Finite separation of a nonlinear class-mediated response¶
The two-probe theorem derives nonlinear local curvature while proving overlap of four final observation records at its short horizon. A nonzero derivative does not remove that obstruction. This owner admits a longer-horizon comparison under the same acquired source, complete law and readout error. Its prospective design is fixed before calculating the finite coefficient. The resulting finite negative mixed response separates the full nonlinear and same-source tangent four-record sets at the inherited noise budget. No trajectory, reserved response or physical data is acquired, and the earlier theorem and frozen evidence remain unchanged.
The execution plan owns this bounded admission. The coefficient calculation, full nonlinear remainder, source uncertainty and observation margin have separate roles.
F1-F2: fixed complete source, law and observation¶
Retain the three-C9 donor, mediator and receiver support with both central contacts, original unit capacities and classes \((1,2,1)\). The mediator class is fixed before the coefficient calculation. All 54 form and primitive-phase coordinates remain present, with actual central degrees \((3,4,3)\), total degree mass 58, and the inherited rows
Primes refer to structural time \(\tau=et\), \(e=1023/1024\). Form has the previous normalized structural units, angles are radians, and target deviations \(y=\theta-\Theta_2\) retain continuous lifts. No laboratory-unit conversion or physical noise model is supplied.
The original formation and dwell remain separate matched obligations of the acquired response owner. This theorem consumes its conditional reached-state family: each component's form and phase-deviation Euclidean norms are at most \(\epsilon\), with the original separate zero unweighted sums. Every allowed residual remains present; it is not made reflection symmetric. All four continuations start at the same complete actual state, including the hidden mediator initialization.
Supply donor central form impulses \(a\) at time 0 and \(b\) at delay \(s\), in the four histories \(00,10,01,11\) defined in the previous theorem. All rows and coordinates continue across the delay. The delayed-only history has its own unprobed preevent state. Read receiver central form at the common time \(T\), and retain
The comparison is the same-source complete tangent law, equivalently its exact linear memory with hidden initialization. Its noiseless mixed statistic is zero for every common full initial state. No state reset, changed observation or refitted comparator is admitted.
The single prospectively fixed analytic design is
Contact work allowance is \(10^{-12}\); each impulse has its own allowance \(2\,10^{-6}\). Thus preparation precision, amplitudes, identity radius and readout noise remain as in the split-probe design; the delay and observation horizon explicitly change. The short-time \(1/(1-3T)\) estimates are not extended to this domain.
Actual-source transfer without a short-time denominator¶
The normalized heat semigroup \(P(t)=\exp(-At)\) contracts maximum norm. The sine map is globally Lipschitz with normalized constant two. For actual and ideal trajectories with the same events, write \(X,Y\) for their form and phase maximum-norm differences. Then
For \(\gamma\le g<1/3000\) and \(2gT<1\), this gives the whole-window comparison
The same argument applies to the tangent law. It works in the original coordinates, with no phase uncertainty divided by \(\gamma\). Form jumps cancel in these source comparisons. Consequently a finite ideal mixed-response enclosure transfers to the actual family with additional absolute error at most
This preserves arbitrary source residuals and the shared initial state without claiming they cancel in the nonlinear law.
F3: both event histories retain their work and identity¶
For absolute supplied amplitude budget \(A_*\), diffusion contraction and phase integration give
whenever the denominator is positive. The bound follows from the complete law and the declared events, not a new held-state assumption.
The exact work of a central donor form jump \(q\) is \(q(Lx^-)_D+3q^2/2\). Thus each second work uses its own preevent history. Uniform bounds for the four histories are
Absent impulses use zero work; the delayed-only history has the smaller \(Q_0(s)\) preevent bound. At (3), exact rational substitution with \(g=1/3000\) yields both work bounds below \(2\,10^{-6}\) and
Contact work remains at most \(8\epsilon^2<10^{-12}\). The representative squared-radius ceiling
admits both postevent states. The strict radius/storage guards therefore retain all three cycle identities and unforced recovery after the last event. These identity conditions are distinct from compliance with the separate work allowances. Continuous storage loss does not become an undeclared event reservoir.
