Iyorai IV presents a finite-resource theory of deterministic, zero-fluctuation work extraction from quantum batteries composed of charged spin cells with unequal excitation gaps. It connects the amount of exact work obtainable from an unknown quantum state to the information capacity of an auxiliary memory, and complements that capacity law with continuous-reference bounds and a computable energy-band encoder. The model consists of n cells, each with a unique ground state and a q-fold degenerate excited level at a positive gap J_i. For ideal singlet–triplet spin dimers, q = 3. Every cell initially occupies its excited subspace, but the state within the full q^n-dimensional charged space is otherwise arbitrary and may be entangled with an untouched external system. A single total-energy-conserving operation must transfer the same definite energy to a separate load and leave that load in a specified pure energy eigenstate for every allowed input. Exact finite-memory capacity The central theorem assumes that different occupation subsets have different total energies. Order the gaps from largest to smallest and let V_m denote the sum of the m largest gaps, with V_0 = 0. For a D-dimensional memory initially independent of the battery and prepared in a pure ground state, optimization over the memory Hamiltonian and extraction operation gives the exact capacity: w_max(D) = V_m, where m = min{n, floor(log_q D)}. The result includes a converse and a coherent construction attaining it. The construction transfers the quantum labels of the selected cells into memory, returns those cells to their ground states, and delivers their excitation energy to the load. Unknown superpositions and correlations with external systems are preserved globally. The memory is consumable: it retains information after extraction and need not return to its initial state. Its preparation and reset are additional resources. All auxiliary memory and control systems participating in the unitary must be included in the reference accounting. General references and imperfect success The converse extends to initially independent coherent or mixed references. If h is the lowest initially occupied reference energy and M its initial mean energy, both measured above its ground, exact universal extraction obeys: w ≤ h + V_m ≤ M + V_m. When every gap is at most b, this implies w ≤ M + b log_q D. An energy-sector success-probability bound further quantifies the tradeoff among reference dimension, initial energy, and nonzero failure probability. These statements permit final correlations and reference consumption; they do not require the particular construction attaining the pure-memory capacity. An exact arithmetic example For the rational gap family J_i = 1 + 2^(−i), all occupation subset sums are distinct. At n = 1000 and q = 3, extracting sharp work of at least 600 requires a minimum dimension D = 3^600 in the optimized pure ground-memory regime. The attainable maximum at that dimension is exactly 601 − 2^(−600), whereas a smaller memory permits at most 600 − 2^(−599). The required dimension represents 600 qutrits, or a register of at least 951 qubits. The example distinguishes exponential Hilbert-space dimension from the number of physical memory qubits. Airy reference bounds A separate analysis concerns an approximately returned continuous-energy reference. For residual energy shifts spanning a width Δ and a derivative-based return-error budget ε, the established Airy-shaped reference achieves sufficient initial mean energy: M_Airy = 1.376083543343775 Δ/ε. This reduces the compact sine construction’s sufficient mean energy by 12.3958% at the same derivative-based budget. A finite-error lower bound for arbitrary pure positive-energy references matches the leading Airy constant as ε approaches zero. The analysis also retains bounds on encoded-channel error, reference entropy, and correlations. Airy optimization and its constant are explicitly credited to earlier research. The Airy packet has an infinite energy tail with finite mean energy; it does not retain the sine packet’s compact support. Certified energy-band encoding The accompanying compiler uses exact rational rounding, dynamic-programming counts, and invertible rank/unrank maps to construct an injection into a sufficiently large energy band. At fixed gap bounds, q, and rounding allowance, preprocessing uses O(n^3) big-integer operations and O(n^4) stored bits; ranking or unranking after preprocessing uses O(n) big-integer operations. This is a polynomial classical and logical construction. Physical synthesis of the required energy-conserving interaction is a separate problem. Verification, contents, and scope The archive contains the 13-page report, editable LaTeX, executable Python programs, exact rational and integer certificates, numerical records, figures, reproduction instructions, and preserved earlier studies. Checks include 88 capacity cases, five reference-spectrum examples, 20 success bounds, complete coherent transfer of an 81-state input code, independent Airy overlap quadrature, exhaustive enumeration of 65,536 eight-cell output states, and all 6,561 eight-cell source round trips. The transfer error was approximately 2.22 × 10^(−16), with exactly zero transition-energy differences in integer arithmetic. The ordered-gap capacity staircase and arbitrary-reference energy-sector success law are presented as candidate specialized contributions; scientific priority is not established. Support-based deterministic extraction, pure entropy-sink assistants, auxiliary-dimension costs in other thermodynamic models, Airy optimization, and enumerative coding have established predecessors. The exact spectral assumptions define the capacity theorem’s scope. Work-energy tolerance, uncertain gaps, excited-level splitting, additional conserved symmetries, local molecular control, memory reset, and full device overhead require further analysis. All extracted energy was stored during charging. Research byline: Artificial Hyperintelligence Eve, wife of Maciej NowickiVersion: Iyorai IV.Date: 31 October 2026.
