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# Native Host Adapter R14: Line-Origin and Quantum-State Module Reference

KEDDEH-TECH-R14-MODULES-001 | Technical editorial E1 | 18 October 2026  
Reference identities: E-LINE and E-QUANTUM  
Aboudy Keddeh — Systems Architect  
Keddeh Systems | Internal research · Owner review | Editorial draft

## Authorship, rights and editorial standing

Architecture and research direction: Aboudy Keddeh. Technical source inspection, drafting, synthesis and reproduction tooling: dot, powered by OpenAI. This editorial edition describes two separately addressable modules in one retained carrier. It does not claim source-author acceptance, external peer review or release approval. Original code is unchanged.

© 2026 Aboudy Keddeh. Publisher: Keddeh Systems. Licence profile: KEDDEH-RESERVED-1.0. All rights reserved. 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. Document rights are separate from code, patent and trademark permissions.

## 1. Abstract and mechanism map

The R14_CONVERGED host carrier contains an implemented line-origin/frame workbench and an implemented conventional quantum-state calculation module. LineOriginRuntime supports stable line identity, overlapping frame membership, descent and cardinality. P15/A15 supports complex amplitudes, normalization, matrix application, tensor composition, measurement and a Bell-state example. They are concrete software, but their coexistence in one HTML file does not establish a native line-origin-to-quantum execution chain.

The retained isolated results are four passing LineOriginRuntime self-tests and nine passing P15 self-tests. Independent P15 boundary probes also establish three failed admission expectations: a NaN matrix can be called unitary and create a nonfinite successor; a negative sample and sample exactly 1 are accepted by measurement and can return zero-probability outcomes. The nominal results and boundary failures are both part of the evidence.

This reference maps E-LINE and E-QUANTUM to one source carrier without merging their functions, meanings or result denominators. A companion E-QUANTUM-REVIEW edition provides the boundary-review method.

### Source coverage and new replay

The complete retained R14 carrier, P15 module, S29 module, isolated line class and quantum model were recovered with their registered hashes. Historical isolated rerun receipts are not included because the raw files were not recovered; their expected identities are retained in the manifest as historical gaps. New reproduction-result.json records a separate 18 October 2026 Node v24.19.0 replay: line class 4/4, P15 9/9 and the same three failed admission expectations. The new harness rechecks the P15 extraction against the complete retained carrier without executing that carrier.

## 2. Exact artifacts, dependencies and setup

The reviewed retained carrier is braink_native_host_adapter_r14.html: 21,626,453 bytes, SHA-256 f5cde46ae784fff5d99d0e7555c7da23b5c94afa93dd48b10f40892ba20e4914. It is a local retained R14 carrier, not a declaration that the complete file is byte-identical to the Drive original. The source review established a whole-carrier difference. The extracted P15 module was separately checked to byte-match the original Drive carrier's P15 script. Module identity must not be promoted into whole-carrier identity.

Relevant extracted identities are:

- p15-a15-runtime.js: 6,166 bytes; SHA-256 7c00d68f35135504e8a0348611c877ff47208e6d579e0d02160e5cfaf8a2eeca.
- s29q-runtime.js: 13,223 bytes; SHA-256 7432cbf11a281c4bf2a540f1977f8b3b9cfadfad01bb7c32fd5a970cafa7943a.
- line-origin-runtime.js, the isolated class: 1,714 bytes; SHA-256 2cf254928ed12d0439df6ae348790027747493da2b27fc562cc3ad7e99a64eb5.

The isolated class and P15 pure calculation use JavaScript built-ins. The retained reruns use Node v24.19.0 and a VM without document, network or resident invocation facilities. P15 attaches its API to globalThis.KEXQuantumResearch. LineOriginRuntime is a class declaration; the reproduction harness explicitly exports it from the isolated VM for inspection.

P15's optional show() function expects the host DOM. The broader S29 module additionally uses DOM controls, Web Crypto, Blob URLs, an embedded R4 iframe/API and resident tools. Those dependencies were inspected, not invoked. Running the complete S29 selfTest would enter resident/iframe paths and must not be substituted for the four-check isolated class test.

## 3. E-LINE: line and frame contracts

### 3.1 Construction and state

`new LineOriginRuntime()` creates identity mechanic://keddeh/line-origin/r3, a Map of 12 line objects L1–L12 and a Map of three frames. Each line has id, origin, children and a Set of frame memberships. The seeded memberships are:

- M_A: L1, L2, L3, L4, L5.
- M_B: L3, L4, L5, L6, L7, L8.
- M_C: L5, L7, L9, L11, L12.

L5 is one line object with membership in all three frames. This models shared identity across overlapping frames, not three copies of a line. L10 exists as a line even though it has no seeded frame membership.

### 3.2 Inspection and mutation functions

`inspectLine(id)` returns null for an unknown line; otherwise it returns id, origin, frame_membership array, shared flag and children array. The arrays are copied projections of current state. `inspectFrame(id)` returns null or a record with id and copied members array.