The form mean shifts by \(3a/58\) and \(3b/58\) in histories where those events occur; the phase mean is unchanged. No common mean is reset at the delay, and recovery refers to each resulting mean leaf.
Finite heat-convolution coefficient¶
Let \(c_{ij}=\cos(\Theta_j-\Theta_i)\). These are \(\cos(2\pi/9)\) on donor and receiver cycle edges, \(\cos(4\pi/9)\) on mediator cycle edges, and one on contacts. The coefficient and remainder proofs also apply to mediator class \(k\in\{1,2\}\), using \(\cos(2\pi k/9)\) on its cycle edges; the numerical design and separation below concern only the fixed class two. Define the homogeneous cubic map
This is the cubic part of the reflection-even sine residual, derived from (1); it is not a supplied new interaction law. For \(t\ge s\), put \(p(t)=a[I-P(t)]e_D\) and \(q(t)=b[I-P(t-s)]e_D\). The ideal heat references are obtained by setting phase feedback to zero in the form row and integrating the unchanged phase row. Their phase deviations are \(\gamma p\), \(\gamma q\) or \(\gamma(p+q)\). The mixed coefficient is
For an oriented edge \((i,j)\), writing \(\Delta p=p_j-p_i\) and \(\Delta q=q_j-q_i\), its integrand is
Both orientation reversals cancel. The predicted contribution is \(\gamma^4\mathcal C_k\), with the full support, time shifts and degree normalization retained. The finite coefficient uses all internal cosine weights, so its class dependence must be kept even though the earlier joint-short-time leading term was class blind.
A controlled full-law remainder at the longer horizon¶
For an ideal history with total absolute impulse budget \(A_*\), put \(D=1-2g^2T^2\) and \(L_*=1-2gT\). Markov contraction gives \(\|[I-P(t)]e_D\|_\infty\le1\), hence the heat phase is at most \(gA_*\). Nested form/phase integrals imply
This sharper envelope, rather than a linear growth estimate for the heat phase, is used at \(T=2\).
The reflection projections from the two-probe theorem commute with the full tangent law; all supplied central jumps are even. The complete quadratic residual bounds and heat contraction yield
Odd internal corrections are retained. The even forcing error after replacing the full phase by the heat phase in the cubic term is bounded by the sum
The first term uses the cubic derivative and (13); the second retains coupling to (14); the third is the fifth-order sine remainder. These are global sine inequalities on the retained lifts, not an assumption that the nonlinear even subspace closes.
The even nonlinear-minus-tangent form discrepancy is at most \((4/3)g^4A_*^3t/(D^3L_*)+(8/3)g^6A_*^3t^3/(D^3L_*^2)\). Replacing propagation of that discrepancy by heat adds at most \(4g^2\int_0^T(T-t)|x_{\rm even,nonlinear}-x_{\rm even,tangent}|\,dt\). Integrating these terms and the forcing errors gives the per-history bound
The ideal unprobed history is stationary, so the mixed nonlinear remainder is bounded by \(B(|a|+|b|,T)+B(|a|,T)+B(|b|,T)\). The actual-source error is still (6). This compares the complete sine law with its complete tangent law and cubic heat correction, not a spatially truncated mediator model.
Exact polynomial integration and an explicit heat tail¶
The coefficient calculation fixes degree \(N=32\). Replace each heat matrix by \(P_N(t)=\sum_{n=0}^{32}(-At)^n/n!\). Because \(\|A\|_\infty\le2\) and the exact heat semigroup contracts, Taylor's integral remainder gives, for \(0\le t\le T\),
No exponential amplification factor is needed. The rational spatial matrix, polynomial products and integral over \([s,T]\) are evaluated exactly. They produce three rational channels multiplying the donor/receiver cosine, the mediator cosine and the contact weight one. Ideal cosine and \(\gamma\) definitions retain outward enclosures separately.
There are three phase factors and one propagated heat factor in (12). Their exact phase columns have norm at most one before amplitude scaling; each polynomial replacement changes its norm by at most \(\eta_N\). Using edge differences and the normalized cubic map gives the coefficient tail
Multiply this tail by an outward bound for \(\gamma^4\), then add the three remainders (15) and the actual-source allowance (6). This yields a finite interval for the true mixed statistic. Sensor errors are added afterward. The computation is a finite algebraic coefficient enclosure with proved tails; it is not a numerical full trajectory or an observation of the four acquired continuations.
