Acquired-child THOL admission and word completion

The acquired child 2_sub_0 has completed one actual OZ,THOL,SHA word under the unchanged default THOL and SHA policies. Its own OZ context and three samples supply the temporal and grammatical premises. Independent admission precedes the separately frozen continuation: THOL creates the predicted isolated descendant, and SHA changes only the actor's capacity and lifecycle state. No trajectory or new temporal samples are evaluated in that continuation. The reset requires the actor's actual neighbor, hierarchy, identifiers and represented arithmetic.

The research program owns status. The acquisition owner owns the numerical history; the operator contract, collective hierarchy and frozen-isolate completion own the general event and continuation mechanisms. Sections 1–5 give the source-specific prospective admission; Section 6 records the one evaluated continuation. Neither transfers the earlier parent's coefficients or outcome.

1. Actual source and read-only admission

Use the acquired endpoint at structural time 3683329/524288, with all 21 nodes, 53 positive-conductance edges, held positive capacities and declared real phase lifts. There is no forcing or continuous loss. The actor's sole neighbor is node 2. Its represented state is approximately

\[ x_c=0.21039599029387335,\quad \theta_c=1.1469302531056795,\quad \nu_c=121.6,\quad p_c=0.03652776817595776. \]

These decimals identify retained binary64 values, not adjustable parameters. The actor has hierarchy level and bifurcation level 1, parent 2, path [2], no existing children, operator step 1 and executed glyph history OZ with U2 debt 1. The graph hierarchy retains 2 -> 2_sub_0.

The source reader checks the original artifact associations and rebuilds consumed sample and pressure bounds from the original certificate. It restores the actual sample graphs and re-admits their state, support, capacity, clock, hierarchy, configuration and live history. Cached success flags, reported acceleration and certificate summaries are not substitutes for those primitives. The retained four-stage trace keeps its separately audited provenance; this admission neither reruns that acquisition nor regenerates its exact-flow producer. Receipts associate bytes; they do not authenticate occurrence.

The authoritative timestamped samples give the actual reader 120.04361511376919, exactly its rational represented-sample stencil. Its final time and form match the live actor. The unchanged minimum form is represented 0.2, the minimum capacity 0.1, minimum degree 1, minimum history length 3 and acceleration threshold represented 0.1. The source passes those conditions and the strict read-only probe. The core context OZ,THOL,SHA admits THOL at step 1, using the actor's own OZ history. The older one-entry legacy form history cannot replace this active history.

2. Independent reset and resources

The predictor uses primitive state and independent algebra. It calls neither the retained source's THOL proposal nor its metabolic implementation. The numerical allowance 2^-44 for later amplitude/signal/pressure comparisons is a supplied acceptance budget, not a universal bound on transcendental implementations.

Let n=2 denote the sole neighbor, and let s, g, k be the exact represented defaults 0.3, COUPLING_MODERATE and COUPLING_GENTLE. A singleton neighbor resultant has mathematical modulus one, hence exact ideal circular variance zero. Therefore the ideal metabolic amplitude is

\[ z=sx_c+g(x_n-x_c)\simeq0.07840636486956473. \]

It lies strictly inside the admitted child rails [0,1]. The independent interval evaluation encloses this identity; the eventual runtime variance and amplitude retain their rounding budget. The phase-affinity signal is telemetry here, not an additional amplitude factor. Acceleration determines eligibility and the pressure jump, not the amplitude again.

The new identifier is 2_sub_0_sub_0, absent from the source. With no existing actor children and one stage target, the shared collision allocation selects that identifier. Hierarchy level and bifurcation level become 2, below the default depth limit 5; the child's path is [2, "2_sub_0"]. Its parent is 2_sub_0. The existing hierarchy and boundary edge to node 2 remain intact. The sub-EPI record has operator-step timestamp 2, the actual acceleration and threshold, and the independently predicted network signals.

Capacity needs a new arithmetic check: unlike the earlier 128 -> 121.6 birth, multiplying the actual represented 121.6 by represented 0.95 is not exact in binary64. The predicted rounded child capacity is approximately 115.52; its difference from the exact represented-input product is below 6.83e-15. The positive capacity and finite output are admitted separately. The in-range actor phase is copied without a wrap change. New pressure and degree are zero. The new node has one initialized legacy EPI sample and empty glyph history; it has no acquired acceleration observation.