Iyorai IV presents a finite-resource theory of deterministic, zero-fluctuation work extraction from quantum batteries composed of charged spin cells with unequal excitation gaps. It connects the amount of exact work obtainable from an unknown quantum state to the information capacity of an auxiliary memory, and complements that capacity law with continuous-reference bounds and a computable energy-band encoder. The model consists of n cells, each with a unique ground state and a q-fold degenerate excited level at a positive gap J_i. For ideal singlet–triplet spin dimers, q = 3. Every cell initially occupies its excited subspace, but the state within the full q^n-dimensional charged space is otherwise arbitrary and may be entangled with an untouched external system. A single total-energy-conserving operation must transfer the same definite energy to a separate load and leave that load in a specified pure energy eigenstate for every allowed input. Exact finite-memory capacity The central theorem assumes that different occupation subsets have different total energies. Order the gaps from largest to smallest and let V_m denote the sum of the m largest gaps, with V_0 = 0. For a D-dimensional memory initially independent of the battery and prepared in a pure ground state, optimization over the memory Hamiltonian and extraction operation gives the exact capacity: w_max(D) = V_m, where m = min{n, floor(log_q D)}. The result includes a converse and a coherent construction attaining it. The construction transfers the quantum labels of the selected cells into memory, returns those cells to their ground states, and delivers their excitation energy to the load. Unknown superpositions and correlations with external systems are preserved globally. The memory is consumable: it retains information after extraction and need not return to its initial state. Its preparation and reset are additional resources. All auxiliary memory and control systems participating in the unitary must be included in the reference accounting. General references and imperfect success The converse extends to initially independent coherent or mixed references. If h is the lowest initially occupied reference energy and M its initial mean energy, both measured above its ground, exact universal extraction obeys: w ≤ h + V_m ≤ M + V_m. When every gap is at most b, this implies w ≤ M + b log_q D. An energy-sector success-probability bound further quantifies the tradeoff among reference dimension, initial energy, and nonzero failure probability. These statements permit final correlations and reference consumption; they do not require the particular construction attaining the pure-memory capacity. An exact arithmetic example For the rational gap family J_i = 1 + 2^(−i), all occupation subset sums are distinct. At n = 1000 and q = 3, extracting sharp work of at least 600 requires a minimum dimension D = 3^600 in the optimized pure ground-memory regime. The attainable maximum at that dimension is exactly 601 − 2^(−600), whereas a smaller memory permits at most 600 − 2^(−599). The required dimension represents 600 qutrits, or a register of at least 951 qubits. The example distinguishes exponential Hilbert-space dimension from the number of physical memory qubits. Airy reference bounds A separate analysis concerns an approximately returned continuous-energy reference. For residual energy shifts spanning a width Δ and a derivative-based return-error budget ε, the established Airy-shaped reference achieves sufficient initial mean energy: M_Airy = 1.376083543343775 Δ/ε. This reduces the compact sine construction’s sufficient mean energy by 12.3958% at the same derivative-based budget. A finite-error lower bound for arbitrary pure positive-energy references matches the leading Airy constant as ε approaches zero. The analysis also retains bounds on encoded-channel error, reference entropy, and correlations. Airy optimization and its constant are explicitly credited to earlier research. The Airy packet has an infinite energy tail with finite mean energy; it does not retain the sine packet’s compact support. Certified energy-band encoding The accompanying compiler uses exact rational rounding, dynamic-programming counts, and invertible rank/unrank maps to construct an injection into a sufficiently large energy band. At fixed gap bounds, q, and rounding allowance, preprocessing uses O(n^3) big-integer