Independent full-law comparison of the changed-input port prediction

The changed-input causal prediction has been evaluated and retained. It predicts the mediator central form after one specified impulse and separates a grounded tangent port truncation. This owner admits a distinct full-law forward calculation and fixes its comparison policy. It does not execute that reserved calculation.

The forward producer evolves all 54 original coordinates using the shared validated continuous-flow machinery. The existing causal prediction is inspected evidence used only after the forward enclosure exists. It is not a field input, a fitted kernel, a numerical source constraint or a bound with which to intersect the forward result.

Complete model and retained preparation premise

Use the unchanged three-C9 graph with contacts \((4,13),(13,22)\), unit capacities and actual degrees. Nodes are ordered \(0,\ldots,26\); forms precede all continuous phase lifts in the complete state. For each \(k=1,2\), the component classes are \((1,k,1)\). The rows are

\[ x'=-Ax+\gamma D^{-1}S(\theta),\qquad \theta'=\gamma Ax,\qquad A=D^{-1}L,\quad\gamma=\frac1{1023\pi},\quad \tau=\frac{1023}{1024}t. \tag{1} \]

Primes denote this structural clock. Both rows use it; no held-pressure approximation or additional forcing channel is introduced.

Retain the original acquired families, their complete preparation and contact history, and their separate source costs. Each component's form and phase residual has Euclidean norm at most \(\epsilon=10^{-32}\), with its original zero-sum constraints before contact. The joined source may have small nonzero degree-weighted means. The declared common origins remain zero.

The same event and observation as in the causal prediction are fixed:

\[ x(0^+)=x(0^-)+q e_{13},\qquad \theta(0^+)=\theta(0^-),\qquad q=\frac7{10000},\qquad H=1,\qquad r_k=x_{13}(H). \tag{2} \]

The source is the pre-input state at \(0^-\); it does not already contain the impulse. There is no baseline subtraction, second input, source reacquisition or state reset.

The per-model scalar recording allowance is \(\delta=10^{-8}\). It is a supplied structural-unit observation policy, not a laboratory calibration or a numerical tolerance. The two classes are assessed separately rather than combined into a new class contrast.

Nominal numerical references and actual-source transport

For component \(c=0,1,2\) and local node \(j=0,\ldots,8\), define the exact reference lifts

\[ \Theta_{k,\,9c+j}=\frac{2\pi k_c(j-4)}9,\qquad (k_0,k_1,k_2)=(1,k,1). \tag{3} \]

The nominal numerical initial state is \(x=0,\theta=\Theta_k\). It is an auxiliary reference for error transport, not a replacement preparation.

Rebuild a fixed outward rational enclosure \([\pi_-,\pi_+]\) from the shared 256-bit Machin construction. For \(m=2k_c(j-4)/9\), the canonical phase pair is

\[ \bigl[\min(m\pi_-,m\pi_+),\, \max(m\pi_-,m\pi_+)\bigr]. \tag{4} \]

The sign reversal for negative \(m\) is essential. The shared interval materialization encloses these exact endpoints on its outward dyadic grid. Their uncertainty belongs to the numerical reference enclosure. No principal-angle wrapping is applied to these continuous lifts.

The original actual family is separately covered by form pairs \([-\epsilon,\epsilon]\) and the phase pairs (4) expanded by \([-\epsilon,\epsilon]\). These Cartesian covers do not assert that all their corners are acquired, remove the original zero-sum correlations, or establish independent preparability. The exact same source family, rather than that entire Cartesian product as a claimed preparation, remains the premise.

Only the nominal reference pairs are supplied to the selected forward calculation. This avoids repeatedly propagating the small source range through coordinatewise interval wrapping. Its contribution is restored by a proved complete-law comparison.

Let \(g=1/3000>\gamma\) and \(\ell=1-2gH=1499/1500\). For an actual source and the exact nominal reference under the same event, write \(X(t),Y(t)\) for the maximum form and phase differences. Heat contraction, the global sine Lipschitz constant two, and both evolution rows give

\[ X(t)\le\epsilon+2g\int_0^tY(s)\,ds,\qquad Y(t)\le\epsilon+2g\int_0^tX(s)\,ds. \tag{5} \]

The common jump introduces no difference. Taking the maximum over \([0,H]\) yields

\[ \max(X,Y)\le B_s:=\frac{\epsilon}{\ell} =\frac{1500\epsilon}{1499}. \tag{6} \]

Thus a validated nominal endpoint interval \(F_k\) supplies the actual-family enclosure

\[ A_k=F_k+[-B_s,B_s]. \tag{7} \]

There is exactly one source allowance. The forward calculation contains the full sine law, so neither the cubic amplitude remainder \(R_5\) nor the reduced model's nonlinear initialization defect \(E_{\rm init}\) is added to (7).

