The same quantum channel can hide different resource costs \[\boxed{C_{\mathrm{loc}}=\varepsilon(\mu_M-\mu_0)+k_{\mathrm B}T_0\left[\sum_{j=1}^{M}h(q-\mu_j+\mu_{j-1})-Mh(q)\right].}\] Two finite supply devices can implement exactly the same complete quantum channel while depleting different amounts of locally recoverable free energy. Even perfect endpoint process tomography need not determine that supply cost. This paper proves an explicit counterexample, then identifies the extra records that reconstruct the resource without fitting a relaxation rate: the intermediate mean excitation numbers, together with independently known preparation and energy scales. For a qubit contact with fixed population contraction \(\Lambda\), prepared supply population \(q\), initial system population \(p_0\), and \(M\) contacts, write \(\Delta=(q-p_0)(1-\Lambda)\). The full dynamically attainable resource interval is \[C_{\min}=\varepsilon\Delta+k_{\mathrm B}T_0[h(q-\Delta)-h(q)],\qquad C_{\max}=\varepsilon\Delta+Mk_{\mathrm B}T_0[h(q-\Delta/M)-h(q)].\] Both endpoints are constructively attainable when idle contacts are allowed. Every intermediate value occurs with the same complete reduced channel. The paper supplies the realizing contact angles, the refinement limit, an explicit correction for outgoing-unit coherence, and finite-error bounds that include uncertain energy and temperature scales. The collective extension gives the exact Dicke collision kernel, a controlled weak-collision limit, finite-contact parameter identification, and a stationary Otto-cycle resource balance. The reconstruction archive independently builds the joint unitary, partial traces, full reduced superoperators and a second Markov propagator. It reproduces the published collective-engine benchmark and includes all numerical cases, code, plot data and checksums. Scientific status. These are conditional mathematical theorems with reproducible synthetic verification. They extend the QTT physical-contact program by separating endpoint selection from resource selection. The chosen exchange contact has a matched conventional quantum realization. The work neither reports a laboratory detection nor claims an engine-specific axiom-only value of its coupling. Its operational advance is an explicit resource-selection criterion and a reconstruction that requires no coupling fit. Dependencies: QTT Physical Contact Selection and Predictive Transfer and Completed-Event Transport and Quantum Coherence. Independent benchmark: Garcez and colleagues, collective Dicke Otto engine. Corpus Tree. The PDF is the main paper and default preview. The ZIP contains the complete editable and executable reconstruction package.
The same quantum channel can hide different resource costs [\boxed{C_{\mathrm{loc}}=\varepsilon(\mu_M-\mu_0)+k_{\mathrm B}T_0\left[\sum_{j=1}^{M}h(q-\mu_j+\mu_{j-1})-Mh(q)\right].}] Two finite supply devices can implement exactly the same complete quantum channel while depleting different amounts of locally recoverable free energy. Even perfect endpoint process tomography need not determine that supply cost. This paper proves an explicit counterexample, then identifies the extra records that reconstruct the resource without fitting a relaxation rate: the intermediate mean excitation numbers, together with independently known preparation and energy scales. For a qubit contact with fixed population contraction (\Lambda), prepared supply population (q), initial system population (p_0), and (M) contacts, write (\Delta=(q-p_0)(1-\Lambda)). The full dynamically attainable resource interval is [C_{\min}=\varepsilon\Delta+k_{\mathrm B}T_0[h(q-\Delta)-h(q)],\qquad C_{\max}=\varepsilon\Delta+Mk_{\mathrm B}T_0[h(q-\Delta/M)-h(q)].] Both endpoints are constructively attainable when idle contacts are allowed. Every intermediate value occurs with the same complete reduced channel. The paper supplies the realizing contact angles, the refinement limit, an explicit correction for outgoing-unit coherence, and finite-error bounds that include uncertain energy and temperature scales. The collective extension gives the exact Dicke collision kernel, a controlled weak-collision limit, finite-contact parameter identification, and a stationary Otto-cycle resource balance. The reconstruction archive independently builds the joint unitary, partial traces, full reduced superoperators and a second Markov propagator. It reproduces the published collective-engine benchmark and includes all numerical cases, code, plot data and checksums. Scientific status. These are conditional mathematical theorems with reproducible synthetic verification. They extend the QTT physical-contact program by separating endpoint selection from resource selection. The chosen exchange contact has a matched conventional quantum realization. The work neither reports a laboratory detection nor claims an engine-specific axiom-only value of its coupling. Its operational advance is an explicit resource-selection criterion and a reconstruction that requires no coupling fit. Dependencies: QTT Physical Contact Selection and Predictive Transfer and Completed-Event Transport and Quantum Coherence. Independent benchmark: Garcez and colleagues, collective Dicke Otto engine. Corpus Tree. The PDF is the main paper and default preview. The ZIP contains the complete editable and executable reconstruction package.
