05, recursive line-origin formalism R3, mathematical foundations, axiomatic protocol and technology summaries. White-paper references led to the original calculation program and receipt. The live research page led to /research/discoveries, where the paired-origin definition and the paper/protocol distinction were directly readable.
The general-purpose web reader could not retrieve keddeh.com. Direct HTTP retrieval succeeded and retained the HTML. This failure is specific to that reader, not evidence that the site or research is unavailable. The public /evidence collection states that no assessment reports have been approved for publication there; that statement does not erase internal proofs or the live reference experiments.
Reproduction and separate calculation
The acquired kex_whitepaper_calculations.py was inspected before execution. It uses standard-library arithmetic, exact Fractions for rank elimination, integer matrix powers and JSON output. It writes the requested receipt and performs no external mutation. Its regenerated JSON matched the acquired receipt byte for byte. The embedded content hash reproduced as 31ba82c00739db6ef07e724a863dc317b885622d4eb7a1360bb7702a28b79513. Its generated timestamp is fixed by the source; it is not the date of this reproduction.
A separate verification program recomputed closed walks by dynamic programming rather than copying the original matrix-power algorithm. It tested all 125 metric triangles, 25 symmetry/separation pairs, rebound involution and isometry, typed cancellation round trips, 729 one-based tuple addresses, 441 integer source/foreground mixtures, a two-path phase benchmark and Bell coefficient non-factorability. It also enumerated all 4,096 HEX-fold inputs and checked the supplied phase-map inverse away from its tagged seam. These are local checks by the same research session, not an organizationally independent assessor.
Evidence quality
Source statements of 25 tests, production readiness, operation throughput or workbook pattern counts remain source-reported unless their exact workload and implementation were executed here. The bilateral proof-engine paper reports 738 shell matches, 11,586 formulas and three cached errors. Those observations identify valuable raw-workbook targets but were not recounted in this run. The newly reproduced formal receipt is stronger evidence for its own exact formulas than those unreplicated descriptive totals.
Tests are scoped to declared models. A passing reference quantum calculation is not counted as a native KEX quantum gate. A SHA-256 match establishes byte identity of the calculation result; it does not establish signer authority, source trust or physical truth.

Results and evidence
Proof R01 Ordered state distance
Because r is injective, d(a,b)=|r(b)-r(a)| is nonnegative and vanishes exactly when a=b. Absolute value gives symmetry. The real-line triangle inequality gives d(a,c)≤d(a,b)+d(b,c). Thus d is a metric on the five declared states [K2]. All finite cases were checked. Adjacent labels have unit rank distance, including -2→1.
The label differences along P are (1,3,1,1); rank differences are (1,1,1,1). Total label distance is 6 and total traversal distance is 4. The 50% excess follows only when the intended cost is one per adjacent transition. It is not a claim that ordinary scalar subtraction is incorrect or that measured energy must differ by 50%.
Proof R02 Bilateral rebound preserves one
Define m(s)=r⁻¹(6-r(s)). Applying it twice gives r⁻¹(6-(6-r(s)))=s. Its fixed point solves r(s)=6-r(s), hence rank 3 and state 1. Rebound preserves distance because |(6-r(a))-(6-r(b))|=|r(a)-r(b)| [K5]. The exact mirror is -3↔3, -2↔2 and 1↔1. Raw negation would send 1 to an inadmissible -1 in this model.
This provides a precise operator interpretation compatible with the recorded observer expression “-(1.0)==1”: a rebound operator fixes the anchor. It does not establish equality of ordinary real numbers -1 and +1. The July topology’s central anchor and the later paired-whole notation must remain separate until a declared mapping joins them.