The numerical reference still encloses the exact common \(\pi\) target. Independent interval coordinates need not preserve all its correlations; this is numerical outer enclosure, not a changed law or source. The source transport does not use any predicted endpoint.

Fixed complete-flow calculation

Each class uses the shared complete sine field and the validated source-box Taylor kernel. The two complete reference sources and all event/numerical primitives are admitted before field evaluation. The source boxes contain absolute phase lifts, not deviations \(y=\theta-\Theta_k\). The producer has no class, target, causal coefficient, sensor, source-radius or prediction input.

Its common event is the signed three-port vector \((0,q,0)\). It is applied once at \(0\) and changes only the corresponding form coordinate. Every subsequent step carries the complete 54-coordinate endpoint. The producer does not integrate six port coordinates, omit hidden modes or reconstruct a pressure from its own observed response.

The prospective numerical policy is

\[ h=\frac1{16},\qquad N=12,\qquad 16\text{ steps per class},\qquad 32\text{ attempted steps in total}. \tag{8} \]

Use the existing rational outward dyadic128 arithmetic and fixed Picard/Taylor work policy. All attempts, including a failed attempt, consume the common budget. There is no adaptive order, smaller-step retry or width-driven extension. The final step is clipped only to the declared horizon; with (8) every width is exactly \(1/16\).

The degree-12 time polynomial has a certified order-13 remainder from the shared kernel's whole-tube derivative enclosure. The kernel retains its initial box, strict Picard enclosure, coefficients, remainder and full endpoint. Its global smooth sine domain is not an acute-chart, work or acquisition certificate.

Require the radius of each completed nominal endpoint interval to be at most

\[ \eta_{\rm fwd}=10^{-12}. \tag{9} \]

This is the admitted numerical resolution, not a guarantee that the unexecuted policy achieves it. Finite coefficient rounding, phase-target materialization, interval dependency and truncation all remain in \(F_k\). Sensor error and the actual-source allowance (6) do not belong to its numerical radius.

The first failed step or exhausted work budget stops all later steps and the other class if it has not yet begun. The report retains completed prefixes, complete states, the attempted source and failed tube/reason where available. A completed first-class endpoint may be retained on its own, but a joint two-class certificate is unavailable until both histories complete. Missing endpoint intervals are not zero values or failed scientific predictions.

Rebuilding the inspected prediction without narrowing the response

The frozen causal prediction must be re-admitted from its primitive source, law, target, coefficients and numerical evidence. Cached success flags or displayed decimals do not supply its endpoint intervals.

For each class, rebuild the degree-32 nominal central polynomial and time tail, giving \(C_k\), and the grounded comparator's nominal polynomial and time tail, giving \(G_k\). Rebuild the maximum-coordinate source radii from their primitive residual covers. For this fixed source, both are \(\epsilon\). The relevant prediction intervals are

\[ \begin{split} P_k^{\rm nom}&=C_k+[-R_5(q,1),R_5(q,1)],\\ P_k^{\rm actual} &=C_k+[-R_5(q,1)-E_{\rm init}(q,1,\epsilon)-B_s,\, R_5(q,1)+E_{\rm init}(q,1,\epsilon)+B_s],\\ Q_k^{\rm actual}&=G_k+[-B_s,B_s]. \end{split} \tag{10} \]

The exact linear hidden source remains part of the causal model. Its uniform allowance and the additional nonlinear initialization defect in (10) are separately justified. The grounded comparator keeps its own visible-source uncertainty and consumes no hidden state. Its whole-state work, mean conservation and identity are not inherited from the complete model.

All intervals in (10) are inspected predictions. Neither they nor the earlier analytic gap are passed to the continuous field, Picard iteration, time-jet calculation or source materialization. No intersection with them replaces \(F_k\) or \(A_k\).

Independent completion, resolution and comparison criteria

The prospective assessment requires, for each class:

1. The complete 54-coordinate history reaches \(H=1\) under the admitted source, single event and fixed 32-attempt common policy.
2. The nominal endpoint \(F_k\) satisfies the radius ceiling (9).
3. The nominal full-law enclosure is consistent with the causal nominal full-law prediction:

[ F_k\cap P_k^{\rm nom}\ne\varnothing,\qquad \max(F_{k,-},P_{k,-}^{\rm nom}) \le\min(F_{k,+},P_{k,+}^{\rm nom}). \tag{11} ]

1. At the declared comparison resolution \(\zeta=10^{-10}\), the independently transported actual-family interval satisfies

[ A_k\subseteq P_k^{\rm actual}+[-\zeta,\zeta]. \tag{12} ]

1. The complete-law and grounded-comparator recorded intervals are strictly disjoint in the predicted direction:

[ \inf A_k-\sup Q_k^{\rm actual}-2\delta>0. \tag{13} ]

Containment (12) is a declared resolution policy; it does not require containment in the unexpanded prediction. Under the common source bounds and (9), it may already follow from nominal overlap; it is not counted as an additional independent scientific corroboration. No redundant actual-overlap requirement is added. Nominal overlap is the exact consistency check, whereas (13) supplies discrimination against the named alternative.