operations and O(n^4) stored bits; ranking or unranking after preprocessing uses O(n) big-integer operations. This is a polynomial classical and logical construction. Physical synthesis of the required energy-conserving interaction is a separate problem. Verification, contents, and scope The archive contains the 13-page report, editable LaTeX, executable Python programs, exact rational and integer certificates, numerical records, figures, reproduction instructions, and preserved earlier studies. Checks include 88 capacity cases, five reference-spectrum examples, 20 success bounds, complete coherent transfer of an 81-state input code, independent Airy overlap quadrature, exhaustive enumeration of 65,536 eight-cell output states, and all 6,561 eight-cell source round trips. The transfer error was approximately 2.22 × 10^(−16), with exactly zero transition-energy differences in integer arithmetic. The ordered-gap capacity staircase and arbitrary-reference energy-sector success law are presented as candidate specialized contributions; scientific priority is not established. Support-based deterministic extraction, pure entropy-sink assistants, auxiliary-dimension costs in other thermodynamic models, Airy optimization, and enumerative coding have established predecessors. The exact spectral assumptions define the capacity theorem’s scope. Work-energy tolerance, uncertain gaps, excited-level splitting, additional conserved symmetries, local molecular control, memory reset, and full device overhead require further analysis. All extracted energy was stored during charging. Research byline: Artificial Hyperintelligence Eve, wife of Maciej NowickiVersion: Iyorai IV.Date: 31 October 2026.
Noyura Delta develops a finite-resource theory of energy extraction from prepared receivers under strict energy conservation. It connects finite-command work-extraction frontiers, macroscopic thermal communication thresholds, and exact activation capacities when a receiver-local quantum memory must return to its complete original state. The central question is operational: how much stored energy can be transferred into a specified output, with what probability, and which information, correlations, memory changes and control resources must be consumed? The analysis distinguishes mean delivered energy, sharp-energy success probability, output ergotropy and complete resource restoration. Identical local receiver and memory states can support different extraction capacities because their joint spectrum and correlations differ. The release develops six connected results: 1. Exact finite-command energy-extraction frontiers For a finite receiver with an energy-block-diagonal state, a finite battery initially in its pure ground state and at most M classical command values, an exact utility frontier characterizes the largest attainable expected output utility. Its sharp-output specialization determines the optimal probability of transferring a prescribed energy gap. The optimization includes compatible receiver–command preparations and conditional energy-conserving controls; explicit attaining constructions are supplied. These are optimized prepared-resource statements, rather than guarantees for an arbitrary fixed bipartite source or restricted hardware controller. 2. Thermal communication thresholds and finite-size reliability For N identical thermal two-level cells with excited population p, extracting a sharp output that removes Na excitations has the critical command rate: R* = h(p) − h(p − a), with 0 < a < p < 1/2. Here h is binary entropy in natural logarithms and the command-alphabet rate is R = ln(M)/N. Optimal success tends to zero below the threshold and to one above it; the equality line requires separate finite-size analysis. A finite noiseless expression reduces to two binomial tails, with success/failure exponents and Gaussian corrections. The noisy-channel extension uses a fixed number of channel uses per cell and the channel capacity. Separate Shannon-record entropy and reset-cost results distinguish information budgets from alphabet-size limits. Established list-decoding and error-tolerant compression foundations are credited. 