This preprint studies a cycle-reflection operation on a supplied six-qubit realization of paired trigram configurations. A four-matched-pulse identity and a minimum within its stated serial grammar are separated from an ordinary-exchange endpoint construction. The raw full-source reflection and its full domain-safe alternative are different tasks: the latter is excluded by a collective-symmetry obstruction in the admitted source-only exchange model. Strict preservation of the addressable sector throughout the path is also excluded for the full task, while finite-action lower bounds quantify peak no-address population and time-integrated exposure. The paper presents an explicit low-excursion balanced word and a conditional joint clock–amplitude error certificate. Root settings and trajectory inputs remain tied to their supplied computer-assisted certificates. The second internal review reproduced all ten advertised numerical routes and twenty-four outputs using the original programs; this is same-program reproducibility, not independent implementation or external peer review. A separate Lean supplement covers the finite raw/safe operator algebra and the obstruction for arbitrary finite words of the declared algebraic factors. It does not formalize the numerical roots, matrix exponentials, continuous-time dynamics or resource theorems. No global pulse optimum, measured hardware feasibility, general noise tolerance, or automatic connection to the companion recovery code is claimed.
A physical identification requires a domain of experiments, a realization, and an observation that distinguishes competing mechanisms. We construct these for the δ framework. Within finite causal quantum experiments, computable Choi data are equivalent to finite arithmetic programs producing valid instrument approximations at every requested accuracy. A separate pointer reader preserves the quantum posterior and supports adaptive composition. For the native two-atom census, the actual join update and common-mode retention select golden scaling and a signed contraction. Coherent return selects its minimal conserving completion; an independently calibrated spectral band then selects its constant interaction. A bright-mode construction and a stable short-time calibration procedure supply an explicit realization and uncertainty budget; measured duration and frequency supply the dimensional units. We derive a general endpoint identity between stored record energy and comparison imbalance, and distinguish the monotone fresh-record trajectory from coherent recurrence. The logical-to-physical bridge also has a sharp boundary: an explicit instance of the proposed completion generator has no effective value-reflecting physical reader or numerical comparison receipt. Sequence completion requires precisely the corresponding halting-oracle resource, not an unexplained scalar cost. This obstructs operational completion while leaving purely proof-language transport distinct. Native implementations of identical logical strength nevertheless carry different physical receipts. Joint covariance and the exact endpoint law state the valid relationship between those quantities. Finally, calibrated return and three-outcome tests distinguish the relevant phase and recording alternatives, with quantitative error bounds. First public preprint release, version 1.0. The files include the PDF and the main TeX file. AI-use disclosure: AI assistance was used for source analysis, mathematical exploration, manuscript drafting and revision, diagram preparation, and computational verification support. GPT-6 Astra reviews assessed arguments, scope, readability, and schematics. These were internal model reviews, not external peer review. Jonathan Washburn is the sole listed author and is responsible for the released manuscript.