F4: recorded sign and complete-record separation¶
A proved true lower bound \(M\ge m>4\delta\) would make every allowed nonlinear recorded mixed statistic positive. It would not alone exclude the tangent model, whose four scalar errors permit any recorded mixed value in \([-4\delta,4\delta]\). A sufficient strict condition for disjoint nonlinear and tangent four-record sets is instead
Then the nonlinear recorded mixed value is always greater than \(4\delta\), outside the tangent range. The analogous negative condition uses a strict upper bound less than \(-8\delta\). This suffices for record-set separation because the mixed statistic is a fixed linear function of the same four readings; it does not claim that every possible model can be discriminated by those readings.
Any such conclusion requires a finite nonlinear coefficient enclosure, its complete remainder and (6). A formal coefficient, an unavailable overlap certificate or a local nonzero derivative is insufficient. Failure of this sufficient separation test would retain an unresolved design, not prove equality of the complete laws. The supplied law, preparation, support and event choices also remain independent of any subsequent physical interpretation.
A signed finite result at the declared design¶
For the fixed class-two design (3), exact degree-32 integration, outward trigonometric factors and the heat tail (17) give
These decimal bounds denote exact terminating rationals; both strict endpoint comparisons are checked in exact arithmetic. Independently, substitution of \(g=1/3000\) in (15) gives
Thus every admitted actual nonlinear four-history family obeys the conservative enclosure
The negative sign was obtained from the one declared coefficient calculation; neither class, source, delay, horizon nor error budget was changed to obtain it. It is compatible with the positive formal joint-short-time term in the earlier theorem: (12) retains the complete finite-time propagation and every cosine-weighted edge contribution. A short-time coefficient does not fix the sign at all later horizons.
At \(\delta=10^{-30}\), even the conservative signed true margin \(3\,10^{-27}\) exceeds \(8\delta\). Every nonlinear recorded mixed value is less than \(-2.996\,10^{-27}\), whereas tangent recorded mixed values lie in \([-4\,10^{-30},4\,10^{-30}]\). Consequently the complete four-endpoint record sets are disjoint under the declared error model. This statement retains all actual source residuals and the two event histories, not merely a nominal trajectory.
The same conservative calculation exposes sufficient noise ceilings: \(\delta<7.5\,10^{-28}\) guarantees recorded sign, while \(\delta<3.75\,10^{-28}\) guarantees disjoint tangent/nonlinear four-record sets. These are sufficient bounds of this method, not optimal information limits or independently attainable instrument errors. The work and identity obligations (8)-(10) pass separately. No probe schedule, interaction graph or preparation process becomes autonomous.
This is a conditional finite-response theorem established by coefficient arithmetic and error bounds. It is not a retained numerical full-flow experiment, physical observation or identification of a fundamental particle property. The earlier short-window overlap remains true in its own domain; the longer-horizon result does not rewrite that evidence.
Implementation and independent checks¶
bound_sine_class_nonlinear_protocol
admits the same eleven primitive class, impulse, source and policy inputs
as the superposition calculator, with a separate horizon domain up to two.
It fixes heat degree 32, rebuilds the rational channels and retains exact
rational endpoint pairs before outward display intervals. Its observation
flags distinguish true sign, recorded sign and disjoint four-record sets;
work and strict identity flags remain separate conditional statements.
An unavailable sufficient separation proves neither overlap nor linearity.
The contract and guide keep coefficient calculation distinct from nonlinear response generation. The selected controls check admission, exact coefficients, independent full-support algebra, finite tails and error thresholds. Formation remains a matched proof premise, not a verdict inferred from a positive or negative response bound.
Validated four-history observation admission¶
The analytic coefficient above predicts a complete-law response without
producing its four trajectories. A separate forward instrument must
retain the same fine state and event history, and may return unavailable
finite evidence. The
bound_sine_class_four_history_readout
producer consumes primitive source bounds and a declared numerical budget;
it consumes neither the coefficient, a desired sign nor a cached source
verdict. This admission does not evaluate the reserved class-two design.