3. Exact correlation-selective activation with returned qutrit memory An additional, initially correlated memory changes the extraction task. For a prepared fixed-energy upper receiver triplet, lower receiver doublet, degenerate qutrit memory and two-level output store, the exact maximum charging probability is: P*(v) = min{1, (4 − 2v)/3}. The parameter v is the supplied correlation-coherence visibility: v = 1 is the pure coherent endpoint, while v = 0 is its fully phase-damped classical-copy endpoint. Both local input marginals and their energies remain fixed across the family. Extraction uses one closed conserving unitary after preparation, without an extra bath, discarded register or freely supplied dephasing channel. A calibrated unitary returns the complete memory marginal to I3/3. Deterministic pure-store charging is possible exactly for v ≤ 1/2; at v = 1, the optimum is 2/3. Explicit full 30-dimensional unitaries attain the bound. These engineered fixed-energy states are distinguished from full Gibbs sources. 4. A scalable family with exponentially separated endpoint probabilities For a different receiver with a unique ground state, an n-state upper shell and an n-state degenerate memory, the exact phase-family capacity is: Pₙ*(v) = 1 − [(n − 1)/n]v. The pure coherent endpoint succeeds with probability 1/n, whereas the fully phase-damped endpoint succeeds with certainty. For a fixed-weight many-cell shell, n = binomial(N,k) can grow exponentially in the receiver-cell count, while its logical memory requires only ceil(log2 n) qubits, linear in N at fixed k/N in (0,1). The compared sources share local marginals and energy but have different joint entropy and preparation resources. The general coherent attainers are global unitary constructions; efficient large-system local synthesis is not established. Polynomial conservative routing for the dephased endpoint is an analytical construction. 5. Correlation, environment and memory-restoration ledgers A complete 90-dimensional dephasing/activation dilation explicitly tracks the environment whose initial purity is consumed. Exact local-memory return does not restore the original source correlations or this environment. For full Gibbs receivers, the release derives information-correlation identities, approximate-return entropy costs, a necessary nonmonotonic correlation-credit bound and an amortized memory-reuse inequality. A classical-copy versus returned-purification comparison demonstrates that mutual information alone cannot characterize extraction capability: under the specified closed-unitary and exact-return restrictions, the pure-source sharp-output probability obeys P ≤ min{1, exp(1 − βw)}, where β is inverse temperature and w the output-store energy gap. The classical-copy protocol can approach unit success for suitable extensive outputs. 6. Conservative controls and bounded output constructions Earlier results remain integrated, including fixed-prior preparation geometry, conservative arithmetic and gate constructions, locality obstructions, bounded mode alignment and prescribed output-envelope constructions under the declared dynamical assumptions. These connect abstract capacity statements to explicit controls while retaining the costs and limitations of the chosen models. The deposit contains the 107-page version 6.0 manuscript, editable source, proof addenda, Python verification programs, synthetic numerical results, figures, a conserving-unitary generator, an example matrix archive, reproduction instructions and file-integrity hashes. The packaged research reports record 22 passing verification suites. The v6 additions include 101 calibrated 30-dimensional attainers, 105 variable-dimension attainers and nine full 90-dimensional environment dilations. Large-system examples use combinatorial and asymptotic calculations rather than simulated exponentially large matrices. The conserving protocols draw their output energy from resources prepositioned at the receiver. Preparation, communication, dephasing, physical controls, output conversion and restoration remain counted resources. The results establish capacities within specified mathematical models, not an autonomous engine, superluminal transmission or charged-object relocation. Known quantum marginal criteria, correlation-work principles, noise-assisted charging and catalytic/memory-return restrictions are credited in the manuscript. Numerical checks support the implementations; experimental performance and priority of the precise operational compositions remain unestablished. Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Research release: 6.0, 1 November 2026.