For observed acceleration \(\widehat A\), the raw actor pressure is

\[ p_c^+=p_c+k\widehat A\simeq9.589295134164619. \]

This finite value is permitted: pressure has no unit-interval constraint in this contract. All old forms, phases, capacities, edges and structural time stay unchanged. The actor gains child records and acceleration telemetry; its history becomes OZ,THOL, operator step 2 and U2 debt zero. Actual shared stage and lifecycle effects, including their raw callback boundary, require the separately frozen execution check recorded below. Optional metrics are not requested; birth does not supply the independent child-rate evidence needed for U5 telemetry.

The event does not deplete the actor's form or capacity. These are configured new coordinates, not an additive material inventory. The event occurrence, available substrate and hierarchy policy remain supplied premises.

3. Complete successor and surviving information

The connected-only sine reader must reject the full 22-node successor. Select the explicit frozen-isolate completion: on the original connected component retain

\[ S_i=\sum_{j\sim i}\sin(\theta_j-\theta_i),\quad p_i=\frac{S_i}{\pi d_i},\quad \dot x_i=\nu_i p_i,\quad \dot\theta_i=\frac{\nu_i}{\pi d_i}(L_Wx)_i. \]

On the new isolate supply p=xdot=thetadot=0 with held form, phase and capacity. This is a declared law, not evaluation of 0/0, a native dispatcher installation or a derivation of substrate origin. The fresh constitutive pressure on each old node equals its pre-event map at the unchanged point. It erases the actor's direct pressure increment. Consuming the large raw pressure over an interval would be a different model.

For the existing edge-only storage

\[ H=\frac12\sum_{\{i,j\}}W_{ij}(x_j-x_i)^2+ \sum_{\{i,j\}}[1-\cos(\theta_j-\theta_i)], \]

the jump is exactly zero: every edge argument is unchanged and no new edge is created. The old component's means with weights d_i/nu_i, its instantaneous principal branches and its complete continuous rows are also unchanged. A pressure-square diagnostic has a different, positive raw jump; it is not this law's storage. Assigning a zero mean weight to the isolate does not give a positive metric or a complete observation of the enlarged state. An intrinsic child energy or material conservation law would require additional premises.

The original exact-flow retention certificate remains valid for its original solution. The acquired binary64 endpoint differs from that exact solution by the certified acquisition error. Consequently unchanged rows do not automatically turn that old certificate into a future enclosure starting at the acquired endpoint. Such continuation requires transported initial error or a newly admitted enclosure. No new all-time or enlarged-identity claim is made here.

THOL would discharge the actual OZ debt and fulfill the promised handler; it would not close the selected word. SHA remains its selected remaining closure, one of the grammar's available closure roles. Its capacity reset changes the subsequent continuous law and needs its own admitted comparison before execution. The newborn is initially below the default form minimum, isolated and without sufficient history; this construction does not license an immediate recursively repeated THOL.

4. Verification and claim boundary

Source controls exercise primitive/provenance and live-evidence rejection; prediction controls check the independent metabolic and represented-product algebra. Synthetic stage controls use distinct manufactured states to test shared atomic THOL, nested identity, history, pressure handoff and rejection. They do not evaluate this reserved source or manufacture a new source response.

This admission establishes conditional executability with a complete declared successor; the later actual event is evaluated separately below. Numerical U5 across levels, cross-birth U6, autonomous occurrence, coupled descendant maintenance, population growth and physical identification retain separate obligations.

5. Prospective completion by SHA on the same actor

The word predictor extends the independent THOL reset to the selected remaining closure. THOL preserves the actor coordinates consumed by SHA's strict precondition. A detached grammar-only view applies the shared bookkeeping recurrences for the conditional successful THOL; it creates no node and executes no event. That view admits SHA at step 2 of the already selected OZ,THOL,SHA word. Its scope is conditional admission, not an observed prefix.

Resolve the default factor through the shared registry, f=SHA_vf_factor, and predict both the exact represented-input product f*nu_c and its binary64 implementation nu_c'. Their difference is retained. The newborn keeps its independently predicted capacity; the old actor alone is attenuated. All forms, real phase lifts, edge support and conductances are unchanged. The full post-closure law holds those new capacities and retains the explicit frozen-isolate rule.