Source enclosure and its association with acquisition¶
The input is one Cartesian box of all 27 signed forms and all 27 continuous phase lifts. It is enclosed once and shared by the four continuations. No centering, wrapping, class substitution or scalar-mean reconstruction replaces those inputs. A supplied outer box can contain the actual correlated reached family without every corner being acquired. Numerical flow on that box proves neither its acquisition nor the exact zero-sum, identity or work premises of the preceding theorem.
For the canonical family, let \(\Pi\) be an independently certified rational enclosure of \(\pi\), and retain the already proved endpoint radius \(\epsilon\). In component order \(k_c=(1,2,1)\), a sufficient coordinate cover is
Use outward interval arithmetic for both signs of the coefficient and retain all rational endpoints. Componentwise Euclidean norm caps imply each coordinate cap, so every actual reached state is covered. The original zero sums and norm correlations select a subset of (22); they are not imposed by independent choices of interval endpoints. Uncertainty in the target enclosure must also be retained, rather than treating a rounded multiple of pi as the exact acquired phase.
Equation (22) is an outer cover derived from the original handoff proof, not an instruction to prepare a new target state. A later experiment must associate the declared source family, its original preparation proof, its chosen enclosure and the fixed target/law parameters before using the analytic prediction. A successful forward interval alone cannot establish that association or narrow the acquired family after seeing a response.
Complete flow and exact branch events¶
The producer uses the same 27-node support, normalized degrees and both rows of (1), in their original 54 coordinates. The sine law consumes the primitive phases, so no mediator-class label is needed by the forward field. Class and acquisition claims remain separate source associations. The held law parameters, support, node order and structural clock are retained throughout every step. The globally smooth sine extension does not require an acute chart; a successful domain check therefore certifies flow availability, not winding retention or the storage barrier.
The two prefixes run from zero to the declared delay: one unprobed and one after the first donor form jump. At the delay, each validated full endpoint box supplies two suffixes, with and without the second jump. Every event changes only donor form coordinate 4 by its exact admitted amplitude. All phases, other forms and hidden coordinates carry unchanged through that event. Each suffix then reaches the same requested final time. Prefix sharing saves identical work without replacing the delayed control by a shifted initial-state solution.
The fixed step grid is clipped only at the declared delay and final boundaries; the caller supplies step size, Taylor order and a total unique-step attempt budget in advance. Zero-length segments contain the declared events but no invented continuous evolution. A zero delay composes the two applicable jumps at time zero. A jump at the final time is retained in the final state even though it does not directly change the receiver form observation.
Finite enclosures and partial failure¶
The shared validated Taylor kernel checks strict Picard inclusion for a complete 54-coordinate tube. For an admitted source box \(B_0\), order \(p\) and step \(h\), its source-box jets \(J_n(B_0)\) enclose the initial derivative coefficients; the order-\(p+1\) coefficient on the tube \(B\) bounds the remainder:
The endpoint also lies in the validated tube. Smoothness, all consumed rows, strict inclusion and the coefficient enclosures are premises of this statement. A midpoint trajectory or a Taylor polynomial without its remainder is not the same certificate. Full endpoint handoffs and exact jump maps propagate the enclosure to each branch by induction.
A global first failure stops further kernel attempts. The report retains completed steps and prefixes, the failed segment/step and available tube, the actual attempted count and the segments not attempted. A budget stop is distinct from failure of strict Picard inclusion. Missing final endpoints remain unavailable; a last successful prefix cannot be renamed the requested final state. Valid primitive input does not promise a successful or sufficiently narrow enclosure at its supplied budget.
When all four histories reach the common final time, the primary mixed readout uses the receiver increments on the four suffixes. The common prefix receiver value cancels in each kicked/unkicked pair, and a donor jump does not change receiver form. Exactly,
Each suffix increment is the sum of its shared-kernel step increments at receiver coordinate 22, not subtraction of two widened endpoint boxes. This preserves the proved prefix cancellation without constructing a joint 216-coordinate flow or consuming the analytic prediction. All 54 coordinates still carry through every prefix, event and suffix.