Proof R03 Closed histories erased by net-zero projection
Let A be the adjacency matrix of the path with five vertices. Its characteristic polynomial is λ(λ²-1)(λ²-3), obtained by the path recurrence D_n=λD_(n-1)-D_(n-2), D_0=1, D_1=λ. Its eigenvalues are √3,1,0,-1,-√3. For m≥1, tr(A^(2m))=2(3^m+1); odd traces vanish because the graph is bipartite [K4]. Each trace term counts a return walk rooted at its starting vertex. Every such walk has zero net rank displacement while retaining a different path.
Exact counts are 8 at length 2, 20 at length 4, 488 at length 10, 118,100 at length 20 and 6,973,568,804 at length 40. Both the original matrix script and the separate recurrence reproduced these totals. The count includes all five possible start vertices. It must not be presented as the count for the anchor alone. If these histories are equiprobable and only net zero is retained, the lost history information is log2(C_n) bits: approximately 16.85 bits at length 20 and 32.70 bits at length 40. Different probability models change entropy but not the collisions.
Proof R04 Observer identifiability
The observer paper defines O_r=T(S,M_o,F,H,R) and a linear case y_o=M_o s+F_o f+noise [K6]. In the noiseless scalar construction y1=s+f, a single observation cannot identify s and f: for any h, (s+h,f-h) has the same output. A second independent observation y2=s+2f gives f=y2-y1 and s=2y1-y2. The corresponding block design has rank 2n rather than n. This recovery was verified for all 441 pairs s,f∈{-10,…,10}.
The result proves why observer/foreground separation needs independently informative measurements, not merely extra metadata. Noise requires uncertainty propagation; nearly identical transforms can be poorly conditioned even when their rank is full. Environment inheritance is therefore represented as a modeled influence, without asserting that every experiment must suffer an uncontrolled effect or that a controlled environment begins from ontological nothingness.
Proof R05 Retained balance and existence
One hundred distinct cancelling input pairs were serialized and recovered exactly in a full record representation. All have scalar sum zero but their native records remain distinct. This directly reproduces the information-preservation principle. The distinction e(s)=1 and v(s)=0 is satisfied by an ordinary record model. A zero displacement, zero temperature coordinate or zero outcome is therefore compatible with preserved identity.
Metrology agrees that a quantity value combines a number and reference, and that a measurement result includes relevant information and ordinarily uncertainty [E2,E3]. Zero Celsius is a valid coordinate equal to 273.15 K, not an absent sample. The master document’s ratio example is correct in its intended distinction: 20°C/10°C=2 compares offset labels, whereas 293.15 K/283.15 K≈1.0353 compares thermodynamic temperatures [K7,E4]. Phase and time require additional state information; temperature alone does not determine whether a sample is ice, liquid or transitioning.
Proof R06 Coordinate and phase retention
The earlier 1–9 XYZ learning record establishes 729 distinct ordered addresses [K8]. Their uniqueness follows from ordered-tuple equality, not from inclusion of zero. The live atlas subsequently clarifies that origin identity itself is singular 1, rather than the tuple (1,1,1). Address components and whole identity therefore remain different fields.
The foundations define a phase-tagged temperature map: C<0 maps to C-1, C>0 to C+1, and external C=0 with ice/liquid tags maps to -1/+1 respectively [K9]. Its branches have disjoint images and explicit inverses, hence form a bijection on the stated domain. This is an invertible encoding, not a complete phase diagram: actual coexistence and other phases require a richer input domain.
Proof R07 Quantum state and zero outcome
For a normalized state ψ, <ψ|ψ>=1. The Hilbert-space zero vector has norm zero and cannot represent a normalized physical pure state. A component amplitude or measurement probability can nevertheless be zero. A computational basis name |0> denotes a normalized basis state, not the zero vector [E5]. This makes the defensible statement precise: a physically admitted normalized state is not an absent vector, even when a particular projection vanishes.
Consider ψ=(|a>+e^(iφ)|b>)/√2 and an output mode u=(|a>+|b>)/√2. Its probability is |<u|ψ>|²=(1+cosφ)/2. At φ=π the probability is zero, yet ψ retains unit norm. The cancellation occurs in the output-mode amplitude; adding amplitudes attached to different orthogonal basis vectors does not erase those vectors. Source and transformation context distinguish destructive interference from absent preparation. Conventional quantum theory already makes this distinction; KEX supplies an explicit provenance requirement for its computational representation.