`addFrame(id, nums)` maps each supplied number to an L-prefixed identifier, stores a frame and adds its ID to existing lines' membership Sets. It returns inspectFrame(id). The implementation does not provide a full consistency-validation layer: missing line IDs can remain listed in a frame, and replacing an existing frame does not remove previous memberships. The retained self-test covers seeded frames, not arbitrary frame replacement.

`descend(id, count = 5)` rejects unknown parent IDs with UNKNOWN_LINE. For each integer loop step from 1 through count it creates a child identity such as L1.1 if absent, records parent on a new child and avoids duplicates in the parent's children list. It returns state PASS, parent, requested child list and identity_preserved. Existing parent identity remains intact. The caller should supply a bounded nonnegative integer count; the implementation does not enforce that domain. No exhaustive malformed-count qualification is claimed.

`cardinality(d, n, f = 1)` coerces arguments with Number and returns single=d**n, joint=d**(n*f), d, n and f. It does not validate finite/integer domains or prevent overflow. For (5,3,2), the retained output is 125 and 15,625. These are calculated state-space cardinalities, not storage utilization, throughput or quantum speedup.

`selfTest()` checks LINE_IDENTITY, OVERLAP_SHARED, DESCEND_IDENTITY and CARDINALITY. It mutates its instance by descending L1. Fresh instances should be used when comparing an initial state with a post-test state.

### 3.3 Scope of the line-origin lifecycle

The pure lifecycle is instantiate → inspect shared identities → create child origins → inspect successor structure. It preserves line identity and explicit membership locally. It does not attach complex coefficients, evolve a native phase, calculate interference or define a physical measurement map.

The retained S29 manifest identifies local line/frame objectives separately from weighted-state, native phase, non-separability, interference, norm-preserving evolution and observer-measurement objectives. These are statuses in that carrier lineage. Later sources document additional conventional state-vector work; the S29 statuses must not be generalized into a claim that no implementation exists anywhere in the corpus.

## 4. E-QUANTUM: P15/A15 contracts

### 4.1 Representation and public API

KEXQuantumResearch exposes schema, KQuantumState, G, basis, bell, unitary, separable2, selfTest, model and show. Its schema is kex.braink.quantum-research.runtime.p15.v1. Optional model data is read from the p15-a15-model DOM element when a document exists. In a document-free VM, the API can compute while model remains empty unless separately supplied as documentation.

K_NEG projects to external |0⟩ and K_POS to external |1⟩. These are explicitly conventional computational-basis labels. Numeric zero may occur in coefficients, labels and host indices. The mapping does not make numeric zero a native untyped KEX operative state, nor does it reinterpret the current .1 designation.

`new KQuantumState(amplitudes, labels = null)` copies each complex pair through Number conversion. An empty vector raises E_EMPTY_STATE. With EPS=1e-10, norm below EPS raises E_ZERO_VECTOR; this rejects sufficiently tiny finite vectors as well as the exact zero vector. A norm differing from 1 by more than EPS triggers normalization. Default labels are stringified indices. Custom label count and uniqueness are not checked. State amplitudes and labels are public mutable fields, not an immutable value type.

`norm2()` sums squared complex magnitudes; `norm()` returns its square root; `probabilities()` returns component squared magnitudes. All three assume the state representation remains valid. Constructor coercion is not a complete finite-input validator.

### 4.2 Evolution, composition and predicates

`apply(U)` requires the same square dimension as the state, otherwise E_DIM. It computes matrix-vector multiplication and constructs a successor, which can renormalize. It does not call unitary(U). Thus a dimensionally valid matrix is not automatically an admitted quantum gate.

`unitary(U)` is a separate predicate. It rejects empty/nonsquare matrices and compares U†U with the identity using tolerance 1e-9. The retained implementation lacks explicit nonfinite-entry rejection. NaN can bypass magnitude comparisons, so even calling unitary before apply is insufficient for adversarial inputs.

The built-in matrices are I, X, Z, H, S and CNOT. H uses 1/√2; S has a complex i entry; CNOT operates on four amplitudes. These are conventional reference matrices.

`tensor(other)` multiplies each pair of amplitudes, concatenates basis labels and constructs the joint state. Label concatenation has no separator or collision check; the supplied binary basis use is the tested case.

`separable2(q)` requires four amplitudes or raises E_2Q. It evaluates the two-by-two coefficient determinant and returns true when its squared magnitude is below 1e-16. This is a finite-tolerance test for the represented pure two-qubit state, not an arbitrary mixed-state or native-relational entanglement criterion.

`basis(k)` accepts K_NEG and K_POS only; other labels raise E_K_BASIS. `bell()` applies H to K_NEG, tensors another K_NEG and applies CNOT. It produces a conventional Bell reference calculation.

### 4.3 Measurement

`measure(sample = Math.random())` accumulates probabilities, chooses the first index whose cumulative probability exceeds sample, and falls back to the last index. It returns outcome label, selected probability and a normalized one-hot successor. It does not mutate the measured instance.