The four raw endpoint bands and their direct mixed interval remain separate evidence. Both constructions can relax dependencies across steps or suffixes: every same-source response is enclosed, but arbitrary choices from the marginal endpoint or increment bands need not be jointly realizable. Neither construction supplies mixed observations before all four histories complete. A wide interval remains inconclusive and need not contradict the analytic theorem.
Interval width combines supplied source uncertainty, target/parameter rounding, validated truncation and accumulated enclosure widening. It is not automatically a pure numerical error and is not sensor noise. The forward producer supplies no sensor model or nonlinear/tangent comparison verdict; a later declared observation protocol adds recording errors and checks the relevant sign or record-set criterion separately.
The execution contract and guide retain exact input domains, branch provenance and availability. Independent controls use unrelated source fixtures and shared-kernel postconditions. The fixed class-two response must remain unevaluated until its source, protocol, numerical budget and first-outcome retention are separately frozen; this admission opens no physical-data campaign.
Prospective freeze of the matched four-history evaluation¶
This protocol separates the analytic prediction from its future validated forward evaluation. The present admission freezes preparation association, all laws and observations, the numerical policy and first-outcome handling. It generates no reserved trajectory, response or attempt record. Any later outcome belongs in a separate retained record; a freeze receipt is not an execution certificate or evidence of physical measurement.
F1: complete source and the retained information¶
Use the actual acquired family associated with the unchanged class-mediation source proof and its retained evidence. The source has component classes \((1,2,1)\), original preparation errors, formation and relaxation already declared there, and final componentwise form and phase error norms at most \(\epsilon=10^{-32}\), with the original zero unweighted means. Acquisition is a conditional mathematical premise; the new forward calculation neither reruns formation nor replaces its proof by a cached passing flag.
Construct and retain all 54 rational source intervals by (22), including the independent enclosure of pi and the signed phase coefficients. Archive the source recipe, its realized bounds and its association with the original preparation/proof revision. Every acquired state is covered, but the independent interval corners can violate the consumed norm or mean correlations. Keep the correlated family and its Cartesian outer cover as distinct domains throughout the audit.
The one source supplies all four histories in the fixed order \((00,10,01,11)\). Observe signed receiver form at coordinate 22 at their common final time. Four scalar recording errors are each bounded by \(\delta=10^{-30}\). This is a declared observation-error model in normalized structural form units, without an inferred laboratory unit or instrument calibration. Forms, continuous phase lifts, full mediator state and all event ancestry remain in the forward evidence.
F2 and F3: unchanged law, events and numerical policy¶
Retain the complete law (1), unit capacities, the same 27-node support and degree normalization, \(\gamma=1/(1023\pi)\), and structural clock \(\tau=e t\). The donor-only form jumps have \(a=b=1/2000\), delay \(s=1\) and final time \(T=2\). The delayed-only history carries the unprobed prefix; it is not a newly prepared state. The branch tree, exact phase-preserving jumps and full-state handoffs are those of the validated producer above. No source reset, wrapping, mean projection, fitted pressure, alternate law or predicted response enters that producer.
The identity radius is \(r=1/12\), with contact work allowance \(10^{-12}\) and each probe work allowance \(2\,10^{-6}\). The matched source/event theorem supplies their conditional storage and radius bounds. The forward smooth-domain flag alone supplies none of these identity or work conclusions, especially for additional box corners.
Fix one numerical policy before observing any reserved response:
| Quantity | Frozen value or rule |
|---|---|
| Step size | \(1/64\) structural time units, clipped only at declared event/final boundaries |
| Taylor order | 16 |
| Global unique-attempt cap | 384: two prefixes of 64 steps and four suffixes of 64 steps |
| Arithmetic | Shared exact rational and outward dyadic-128 interval arithmetic, with the archived elementary-function implementation |
| Tube admission | Unchanged shared strict Picard inclusion and full source-box Taylor coefficients/remainder |
| Randomness | None; no fitting, seed selection or source sweep |
| Failure policy | Global first failure, with every completed prefix, failed attempt and unattempted branch retained |
For a fixed smooth order-17 remainder coefficient, halving the step doubles the number of steps and reduces their accumulated local truncation scale by \(2^{16}\). This is an a priori policy rationale, not a promise about strict tube admission or final interval width. Source uncertainty, parameter rounding, wrapping and finite arithmetic remain separately relevant. There is no extra width threshold: retain the actual widths and evaluate the declared discrimination margins.