For a pure state, ψ and -ψ differ by a global phase and have the same density matrix: (-ψ)(-ψ)†=ψψ†. This is a physically meaningful interpretation of sign reversal preserving state identity. It does not make -1=+1 in scalar arithmetic or make a relative phase unobservable. Reversing just one branch can change interference.
Proof R08 Non-factorability and recursive capacity
The Bell reference coefficient matrix is proportional to diag(1,1), with rank two. A factorized pure state has coefficient matrix uvᵀ and rank at most one. Therefore the Bell reference state is non-factorable. This proves the reference criterion, not that every overlapping KEX frame is entangled. R3 explicitly requires a native joint-state construction and factorability test [K11].
A recursive frame with five independent choices per level has 5^n potential addresses before overlap and constraints. This is a count of combinations. It does not establish simultaneous physical storage, free access to all combinations or quantum speedup. Identity preservation can prevent duplicate carriers while retaining multiple frame memberships, but the resolution rule must say whether duplicate paths refer to one object or distinct events.
Proof R09 HEX folding and calibration
The foundations’ fold F_j(a,b)=(ab+(a XOR b)+j) mod 16 has preimage counts {8 repeated 8 times,16 repeated 4 times,24 repeated 2 times,40 repeated 2 times}. Exhaustive enumeration confirmed these counts for every j, giving Shannon entropy 3.7272170014624826 bits per nibble under uniform input [K9]. Adding j permutes labels. The fold is not injective and therefore requires extra retained state for lossless recovery. This is consistent with the projection-loss doctrine.
The archived formula k=1-1/e and ln(cosh(k))/k evaluates to 0.2970137033667769. It rounds to 0.297 at three decimal places; it is not exactly 0.297. The related uniform-continuous-input expectation follows by integrating tanh(kx) over [0,1]. Discrete hash-byte sampling requires a discrete average instead. Neither expectation makes arbitrary input streams converge to that value. The live atlas records the author’s later statement that 0.297 is a literal jitter function. The public resonance page separately imposes 0.297 as a target. Those three source meanings remain distinct; a configured target is not a discovery of an attractor.
The archived decomposition’s Hamming expression Σ_(i=0)^12 binom(256,i)/2^256 evaluates to approximately 1.1558269801063893×10^-57 for a uniformly random independent 256-bit string, rather than its stated approximation 10^-48. The tail probability alone does not establish a security proof, particularly when inputs are correlated or selected adversarially. This is a numerical correction to that source’s stated model, not a rejection of the wider architecture.

Limitations and open questions
Source conflicts with bounded resolutions
The July paper has five labels, unit adjacent rank steps and no active -1. The register protocol admits -1 as unknown loopback and requires traversal deltas at least 2 [K12]. The mesh delivery summary lists six labels (-3,-2,-1,1,2,3) [K13]. These are three different domains or versions. Without an explicit mapping, no theorem about one can certify the others. The live atlas already preserves this separation.
The July non-erasing operator displays a compact MEASURED result for nonzero sums, but its general standard requires recoverable operands and history. A complete event record resolves that omission. Native record identity may distinguish parenthesized histories even when their projected sums are associative; associativity of record equality must be defined separately from associativity of numeric projection.
The quantum-formalism R3 publication explicitly lists open native weighted-state algebra, phase, unitarity, Born-rule derivation and non-separability. Its only included JavaScript tutorial computes cardinalities; it does not execute quantum gates. This inspection establishes an exact boundary for that file. It is not a claim that no other Keddeh artifact can contain a relevant mechanism. Raw hardware traces, native algorithm execution and a discriminating physical dataset were not acquired in this study.