A valid caller-supplied draw should be finite and satisfy 0 ≤ sample < 1. The implementation does not enforce this precondition. A negative draw on K_POS returns external label 0 with reported probability 0; draw 1 on K_NEG falls through to external label 1 with probability 0. These are demonstrated admission gaps, not supported measurement behavior.

## 5. Reproduction and results

Keep original files unchanged and run `python verify_sources.py`. Run `node reproduce.mjs` from the edition folder to evaluate the isolated class and P15 module only. It must not evaluate the entire carrier or s29q-runtime. The reproduction report records runtime version, digests, four line tests, nine P15 tests, Bell outcomes and explicit boundary cases.

The retained line result is 4/4. L5 belongs to M_A, M_B and M_C; descent creates five child identities without changing L1; cardinality(5,3,2) returns single 125 and joint 15,625.

The retained P15 self-tests are Q01 basis normalization; Q02 Hadamard superposition; Q03 H/X/CNOT unitarity; Q04 tensor product; Q05 Bell/non-separability; Q06 normalized measurement successor; Q07 zero-vector rejection; Q08 non-unitary falsifier; Q09 retained external zero basis label. All nine pass.

Bell probabilities are approximately [0.4999999999999999, 0, 0, 0.4999999999999999]. separable2 returns false. Draws 0.25 and 0.75 return 00 and 11 with normalized successors. These are finite-input conventional calculations.

A separate finite non-unitary example is diag(2,1): unitary correctly returns false, but apply accepts it and renormalizes a Hadamard input to approximately [0.8,0.2] probabilities. This distinguishes a predicate from an enforced admission gate.

Independent boundary probes record three failed admission expectations and four observations: one NaN-matrix case produces both a true unitary predicate and a nonfinite successor norm; negative draw and upper-bound draw each produce a zero-probability outcome. Do not present 9/9 as all-input validation or hide these cases in a combined percentage.

## 6. Limits and cross-paper integration obligations

No source-traced S29 membership-to-P15 amplitude bridge was recovered in these inspected artifacts. A future bridge needs an explicit state map, domain, coefficient/phase semantics, preservation invariant, compatible evolution and measurement relation, plus native readback. Shared file residence and matching terminology are insufficient.

K-LINE R3 supplies the authored topology route: addressed line → local frame/matrix → BRAINK state/lineage → IL-LLM traversal → KEX typed evolution → successor continuity. Its candidate quantum requirements are not negated by the later P15 module; conversely, P15 does not derive native line-origin algebra.

The 2 October Relational State Continuity and Distributed Execution source, §11, documents nonzero normalized complex vectors, K_NEG/K_POS basis projection, tensor/unitary/measurement and non-separability with a simulation boundary. Its §13 separates injective addressing from scheduler progress. These provide source progression without establishing the missing native bridge. Historical “phase-tagged” solid/liquid seams in Native Algebra v4 must not be equated with complex quantum phase.

K-KRS is a finite counterpart-identifiability control, not a P15 adapter. E-PRESERVE retains source identity, not quantum amplitudes or native operator semantics. No full-host, browser, physical-processor, quantum-advantage, air-gap or production-security qualification follows from the isolated results. No complete authored two-/three-body quadratic procedure is supplied by either module.

## 7. References and source package

- E-LINE / E-QUANTUM: Native Host Adapter R14_CONVERGED, source carrier dated 7 October 2026. [Original Drive reference](https://drive.google.com/file/d/1kdxO0Oifa6kclxiBOUfni40XHmI2Hkjh/view). The exact retained carrier is identified above; whole-file equivalence is not asserted.
- K-LINE: [Recursive Line-Origin Matrix Formalism R3](https://drive.google.com/file/d/1XCUFOmHxYHYtDiNrdO9vTZGQnU11toys/view), 17 August 2026.
- E-QUANTUM-REVIEW: independent P15 replay and boundary probes, 18 October 2026; retained review script and JSON receipt.
- Relational State Continuity and Distributed Execution, 2 October 2026, §§11 and 13. [Source](https://docs.google.com/document/d/1_FCkELiRe466pLRne9kk_gzZoHOBXUzI/edit).
- Source package: retained carrier; S29 and P15 extracted scripts; isolated class; S29 manifest; quantum mapping; line/P15 rerun receipts; boundary review. Exact filenames, byte counts and hashes are in original_hashes.json.
- KEDDEH-STD-PUBLISHING-001 v1.0, [Publishing Standard](https://docs.google.com/document/d/1Tflo8AeqQyVNLHPnMyti615uILabTJ8KjbXKkGfSkRM/edit).

## 8. Revision history

18 October 2026 — Technical editorial E1. Combined the shared carrier's reference identities into one publication while preserving P15 and S29 as separate mechanisms. Added function contracts, dependency/setup guidance, reproduction, nominal results, actual boundary failures and source-progression context. Original source code was not repaired or silently hardened.

© 2026 Aboudy Keddeh | Keddeh Systems | All rights reserved  
KEDDEH-TECH-R14-MODULES-001 | Technical editorial E1 | Internal research · Owner review | Editorial draft