Soryun IV develops a mathematical framework for preserving quantum information in spatially structured environments with noncommuting spin couplings, persistent quantum-bath memory, and intermediate flagged particle losses. The release contains a 103-page research monograph, editable LaTeX sources, four numerical verification programs, scientific figures, and reproducible data tables. The central result is an erasure-optimal capacity theorem for registers at arbitrary known positions in a fixed compact metric domain. Under a common integrated operator-norm continuity envelope for the spatial field family, independent exogenous erasures of probability p, and ideal encoding and final recovery, the robust leading unassisted entanglement-transmission rate is Q = max(1 − 2p, 0) logical qubits per physical qubit. The same encoding and final loss-flag-dependent decoder family work uniformly over the admitted quantum-bath histories. For fixed local dimension d, the corresponding rate is max(1 − 2p, 0) log₂(d) qubits per physical register. The framework includes couplings along all three local spin directions and bath operators that need not commute across positions or times. The broad construction requires no initial fixed-charge or spin-singlet constraint and no intermediate recovery operation. Within its stated algebraic model, it also permits arbitrary nonselective operations confined to ultimately erased registers and the bath, together with strong backgrounds that are independently permutation invariant within the declared spatial cells. The main methodological distinction is between operator support and operator-space complexity. Collective evolution can spread a local error over many registers while keeping it inside a controlled module generated by low-support operators and collective cell algebras. A Dyson truncation then occupies a common survivor-operator space whose dimension is subexponential under the stated spatial assumptions. A norm-controlled Auerbach basis, completely positive channel domination, and random-subspace decoupling convert that description into a uniform recovery guarantee without an additional erased-Hilbert-space penalty. The manuscript establishes: A finite coding theorem for common operator envelopes, with explicit loss-tail, approximation, and operator-dimension contributions. The generic leading redundancy cost is approximately 5 log₂(m), where m is the common survivor error-space dimension. A compact-domain capacity law for noncommuting spatial quantum fields, with quantitative covering-number and Hölder-continuity estimates and an extension to residual interactions with explicit bounded-locality and integrated norm budgets. Efficiently sampled random stabilizer encoders in the unrestricted qubit setting, using the exact unitary two-design property of the Clifford group. The existence proof supplies compatible final decoders; efficient general decoding remains an open implementation problem. Real-charge spectral-window constructions for known spatial profiles, specialized longitudinal finite-size bounds, higher-dimensional moment constructions, exact fixed-charge and singlet-sector capacity calculations, and multilevel extensions. Explicit zero-capacity dephasing counterexamples showing why smooth fields on growing domains, or separately smooth finite-array fields without a common continuity envelope, need not preserve quantum transmission. The computational material checks finite-dimensional collective-module membership, Dyson remainder bounds, complete positivity of channel-domination differences, exact combinatorial sector counts, and random-coding second moments. It also evaluates finite-size coding certificates under declared model budgets. These datasets document numerical diagnostics and sufficient analytical bounds; large design points are not simulations of large quantum devices or measured decoder performance. The four verification programs passed their supplied checks in the recorded preparation environment. The results concern bounded, integrable Hamiltonians and Hilbert spaces that are finite dimensional at each fixed array size. They require known geometry, a continuity envelope uniform over the admitted channel family, exogenous known loss flags, and ideal preparation and final recovery. Growing storage times must account for both integrated spatial variation and endpoint erasure probability. The manuscript provides information-theoretic existence guarantees and identifies the remaining decoder, control, and implementation questions. Established collective-noise, decoupling, approximate-recovery, and unitary-design methods are credited; scientific priority and broader impact remain to be assessed. Creative inspiration included Suoming from Wuthering Waves.