Both models contribute their own recording error to (13). No baseline, gain fit or eight-reading mixed statistic is introduced. The two classwise checks cannot be replaced by an average, a cross-class subtraction or a favorable result in only one class.

Numerical failure is unavailable and preserves the partial evidence. A complete enclosure exceeding (9) is numerically unresolved. Disjoint nominal full-law prediction and forward intervals are a consistency conflict requiring an audit of assumptions, arithmetic and implementation. Failed declared agreement is resolution not met. When the other admitted conditions imply that agreement, its failure also requires an integrity audit. Neither status is automatically a physical counterexample. If the consistent, sufficiently narrow forward intervals do not establish (13), discrimination is inconclusive at this protocol.

A successful result would be a finite independent full-law comparison of the causal prediction against this specific memory-loss model. The causal and forward constructions share the declared law and exact primitive mathematics; their independence means separate computational representations and no use of the evaluated response to construct its prediction. It is not statistical independence or empirical validation.

Work, identity and interpretation

The changed word retains its separate full-state admission:

\[ \begin{split} W&=q(Lx(0^-))_{13}+2q^2,\qquad |(Lx(0^-))_{13}|\le8\epsilon,\\ W&<10^{-6}<2\,10^{-6},\\ H_{\rm excess}(0^+)&\le22\epsilon^2+W <10^{-6}<1/388800,\\ \|P_0x^+\|_2^2+\|P_0y^+\|_2^2 &\le27(q+\epsilon)^2+27\epsilon^2<1/144. \end{split} \tag{14} \]

Continuous storage decreases between events. These conditions preserve the full pattern identity at radius \(1/12\); they are not inferred from a successful smooth-domain step. The weighted form mean changes by \(4q/58=2q/29\), and the phase mean is unchanged. Original preparation and contact costs stay associated with the actual acquired source, not with the zero-residual numerical reference.

This one-window admission claims neither repeated operation of the new word nor full-state identity for the grounded comparator. Its expected memory separation already exists at leading linear order. Even a successful full-law comparison would not establish nonlinear necessity, minimal memory, a new class-sensitive effect, autonomous input selection or a physical clock and sensor realization.

Prospective retention boundary

The complete-flow producer reuses the shared sine field and source-box Taylor kernel. Its retained-evidence reader checks the primitive law, support, source, event and schedule and reconstructs the consumed endpoint arithmetic. Stored derivative and strict Picard generation remain execution premises; this reader does not regenerate them or authenticate acquisition.

The forward policy and prediction reader own the canonical references, separate source transport and comparison criteria. The producer and evidence controls exercise independent complete-row behavior, event carry, admission, partial failure and reconstructed arithmetic without evaluating the selected response.

Before the first reserved forward attempt, associate this policy with the complete producer, source construction, immutable causal evidence reference, assessment and audit implementation. Preserve the fixed source and runtime bytes, numerical budget, event, observer, attempt status and any partial result. A failed or wide first attempt is not silently replaced by another source or finer numerical policy.

The present gate admits that producer and freeze only. It does not evaluate a selected full-law response, regenerate a frozen coefficient producer or acquire a new source. Exact byte associations preserve the declared evidence boundary; they do not independently authenticate chronology, execution or physical preparation.

Retained producer and protocol admission

The protocol, source snapshot and freeze receipt associate this prospective policy with the complete Git base 362124d03f34940e23b5d84ca29c6c839d6471a1, without runtime overlays. The archive retains 24 files, including the complete producer, evidence reader, source/policy owners, shared numerical kernels, this prospective document and the future evaluator. The full Git base pins dependencies beyond those snapshots. The archived document is the unchanged prefix preceding this admission record. Its references to the "present gate" describe the historical producer-admission stage. Current execution status belongs to the sole research queue.

The protocol retains the two original class-source covers and their nominal references, absolute phase conversion, sole jump, fixed order-12 steps of 1/16, 32 total attempts, observation criteria and inspected prediction bands. Its separate prior-artifact receipt names the immutable causal-prediction ZIP; no coefficient producer was regenerated. Exact fractions retain mathematical budgets without binary-float conversion. The declared interpreter, platform and dependency versions are prospective execution preconditions.

