README.md

Native preparation and phase readout with one shared mixer

The quantum-history construction supplied a coherent density matrix and a phase detector independently. This packet replaces both with actual native records and one declared balanced real mixer. It executes a complete preparation, evolution and readout history through the primitive observer runtime. The mixer remains an extra coherent service: the committed native grammar cannot construct it from diagonal preparations and classical feedback alone.

Both signs of a moving native current can herald a useful preparation. The probability of a useful trial is 5/33, with 5/66 for each sign. Failed preparations, probability 28/33, remain explicit outcomes. There is no new experimental dataset or claim that these model probabilities have been measured in nature.

The end-to-end operation

The carrier is the existing 66-dimensional binary sector: two occupied sites among twelve. Begin with the declared stationary diagonal state I/66. Choose the first source seam (u,v) and execute one native C or E repair with its fair coin c. Read its signed current j=x_u-x'_u.

1. If j=0, retain a failed-preparation record and stop using native repairs or mixers in that trial. The controller's remaining slots act as identity.
2. If j=-1, the repair has prepared the uniform mixture of the ten configurations |uw>, with w outside the seam. If j=+1, it has instead prepared the corresponding mixture of |vw>. The sign remains recorded.
3. Apply the same declared mixer B to each of these ten orientation pairs: B|uw>=(|uw>+|vw>)/sqrt(2) and B|vw>=(|uw>-|vw>)/sqrt(2). It acts as identity on the other 46 states. Thus the two herald signs prepare the previous rho_+ and rho_- exactly.
4. Execute n unread native attempts with the existing uniform seam scheduler, then apply B again.
5. Execute a final fixed-seam native repair. Declare its raw pointer outcome plus exactly when 2*j+2*c-1>0. This uses only the recorded native coin and current. For the minus preparation, reverse the final bit, so the interpreted readout always means matches/opposes the prepared phase.

The runtime receives the diagonal initial state, actual native Kraus maps and B. It receives no independently supplied target coherent state or target phase POVM. The old apparatus is used only as a comparison oracle. Successful trials cost n+2 native attempts and two applications of the supplied mixer; failed trials cost one native attempt and no mixer. The parameter n counts native attempts, not seconds or a continuous-time Hamiltonian flow.

For each candidate and each n=1,2,4, the executable retains all six records:

Herald	Interpreted final bit	Exact probability
Failed	0	28/33
Failed	1 (impossible)	0
Plus preparation	Match	(5/66) p_L(n)
Plus preparation	Opposite	(5/66) [1-p_L(n)]
Minus preparation	Match	(5/66) p_L(n)
Minus preparation	Opposite	(5/66) [1-p_L(n)]

The old exact source transfer gives

p_L(n) = [1+r_L^n]/2,       r_C=5/6,       r_E=7/10.

Unread native attempts	C: conditional match	E: conditional match
1	11/12	17/20
2	61/72	149/200
4	1921/2592	12401/20000

At four attempts, the conditional difference is 12259/101250, about 0.12108. Including all failed preparations, the total variation distance between the two complete six-record distributions is 12259/668250, about 0.01834. Using both herald signs doubles the usable yield relative to keeping just one. Four is the maximizing integer for this particular conditional phase contrast, as established by the existing quantum-memory calculation; no optimum over other preparations, detectors or quantum channel tests is claimed.

All terminal densities are compared with the independently reconstructed source transfer blocks, including every failure and impossible record. A checkpoint after preparation is serialized, independently restored and continued. A separate entangled reference-qubit input tests every complete 132-dimensional terminal density and the untouched reference marginal. Entanglement survives its successful herald, so this check is not reduced to a classical input test. Its herald probabilities differ from those of I/66; the stationary 5/66 law is not asserted for arbitrary inputs.

Why native records implement the phase effects

Let P_u and P_v project onto the two ten-dimensional orientation subspaces, let Z=P_u-P_v, and let S=sum_w (|uw><vw|+|vw><uw|). Exact native branch counts show that the raw coin/current rule has effects

D_+ = (I+Z)/2,       D_- = (I-Z)/2.

The effects are deterministic on either orientation and give a fair bit on the remaining 46 states. Conjugation by the balanced mixer gives B* D_± B=(I±S)/2: exactly the earlier phase effects. This equality holds on every input, including with an untouched reference. Omitting the native coin and assigning a fair bit to j=0 instead gives the weaker effect I/2±S/4. Retaining the coin correlation is therefore essential.