From independently qualified work to one interaction and several observations LkerB={0}. When does a device's independently specified work already determine its interaction? In a finite affine constructor, the answer is exact: every unresolved calibration direction must disappear from the observable interaction. The paper proves necessity and sufficiency, constructs a dual certificate, and counts the additional linear probes needed when selection fails. The QTT source-to-contact construction connects geometry, supported work, mode participation and the actual electrode waveform to a single coupling. That same coupling predicts one-excitation transfer, two-excitation redistribution, phase response and parity controls. A finite future-memory theorem identifies what must remain in the retained packet so that later operations cannot reveal something the model discarded. For independently specified insertion magnitudes, the cross-occupation prediction is P11=cos2(FΘ),F2=f2,a2+f2,b2. For symmetric-slot modes, the corresponding frequency ratio obeys (2Ω1Ω2)2=1−2Ka1−2Kb1. Version 2.0 adds complete feasible-set selection, a harmonic three-dimensional drive, unequal-capacity transfer, and the full preparation-to-detector calculation. A cross-Kerr counterexample shows why a perfect one-excitation calibration alone cannot settle the two-excitation prediction. The package contains the manuscript, proofs, executable checks, synthetic examples and a reproducible audit of the public Hou trapped-ion tables. The selection and transfer results are proved within their stated finite classes. The canonical realization shares laboratory probabilities with matched microscopic quantum mechanics; finite-slot discrimination requires independently qualified physical capacities and instruments. The archive is a retrospective eligibility audit. The separate prospective test commits the measurement design before a laboratory supplies its physical capsule. Companion: Artian's Physical Contact Transfer Test. Source dependencies: Completed-Event Transport and Quantum Coherence; QTT Main Book. Independent experimental context: Hou et al., Nature Physics (2024). Browse the corpus. The main PDF is the preview; the ZIP contains the full reconstruction package.
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.
The uncontrolled endpoint channel can conceal how well a quantum process can protect a logical task under time-resolved control. We formulate a fixed-task resource theory of continuous process tensors with physical access interfaces, entrance-erasing free objects, and budgeted free conversions. Complete-record total-variation error measures performance; the calibrated capability is monotone under conversions that preserve a common free baseline. For unknown-state transmission the baseline is exactly 1−d−2. Two qubit processes with the same endpoint channel have optimal errors 0 and p=sin2(2gh) at the same finite pulse budget in an ideal-transparent system-only window architecture, forcing any endpoint-only predictor to err by at least p/2 on one of them. An exactly solvable family shows how the allocation of a fixed interaction phase around a control window sets the attainable error, and a nontrivial perfect echo requires and attains total control action π in that architecture. The separation extends directly to every qubit unitary target at a budget that includes its boundary gate, while unitary tasks in any dimension have baseline 1−d−2 whenever a budget-feasible free realization gives the depolarizing output. Complete-record implementation bounds quantify coherent and dissipative control imperfections. Continuous-process randomized compilation supplies physical instrument pullbacks; compatible completion conditions extend their action, and certified dynamical bounds yield achievable task-error and capability guarantees. The resulting theory identifies temporal structure and control investment that endpoint characterization alone cannot resolve.
Keeping a record changes which alternatives can interfere. On a pair of eight-state clock channels, we derive three recording operations whose identical final measurement has probabilities 1/4, 9/32, and 3/8. The full-current instrument retains fifteen distinct histories and transfers incoming occupation phase into their relative phases. Requiring its physical realization to conserve both native clock energy and occupation has a stronger consequence: every collective one-channel observable is conserved, and all admissible operations lie in the permutation commutant. This yields an exact reference-count balance, a sharp state-dependent disturbance bound, and a finite-reference obstruction to exact neutral recording. We characterize the complete finite-reference attainable region by an explicit finite algebraic synthesis problem, including its no-reference endpoint. A conserving collision construction then supplies a concrete attainable family, with an exact diamond-error formula and a uniform reference-return bound. These results connect the choice of record to observable dynamics and to the reference that pays for their implementation. A finite discrimination protocol states the required preparation, error tolerance, sample count, and independently calibrated time and energy scales. First public preprint release, version 1.0. The files include the PDF, the main TeX file, and a complete source archive with editable schematics and relevant verification supplements. AI-use disclosure: AI assistance was used for source analysis, mathematical exploration, manuscript drafting and revision, diagram preparation, and computational verification support. GPT-6 Astra reviews assessed arguments, scope, readability, and schematics. These were internal model reviews, not external peer review. Jonathan Washburn is the sole listed author and is responsible for the released manuscript.