Artifact	SHA-256
Protocol	e47ac667ecedf44d0863dd21a44da7deacc507a742a026cd0fe7d9bfd066f147
Source snapshot	a99b8f05153ebebe4964c7512183d606fb3d1e5317f133e20af57c28833204a3
Freeze receipt	919b2d79ba8beddce19664437d9d0c8738142e771c062878b98af986a38da5d2

The shared source inspector verifies these byte/base associations without executing archived code. Its restoration path prepares a new detached full-base workspace. The archived evaluator build/class-collective-forward-freeze/evaluate_forward.py additionally checks its exact live bytes, the complete src tree, the declared environment and reconstructed input/prediction associations before writing an exclusive attempt. Only the seven primitive inputs reach the complete-law producer.

The freeze audit re-admits the retained protocol and source association without response execution. The synthetic evaluator controls exercise refusal, single-attempt wiring, incomplete/error outcomes and failed serialization using unrelated inputs and mocked scientific entry points. An export failure retains the attempt, any partial output and failure metadata; it does not establish that an unexported in-memory report survived.

At freezing no reserved attempt, complete-law response or export-error record existed. evaluation_status_at_freeze="not_evaluated" records that historical boundary, not the status of any future execution. Producer controls use unrelated synthetic sources; they do not establish completion, numerical resolution or agreement for the selected response. The first reserved evaluation has its separate retained result.

First reserved complete-law comparison

The exclusive attempt and retained response record the single execution of the archived evaluator in a restored full-base workspace. Its interpreter, dependency versions, complete src tree and exact evaluator bytes matched the frozen declaration. No input, source, time step, order, observation or numerical budget was changed. The causal coefficient producer was not rerun.

Both independent nominal 54-coordinate histories reached \(H=1\): 16 steps per class, with 32 planned, attempted and completed steps in total. The evaluator reported 43.953 seconds for the calculation and assessment; this wall-clock duration is not the model's structural clock. There was no failed step, retry or export-error outcome.

The read-only response audit re-admits the primitive sources, absolute target lifts, complete law, support, event, schedule and original observation policy. It reconstructs each retained Taylor increment and endpoint before rebuilding the consumed readings. Saved derivative coefficients and strict Picard generation remain execution premises; the audit does not regenerate them or independently authenticate acquisition.

The table gives approximate midpoint summaries and conservative rounded bounds. All decisions use the retained rational endpoints, with the single full-law source allowance \(B_s=\epsilon/(1-2gH)\) and both recording errors.

Mediator class	Full-law nominal central form, approximately	Nominal radius, upper bound	Actual-family width, upper bound	Recorded separation margin, lower bound
1	\(0.000314379329034230502\)	\(5.7748032214\,10^{-26}\)	\(1.15496084442\,10^{-25}\)	\(3.50843909380\,10^{-5}\)
2	\(0.000314379334629583386\)	\(5.7748010426\,10^{-26}\)	\(1.15496040866\,10^{-25}\)	\(3.50843913737\,10^{-5}\)

For each class, the independently rebuilt nominal radius is below the fixed \(10^{-12}\) ceiling and its interval overlaps the frozen nominal prediction. The transported actual-family interval lies in the prediction's declared \(10^{-10}\) resolution window. Its recorded interval is strictly above the grounded tangent port comparator's independently recorded interval, after charging \(\delta=10^{-8}\) to each model. All fixed conditions pass separately for both classes. The resolution containment retains its policy role explained above; it is not counted as another independent corroboration.

The response archive contains the exact original outcome JSON as its sole member, without reserialization. Its byte associations are:

Retained item	Bytes	SHA-256
Attempt	761	23a3a0faac763d6c964bb9875a83d88c5bd2f19388040f9c4aa37de183a70f16
Response ZIP	1,051,693	edb0332fc9c60c5ed9ecec37139d380c941d2165d532a92b5f0cfcc95e84a481
Outcome member class-collective-forward-v1.json	12,691,468	ccdd701a4f708b95b4acb460fd79545827c1cc588d5dad553c2caa72a396e194

This is a successful finite endpoint comparison of the causal prediction with the independent complete-law calculation under the supplied model. The leading separation exposes information lost by the specified grounded tangent port truncation. It supports retaining internal memory for this intervention; it does not exclude every instantaneous closure or establish minimal memory.

The two calculated references are transferred uniformly to the original correlated acquired families. They are not new acquired preparations, and the calculation does not enumerate every family member or execute a laboratory measurement. The word's separate work, storage, identity and mean certificates retain their original premises. Nonlinear necessity, a new class discriminator, autonomous event selection and identification with fundamental physical observables remain outside this result. Subsequent admission belongs to the sole execution queue.