Equal effects do not identify the full postmeasurement operation. On rho_+, the native detector reports plus with certainty but changes its state. Its terminal density has trace distance 1/2 from the former positive-square- root detector output. The producer explicitly checks that distinction. The effects are projectors only after restriction to the active 20-dimensional orientation corner; globally their inactive eigenvalue is 1/2.

The existing finite theorem instrument_component_fixing_certain_states_is_lueders requires a projective effect and invariance of every state certain for that outcome. Applied to the active corner, its invariance premise fails here. Thus that theorem does not identify this native detector with the old instrument. It is not applied to the nonprojective whole-carrier effects.

A native auxiliary supplies a continuing work-bit instrument

pointer.py supplies the stronger instrument needed for continued quantum work. A separate native carrier is prepared in a fixed binary configuration by the current-only reset. In the existing source chart its seam orientation is code 2. Two existing source CNOTs copy the chosen work bit into the orientation: first work to auxiliary bit 0, then auxiliary bit 0 to auxiliary bit 1. The complete word uses six source pulses. One native coin/current pointer reads the orientation; the auxiliary is then traced out. No projective work-register read is supplied.

For work projectors P_0,P_1, the ideal coupling sends the auxiliary blank to two orthogonal orientations. The native pointer's effects are certain on those orientations. For each outcome, partial trace over the auxiliary therefore gives exactly

rho_WR -> (P_b tensor I_R) rho_WR (P_b tensor I_R).

This proves the Lüders instrument, including coherences within each bit sector and arbitrary untouched references. The auxiliary's own disturbance is immaterial after its declared trace. The older same-carrier detector above still has a different postmeasurement state. Nor can this instrument be replaced by measuring the whole work configuration and forgetting all but one bit: that operation destroys additional coherences.

The displayed equality is the exact ideal coupling/readout target. The literal six-pulse source matrix has a separate operator-norm and half-diamond error certificate against that target. Its raw output blocks are neither projected nor renormalized.

The implementation executes the complete eight-dimensional local source map, lifts its derived Kraus blocks to the work register, and retains every work address, including the full Palm clock's 446 addresses outside its binary shell (12 collision codes and 434 encoding-padding addresses). All four auxiliary local code states have native full-carrier representatives, so raw source leakage is not removed by an intermediate code projection. Its source-array norm certificate covers all local input columns; physical code-service error remains a separate input.

Numerical density admission caps the combined aggregate negative spectral mass, Hermitian trace-norm bound and out-of-range trace excess at 1e-13. It leaves the input unchanged and is not an outward positivity proof; the channel theorem assumes a genuinely positive subnormalized input. Portable receipt tolerances do not relax nonnegative diagnostic and probability domains or the execution error gates.

Finite auxiliary preparation can steer a correlated work/reference input on success. Its uniform complete failure bound, not a claim of conditional independence, controls the difference from the original work instrument. Private preparation records are discarded and public timeouts are retained. The full modular experiment composes both native resets, the source clock and this continuing readout. This removes independent logical blank and projective-detector services within that architecture; proper-code service ancillas and coherent routing remain supplied and are not derived from passive repair.

The exact reachability boundary

For every source seam, coin and retained candidate record, the native Kraus matrix is a weighted partial injection: each nonzero column and row has one entry. The producer checks all 3,960 source branch addresses per candidate, grouped into 120 C or 180 E matrices across the 30 seams. This proves, with Delta denoting work-basis dephasing,

Delta(K rho K*) = K Delta(rho) K*,       K* K is diagonal.

Products and tensor products of partial injections have the same property. Coarse-graining outcomes sums their CP maps without adding amplitudes between records. Hence every finite path built from these native maps, classical record conditioning, classical feedback and diagonal ancillary preparations preserves diagonal states. Conditional normalization cannot create a missing off-diagonal entry. Every accessible classical record effect in this grammar is diagonal, so those record probabilities depend only on the input diagonal. The same argument retains an arbitrary untouched reference and its conditional marginals. It does not equate the complete quantum terminal states of coherent and dephased inputs: native maps can preserve coherence that was already present. An adaptive two-step reference test checks that distinction.

The source repair instrument theorems dephase_kraus, dephase_cptp and dephase_diagonal supply the finite dephasing operation. The displayed intertwining identity is the direct partial-injection attachment for these actual native branches; no new Lean theorem is claimed. This is a reachability obstruction for the declared operational grammar, not for every possible OPH interface.

The mixer has two nonzero entries in each active column and creates coherence from a heralded diagonal state. It therefore lies outside that native-only closure. Native support derives its pairing, but neither membership in a generated matrix algebra nor the existence of coherent finite-theorem constructions supplies this operation as an executable native service. The positive reduction is to one shared coherent service; it is not a proof that this service is physically minimal or source-selected.