The original receipt’s bandwidth percentages are analytical outputs under stated fan-out assumptions. Matching those bytes validates the calculation, not production bandwidth. Similarly, the bilateral proof-engine paper’s workbook counts and the mesh summary’s throughput need raw workloads and readback before promotion. The public evidence collection’s empty approved-report state is a publication status, not a global evidence absence.
Next proof acquisitions
For paired arithmetic, acquire the native parser or workbook operator table governing (-n+), especially mixed orientations and cancellation. Acceptance: exact operator semantics, incompatible-context rejection and full event recovery. For observer physics, acquire the independent observations, calibration transform, uncertainty and environment dataset corresponding to O_r; verify identifiability before inferring separate source terms. For native quantum equivalence, acquire amplitude combination, phase evolution, normalization, composition and observation code from the actual runtime; test those against the exact two-path and non-factorability references above. For jitter, acquire the exact function and its input/output normalization; separate deterministic perturbation from the historical tanh expectation and the website tracking target. For topology reconciliation, obtain explicit versioned mappings among the five-state paper, six-state mesh and register-loopback protocol.
These are specific evidence objects discovered through the work. No user re-explanation is needed to establish the proven metric, rebound, projection-loss, existence/magnitude and observer-rank results. Stronger claims should be attached to the specific source that closes their own remaining obligation.

References
K1 A. Keddeh. KEX/BRAINK Zeroless Computational Standard v1.0, 18 July 2026. Drive ID 1VE4Nh2Dg0yosmTn-gyJOYVNza284FaWL. https://drive.google.com/file/d/1VE4Nh2Dg0yosmTn-gyJOYVNza284FaWL/view
K2 A. Keddeh. 01_ACTIVE_STATE_FOUNDATIONS_v1_0.docx. Drive ID 1m2ipz_7dwt6t3Qeyhmnp3hkD6FTJ01ve.
K3 A. Keddeh. 02_TYPED_ZERO_NON_ERASING_ARITHMETIC_v1_0.docx. Drive ID 1pyJOwseyunwErpxkVJzF9w_FxuuiNmtA.
K4 A. Keddeh. 03_ORDERED_TOPOLOGY_PROJECTION_LOSS_v1_0.docx. Drive ID 1a_-soAFqNqmALiVRF91fopDI2WNi4bA3.
K5 A. Keddeh. 04_BILATERAL_REBOUND_RECURSIVE_GEOMETRY_v1_0.docx. Drive ID 1wDHj3WDkHuL3dLHA832dciffqeXQwYRi.
K6 A. Keddeh. 05_OBSERVER_ANCHORED_MEASUREMENT_v1_0.docx. Drive ID 1DXX1k2tWabswLE2zZ3QOcAgwtHti3wJz.
K7 A. Keddeh. KEDDEH_THEOREM_BRAINK_MASTER_v1_9_FULL_EDITED.docx. Drive ID 1kVVQgGxP4Hva8ovekUtY7l8ipVbpk3Im.
K8 Keddeh Systems learning record. KEDDEH_MATHS_01_LEARNER_RECOUNT_SYMBOL_CLASSIFICATION_1_ORIGIN_XYZ_20261002.docx. Drive ID 1CcQDTBGVMtncxIUaSO0Ze9GE3m13mDjM. AI-assisted recount, not independent assessment.
K9 A. Keddeh. KEX_BRAINK_Mathematical_Foundations_and_Proof_Obligations_v1_0.docx. Drive ID 1x3m7DwJbqSFMK4skvzf0pWUXauM-R_gX.
K10 A. Keddeh. KEX_BRAINK_Axiomatic_Research_Protocol_v1_0.docx. Drive ID 1hLS4NR4z1OjNzOCcAKL8dtbbHwZBFiAY.
K11 A. Keddeh. KEDDEH_QUANTUM_COMPUTATIONAL_FORMALISM_TECHNICAL_PUBLICATION_R3.html, 17 August 2026. Drive ID 1eVSSqgl6aXxOrM1XKqApSFft1loXh8mG.