F4: separate forward, consistency and discrimination claims¶
The previously derived true-response prediction is the open rational band \(J=(-3.2\,10^{-27},-3\,10^{-27})\) on the acquired correlated family. The future forward producer must return its own interval \(I=[I_-,I_+]\) from primitive source bounds and the fixed numerical policy. It must not consume the predicted sign or endpoints, and its interval must never be intersected with \(J\) to manufacture a successful result.
Retain full completion, source association and each of these distinct predicates rather than collapsing them into one passing label:
| Predicate | Meaning when the forward interval is available |
|---|---|
| \(I_+>-3.2\,10^{-27}\) and \(I_-<-3\,10^{-27}\) | Nonempty overlap with the open prediction band; consistency, not independent confirmation of the full prediction |
| \(I\subset J\) | A stronger sufficient enclosure check, including the outer cover's additional states |
| \(I_+<0\) | Uniform negative true mixed response on the forward source cover |
| \(I_++4\delta<0\) | Every admitted nonlinear recorded mixed response is negative |
| \(I_++8\delta<0\) | Nonlinear and same-source tangent four-endpoint record sets are disjoint under their separate four-error budgets |
The mixed tangent response is exactly zero for the same complete initial state and input histories. Its possible recorded mixed values lie in \([-4\delta,4\delta]\), while the nonlinear recorded interval is \(I+[-4\delta,4\delta]\). This explains the strict eight-error separation criterion; the four-error sign criterion alone is insufficient for that claim. These are complete-model software comparisons, not physical identification or observational equivalence of continuous histories.
The primary forward interval uses the suffix increments in (24). Retain its four operands, all raw final receiver bands and the separate raw endpoint mixed interval. Different widths expose different retained correlations; no narrow construction can be substituted after seeing a preferred sign. Width includes source uncertainty and numerical enclosure effects, not a measured sensor error. A wide interval or failed containment can be inconclusive because the Cartesian cover is larger than the acquired family. Missing completion leaves common-final-time predicates unavailable. Keep invalid or missing evidence, complete but unresolved bounds, and disjointness from the open theorem band as distinct outcomes. A conflict calls for auditing the source association, theorem and numerical premises; it is not automatically an acquired-state or physical counterexample. Touching only an excluded theorem endpoint does not establish overlap. Exact equality at a strict margin does not pass.
Archive boundary and the first later outcome¶
Use the stem class-nonlinear-readout-v1. The protocol owns the exact
source recipe and realized bounds, support/node order, held laws and
units, source-proof associations, all inputs/events, branch order,
observation definition, numerical policy, fixed predicate meanings and
first-outcome procedure. The source archive retains the immutable base
revision and any explicit overlays, the prospective proof prefix, the
protocol and isolated evaluator/support dependencies. Record byte sizes,
SHA-256 digests, arithmetic/runtime versions and the exact allowed forward
argument list; the predictor and preparation assessor are not execution
inputs to the forward call.
The freeze consists only of .protocol.json, .source.zip and
.freeze.json, created without replacing earlier evidence. The receipt
associates those immutable bytes and records
evaluation_status_at_freeze="not_evaluated". This historical field
remains true even after a separately admitted later evaluation. It is neither provenance authentication nor a claim that the
archived evaluator has run. Tests may inspect source, hashes, primitive
arithmetic and call isolation without executing the reserved worker.
When a later evaluation is admitted, retain its first outcome under this frozen policy, including strict-inclusion failure, budget exhaustion, partial histories, exceptions or export failure. Do not retry, expand the budget, narrow the source or revise a predicate to turn that outcome into a success. A correction requires separately identified evidence. All earlier frozen protocols and responses remain unchanged. The sole execution queue controls that later admission.
Retained first full-law evaluation¶
The first evaluation following the frozen protocol above completed once
under the complete pinned source revision
fa8e98a9b1bdd755709da481de7fc092b57bfe65. The retained status is
certified_reserved_readout, with no evaluation error: all 384 attempted
steps completed, comprising six segments of 64 steps. No source narrowing,
retry, numerical-budget change or intersection with the analytic prediction
was used. The freeze receipt's not_evaluated value remains its historical
status at freezing, not the status of this later outcome.