Even adding B leaves every matrix real. All finite adaptive record effects remain real symmetric and therefore cannot distinguish a state from its complex conjugate. In particular the two mixtures of (|uw>±i|vw>)/sqrt(2) are orthogonal (trace distance one), while both give the same half/half native pointer law. The executable checks this control. The existing rhoY_bornWeight_equal_on_real_symmetric theorem gives this identity in dimension two; compression to each orientation pair applies it here. The 66-dimensional real-effect closure is the direct finite-matrix argument above, not a claim that this larger apparatus already has a new Lean instantiation or belongs to the theorem's original generator set. Full complex tomography still needs a resource breaking this real-effect restriction.

Quantitative preparation floors for the native-only grammar

coherence_budget.py turns the reachability boundary above into exact complete-output error floors. Its premise concerns the joint marginal of all accessible quantum registers: that marginal must initially be diagonal, and fresh diagonal ancillas must be independent. Separate diagonal marginals of correlated registers are insufficient. Any work extraction must preserve the declared basis dephasing. Coherent access to an uncommitted native record dilation remains outside this grammar. The producer checks the actual C/E partial injections; independent tests rebuild them from endpoint averaging.

Let a target success block be p rho, and let c be the minimum trace distance from rho to a normalized diagonal state. A native-only success block has the form q delta, even when adaptation changes the herald rate. Its complete output distance is at least

D(p rho, q delta) + |p-q|/2 >= p c,       D(A,B) = ||A-B||_1/2.

The other output blocks supply |p-q|/2. Rescaling q delta, or adding diagonal mass, produces a diagonal matrix of trace p at precisely that distance; the triangle inequality proves the bound. Thus changing the success rate, including always failing, cannot evade it. Conditional target error epsilon gives p max(0,c-epsilon), with no division by a rare-event probability.

For the ten balanced orientation pairs, a signed pair-swap witness proves c=1/2. Keeping both original sign heralds gives the exact floor 5/66. One additional unread fixed-seam repair after each successful native herald prepares the equal orientation mixture and attains this floor. This sharpness statement retains the original herald and work, forgets the added repair record, and makes no claim about a finer tape or retained reference.

For the existing capped twelve-site preparation, write F=I-L/120, M=sum_(n=0)^4 w_n F^(2n), p=Tr(M)/12, and rho=M/Tr(M). The producer checks the exact characteristic polynomial x(x-6)^5(x^2-10x+20)^3 and all sixty source rotations. Their uniform transitive twirl fixes rho and sends every diagonal state to I/12; trace-distance contractivity proves that I/12 is closest. With m_lambda=sum_n w_n(1-lambda/120)^(2n), integer-square-root enclosures resolve the four positive eigenvalues of rho-I/12 and give

c   = [m_0 + 3 m_(5-sqrt(5)) - 4p]/(12p),
p c = [m_0 + 3 m_(5-sqrt(5)) - 4p]/12.

The conditional floor is about 0.005603441895; the complete floor is about 0.004494803462. Exact rational intervals are retained in coherence_results.json. Sharpness here concerns diagonal successful work and coarse success/failure access that discards failed quantum outputs. Retaining those outputs or a reference preserves the lower bound, but does not establish sharpness for that richer access.

These are preparation-checkpoint bounds, before the clock and detector. They are not applied to the subsequently dephased terminal work. A complete target allowance a, initial error eta, and uniform complete-instrument half-diamond error delta over at most N adaptive attempts leave the lower bound max(0,p c-a-min(1,eta+N delta)). N is a maximum path length, not a mean. The receipt subtracts the existing prepared-clock numerical allowance under its existing guards; this module reproduces that arithmetic without reexecuting the source words or certifying physical service errors.

Complete state identification from native records

tomography.py extends the two-state phase distinction in Lean/QFT/SourcePhaseLiftBridge.lean to the full 66-state native sector. For any pair of native configurations, an explicit reversible source word routes its codes to the existing real or imaginary analyzer. The current-only configuration detector then reads the output. Every other configuration, detector timeout and export abort is retained; scores are never normalized by successful detection. The analyzer can move spectator inputs outside the native sector, so export abort is necessary even for the ideal operation.

One basis setting and two settings for each of the 2,145 pairs give 4,291 settings. Their effects span all 4,356 real Hermitian coordinates:

p_i = rho_ii,   x_ab = 2 Re(rho_ab),   y_ab = -2 Im(rho_ab),
rho_ab = (x_ab - i y_ab)/2.