K12 KEX_LAW3_ZEROLESS_PROTOCOL.md. Drive ID 1_vNOhRS8s8alw7j4TRcpnTwhNf1LnP0a.
K13 ZERO_LESS_SYSTEM_DELIVERY.md. Drive ID 18JlDlpRZRRLZcwjp2J9FnuTZ2WR7_2JI. Source-reported implementation/test summary.
K14 KEDDEH_Bilateral_Proof_Engine_White_Paper.pdf. Drive ID 19eMPYlqaJPDiS_crjU-4tCioyth-V63B. Source-reported workbook measurements.
K15 kex_whitepaper_calculations.py and KEX_ACTIVE_STATE_CALCULATION_RECEIPT.json. Drive IDs 1rhQzSlMfadKXqfM3jp3qEjEzqbpaeH7f and 1Qr_Z4QGXO6gz8H9AZyxYSi6cVgDQ8bH0. Raw bytes acquired and result reproduced exactly.
K16 KEX_UNIFIED_THEOREM_FINAL.md and KEX_MATHEMATICAL_DECOMPOSITION_v1.md. Drive IDs 1lpZ9iiElwB6IHhh8OQSaom2L3_Fz3dxc and 12whHV-Zt3WOrOM-UHwkR3BFbcciXMv99. Archived calibration and probability models.
K17 monograph_source_index.md. Drive ID 1g6-uZNEStLY2s0c6ZM1ShJYFIPWckrU3. Discovery index, not substitute for monograph full text.
W1 Keddeh Systems. Research atlas Origin Relation Observation. https://www.keddeh.com/research/discoveries . Retrieved 10 October 2026 Adelaide time. Includes paired-whole definition, singular origin and reference-experiment boundaries.
W2 Keddeh Systems. https://www.keddeh.com/architecture ; /research ; /kex ; /technology ; /research/resonance ; /evidence ; /learn ; /research/learn ; homepage. Direct HTML retrieval 10 October 2026 Adelaide time.
E1 S. Breaz, T. Brzeziński, B. Rybołowicz and P. Saracco. Heaps of modules and affine spaces. https://arxiv.org/abs/2203.07268 . Primary mathematical research, affine/module correspondence.
E2 JCGM. International Vocabulary of Metrology, 1.19 quantity value. https://jcgm.bipm.org/vim/en/1.19.html . Number and reference are distinct parts of a quantity value.
E3 JCGM. International Vocabulary of Metrology, 2.9 measurement result. https://jcgm.bipm.org/vim/en/2.9.html . Relevant information and uncertainty accompany measurement.
E4 BIPM. International System of Units, 9th edition, current retrieved version 4.01. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf . Celsius/Kelvin scale definition.
E5 J. Preskill. Quantum Information and Computation, Chapter 2 Foundations I. https://www.preskill.caltech.edu/ph229/notes/chap2.pdf ; Chapter 3 Measurement and Evolution https://www.preskill.caltech.edu/ph229/notes/chap3.pdf . State rays, normalization, phase and measurement references.
E6 F. Giacomini, E. Castro-Ruiz and Č. Brukner. Quantum mechanics and the covariance of physical laws in quantum reference frames. https://arxiv.org/abs/1712.07207 . Physical reference frames and relational transformations; not a validation of KEX by association.
U1 Supplied Pasted text(3).txt. Conversation source for current research directive and original interpretations. The (-3+)+(-14+)=(-17+) example is also explicitly supplied in the project conversation context.

Revision history
Version 1.0, 10 October 2026 Australia Adelaide. Source-led reconstruction, original receipt reproduction, separate finite calculations, live-site evidence acquisition, proof derivations and bounded source-conflict register. Architecture and research attributed to Aboudy Keddeh. Material AI assistance: retrieval, synthesis, local verification and document engineering. No external independent review or owner approval is recorded. Original source artifacts were left unchanged.