At this unchanged point the constitutive pressures are identical, since they do not consume capacity. Both actor rows are multiplied by r=nu_c'/nu_c; the other nodes' instantaneous rows are unchanged. Subsequent coupled motion need not coincide. SHA latency metadata does not set the actor's continuous rows to zero, and no future retention certificate is transferred across the capacity change.

On the original connected component, put rho_i=d_i/nu_i, R=sum_i rho_i, and let mu_z=sum_i rho_i*z_i/R for either the forms or the declared phase lifts. Only rho_c changes. With delta_rho=d_c/nu_c' - d_c/nu_c, the exact event mean change is

\[ \mu_z'-\mu_z =\frac{\delta\rho}{R+\delta\rho}(z_c-\mu_z). \]

The predictor independently rebuilds the before, ideal and represented component fields and means. It then adds the isolate with its full predicted form interval, without choosing a midpoint. Its zero mean weight does not create a positive metric for the enlarged graph. Each stage has zero work in the supplied edge-only storage by unchanged arguments, while the old component's mean values generally change at SHA.

The executor uses two separate canonical atomic stages with a full guarded pressure refresh after each. The primitive checker reconstructs reset footprints, admitted metabolic outputs, hierarchy, histories, lifecycle, pressure defects and complete-law fields. A committed birth is retained if the later closure fails. Raw callback records precede refresh; committed records follow successful stages. This is not a single whole-word transaction, and external record writes are not rolled back.

The structural clock remains 3683329/524288. The fixed wall-clock metadata value 2030-01-02T03:04:10+00:00 belongs to the execution fixture, not elapsed structural or laboratory time; acquisition receipts record their own actual UTC times. Optional metrics are disabled. The prospective comparison budgets remain 2^-44 for the event algebra and 2^-46 for the pressure writer. No integration, new temporal samples, coupling, repeated birth or physical comparison belongs to this word-completion protocol.

6. One frozen continuation and its retained result

The protocol, independent prediction, complete preparation and producer archive were frozen before either actual proposal. The response and result retain one completed continuation, with separate raw and committed records for both stages. Both primitive reset/law assessments pass. No retry, inserted event, integration step or temporal sample was used.

Observed endpoint	Result
Actor 2_sub_0	Own history OZ,THOL,SHA, operator step 3, U2 debt zero; capacity 111.92337946001277, latent metadata and preserved form
New descendant 2_sub_0_sub_0	Form 0.07840636486956472, phase 1.1469302531056795, capacity 115.52, zero pressure and degree; hierarchy level 2 and path [2, "2_sub_0"]

The support has 22 nodes and the original 53 edges. The original forms, phases and neighbor order remain unchanged. The represented birth and SHA capacity products match the frozen predictions, including their distinct rounding defects. The old component's pressure-writer errors are below 1.42e-17 after each stage, within the frozen 2^-46 budget. Both exact edge-storage jumps are zero by unchanged arguments. SHA changes the component form mean by approximately -6.793201597e-7 and its declared-lift phase mean by -5.464577708e-6, agreeing with the exact weight-change identity. Its two actor rates remain nonzero and have the predicted represented ratio.

The actor's three timed samples and live endpoint association survive unchanged. They were acquired under the pre-SHA capacities; retaining them does not measure a new post-SHA acceleration. The new descendant has only its initialized untimed form entry, empty executed glyph history and no acceleration observation. Structural time remains 3683329/524288.

The independent retained-response audit rebuilds the prediction and both endpoint checks from primitive records, with proposals, events, pressure refresh and flow forbidden. It separately checks represented products, metabolic algebra, edge storage, means, histories and frozen byte associations. The analytical controls and manufactured-state execution controls exercise unsupported inputs, separate stage rollback and retained committed prefixes without replaying this response.

This establishes one nested actor's execution of its admitted canonical word. Event occurrence remains supplied. The descendant is not coupled; its creation does not establish a maintained larger organization, a new collective action domain, autonomous growth, a future retention certificate or physical identification. SHA is the selected closure for this control, not a required ending for other grammatical words.