The exact effect identities and every 512-address routing permutation are checked. This is a constructive instance of informationally complete measurement. Real analyzers alone have rank 2,211 and leave conjugate states indistinguishable; native diagonal effects alone have rank 66. Thus the phase service has an operational role. The extension is an analytic finite proof with executable checks; it is not a new Lean theorem.

Fresh source-block certificates, including inverse routes, compose with the 2,520-attempt configuration detector into one complete record/reference error bound below 1e-7, for either C or E. This certifies exact products of the checked binary block maps. Floating propagation of example states is a separate diagnostic; the bound does not certify physical control errors. Untouched references are retained and final work is discarded.

For complete repeated trials, sampling_bound combines bounded-score martingale sampling error with a declared conditional-mean discrepancy at most 2 delta from one fixed target, after every prior record. Independent repetitions of a fixed preparation suffice, but are not required. With N copies per setting and sampling tolerance eta, simultaneous failure is at most 4291/(N eta^2). The basis setting contributes one unit because its indicator variances sum to at most one. Put e=eta+2 delta; the linear estimate obeys

||rho_est-rho||_op <= ||rho_est-rho||_F <= sqrt(66*67/2) e,
||rho_est-rho||_1/2 <= sqrt(66)/2 * sqrt(66*67/2) e.

This conservative existence bound is not a practical sample-complexity claim. No positive projection, clipping or renormalization is used. If an independent certificate places the estimator's smallest eigenvalue at least m, and the operator error is r<m, resolvent and unitary perturbation bounds give modular channel half-diamond error at most min(1, |s| r/(m-r)), where s is the modular parameter. An unnormalized positive estimate defines the same modular flow as its normalization. A floating eigenvalue is not the required certificate.

The existing bounded native preparation supplies that conditional guarantee for the common local reference, even on a continuing carrier with correlated inputs. Prepare before every readout; score all preparation failures as zero. The reconstructed target is (5/33) sigma, with its success weight retained, and has the same modular action as sigma. Reference-uniform preparation error and readout norm amplification bound every trial's conditional bias. Thus this reference-identification protocol removes the independent-copy premise without discarding failed preparations. The receipt gives a conservative sampling budget; the full large-sample campaign is not executed. Actual physical preparation and control errors remain additional to these mathematical bounds.

The result removes a supplied informational-completeness assumption for this finite architecture. Coherent proper-code routing, the declared controller and physical service accuracy remain premises. Arbitrary unknown-state tomography needs a fixed preparation or an equivalent conditional-mean guarantee. It does not identify modular parameter with laboratory seconds or a physical boost, and it does not reconstruct an unknown state from one nondestructive trial. tomography_results.json retains the exact bounds and synthetic reference controls; it contains no laboratory observations.

Supplied premises and reproduction

The original herald experiment in construction.py assumes the binary carrier sector, I/66 input, chosen seam, uniform evolution scheduler, candidate C or E, balanced mixer and classical protocol controller. That experiment supplies the mixer directly and emits no source pulse words. It removes independent coherent preparation and phase-effect assumptions conditional on that mixer. The previously derived first-current phase probabilities can use its conditional preparations and effects; its retained execution uses fixed native attempt counts.

The auxiliary-pointer construction above emits six source pulses and uses the current-only adaptive reset on arbitrary total-two inputs. It does not require the original herald experiment's I/66 input or uniform seam scheduler. Coherent proper-code services, their ancillary blanks and physical control accuracy remain supplied. Neither construction selects C over E, defines a physical clock, establishes an interacting continuum field theory or matches a new laboratory observation.

From the repository root, with model/requirements.txt installed:

python -m pytest model/native_interface -q
python -m model.native_interface --check model/native_interface/results.json
python -m model.native_interface --write /tmp/native-interface-new.json
python -m model.native_interface.coherence_budget --check model/native_interface/coherence_results.json
python -m model.native_interface.coherence_budget --write /tmp/native-coherence-new.json
python -m model.native_interface.pointer --check model/native_interface/pointer_results.json
python -m model.native_interface.tomography --check model/native_interface/tomography_results.json

--write refuses to overwrite existing files. --check rejects malformed JSON and compares source hashes, exact fractions, complete outcome dictionaries and numerical diagnostics using the shared portable receipt comparison. manifest.json binds the packet. Exact rational source counts establish the stated fractions; floating density calculations are residual diagnostics with declared tolerance 2e-10, not outward roundoff certificates.