The primary, prefix-cancelled interval is exactly
The separate raw endpoint mixed interval is \([-527739886489/2^{127},-526996499279/2^{127}]\). The following decimal bounds are rounded outward; exact rational endpoints in the retained record determine all predicates.
| Quantity | Retained bound |
|---|---|
| Primary true mixed response \(I\) | \([-3.101480631540357847189,-3.097702683844646977897]10^{-27}\) |
| Primary interval width | \(\le 3.777947695710869290439\,10^{-30}\) |
| Raw endpoint mixed interval width | \(\le 4.369237329142707581834\,10^{-30}\) |
| Nonlinear recorded mixed response \(I+[-4\delta,4\delta]\) | \([-3.105480631540357847189,-3.093702683844646977897]10^{-27}\) |
| Four-record separation margin \(-I_+-8\delta\) | \(>3.089702683844646977897\,10^{-27}\) |
All five declared predicates pass: open-theorem overlap, the stronger containment \(I\subset(-3.2\,10^{-27},-3.0\,10^{-27})\), negative true mixed response, negative recorded mixed response and disjoint nonlinear and same-source tangent four-endpoint record sets. The last conclusion uses the separate eight-error margin, not merely the recorded sign. The narrower primary interval comes from the prospectively selected shared-prefix cancellation; both constructions and all operands remain retained.
Retained bytes and read-only audit¶
The exclusive attempt ledger
and compressed response
are associated with the unchanged
protocol,
source archive
and freeze receipt.
Compression changes only the transport: the ZIP contains the single member
class-nonlinear-readout-v1.json, with the exact original response bytes.
| Retained object | Bytes | SHA-256 |
|---|---|---|
| Attempt ledger | 543 | 616361ae09d035199ef672432b6a544f576f344e01c453f6df4f40e1107d6c93 |
| Response ZIP | 10,554,263 | b2e96205ed6f185a1193e4a936735572be8f59fd9a585c13203d53309875fbc5 |
| Uncompressed response member | 191,886,903 | 35c5c049dd00576f515a8ad3e63969a0bf9c12708ded9376beb7f48d7c9e9be2 |
The read-only evidence audit checks the outer and inner bytes, pinned source/protocol/attempt association, primitive source and held-law declarations, every retained step's arithmetic, full-state handoffs and events, both mixed constructions and the five predicates. It performs no producer, field, jet, Picard or archived-worker execution. The archived generation of derivative enclosures and Picard certificates remains a numerical execution premise; reconstructing retained arithmetic does not independently regenerate or prove those derivatives.
The archived prospective proof has 33,289 bytes and SHA-256
5bc192cfa87230c6aaace9def4e98c819d5ec3e9c68f2e2dd38c9da1ca82181d;
its content is preserved above. All earlier frozen evidence is unchanged.
Scope of the observed separation¶
For the declared signed receiver coordinate, \(M<0\) means \(R_{11}-R_{00}<(R_{10}-R_{00})+(R_{01}-R_{00})\): the combined change falls below the sum of the two individual changes. It does not determine the sign of any individual response, a coherence change or a stability verdict. The successful outcome is agreement with a prospective finite prediction and separation from the stated alternative; a negative sign is not itself a criterion of benefit or deterioration.
This is a validated software enclosure for the supplied complete law and source cover. Every conditionally acquired correlated source lies in that cover; an arbitrary Cartesian corner need not be acquired or satisfy the mean, work and identity premises. Those conclusions still use the matched source/event theorem, not the solver's smooth-domain flag. No formation was rerun and no source was reset between paired histories.
The result separates this finite nonlinear interaction from its declared same-source tangent alternative under the fixed four-reading error model. It neither identifies a physical particle or interaction nor establishes attainable laboratory preparation, clock or measurement precision. The finite negative response is consistent with the earlier positive formal joint-short-time coefficient, whose limiting regime differs. Dependence of this nonlinear mixed response on the mediator's acquired class is addressed by the separate scaled comparison, with its own source transfer, eight readings and prospective criteria.