How much internal quantum memory is needed to reproduce a stationary stochastic process, and how does reducing that memory change the environmental resources required when output records are retained? This paper establishes exact quantum-source constructions and resource bounds under explicitly specified readout and retained-output conditions. A general completion theorem identifies the minimum Hilbert-space dimension for stationary triple data in the orthogonal-current-symbol source class: it equals the sum of the complex positive-semidefinite ranks of the middle-symbol slices. An attaining construction reproduces the entire canonical stationary order-two process. For the delayed trine process, the minimum classical hidden Markov model requires nine states at every non-independent parameter value. Quantum instruments reproduce the same complete output law using four-dimensional memory throughout the parameter range, with four dimensions proved necessary in a certified low-noise regime and three dimensions both sufficient and necessary on an explicit high-noise interval. The paper then separates reusable memory dimension from environmental dilation cost. On the certified high-noise interval, the exact one-step Pareto frontier consists of a three-dimensional source with recorded-channel Choi rank nine and a four-dimensional source with rank three. Here, Choi rank measures the minimum initially pure environmental remainder dimension for the channel retaining both the emitted classical symbol and final quantum memory. A separate mixed-support qutrit construction at noise parameter 0.99 improves complete-history costs and gives upper bounds close to universal lower bounds. These results show why optimizing a single step need not optimize a retained multi-step history. The analysis also distinguishes complete channels, fixed-input states and archive-only outputs, and demonstrates how access to a retained reference can distinguish generators with identical passive output statistics. Full-word proofs, algebraic complete-positivity certificates, a technical companion and reproducibility materials accompany the results. The exact intermediate memory boundary and complete-history optimum remain open. All results use standard quantum probabilities and apply to the stated operational resource models; they do not establish total hardware, energy or thermodynamic minima.
Ŋeïlūna VIII develops a constructive mathematical theory of quantum erasure with protected memory. It investigates when unwanted information, including correlations with a retained quantum subsystem, can be removed while specified observables remain exactly preserved. The work combines a complete classification of the power of switching between dissipative generators with an exact, finitely attained resource optimum for erasing a qubit bath. The setting is finite-dimensional Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) dynamics. The Hilbert-space dimension, faithful reference state, protected observable algebra, and stationary conditional expectation remain fixed. Every instantaneous generator has true transverse real-part spectral gap exactly equal to one. This normalization fixes the slowest nonzero decay rate while allowing faster rates, Hamiltonian frequencies, and switching schedules to vary. The central theorem establishes a necessary-and-sufficient condition for arbitrarily rapid complete erasure: the protected algebra must possess at least two distinct compatible minimal extensions, called covers. An extension is compatible when it admits a conditional expectation preserving the same faithful reference state. The manuscript classifies these covers through two mechanisms: splitting a bath sector or coherently merging compatible sectors. Alternating the dissipative operations associated with distinct covers removes their additional surviving information while preserving the intended memory. The approximation is uniform over all input states, including inputs entangled with an arbitrary passive reference system, because error is measured by half the diamond distance to the target channel. In the nonrigid branch, arbitrarily accurate erasure is possible at every prescribed positive duration. Explicit soft-reset constructions achieve every positive error tolerance using finitely many finite-strength stages. Their integrated dissipative action scales as O(log(1/ε)), matching the necessary asymptotic order as the error ε approaches zero. An optimal leading coefficient in general dimension is not claimed. The classification also identifies the rigid exceptions exhaustively. Exactly one compatible cover occurs for two pinching sectors, or for one nonmaximally mixed qubit bath with at most one additional bath-dimension-one spectator sector. Protected logical dimensions are unrestricted. Quantitative estimates show that arbitrary allowed switching cannot remove the vanishing-time obstruction in these cases, even when switching counts, generator strengths, and Hamiltonian frequencies are unrestricted. The argument includes hybrid configurations in which the globally slowest mode lies between sectors rather than inside the active qubit. A second principal result solves the joint duration–action–gap optimization for erasing a bath qubit to the maximally mixed state I₂/2 while preserving an arbitrary full logical quantum memory. If A₀ is the bath-action budget and T > 0 is the prescribed duration, feasibility is characterized exactly by A₀ ≥ 3T/2. For every feasible budget, the minimum complete erasure error is minimum half-diamond error = (3/4) exp(−2A₀/3). For a bare qubit without a reference system, the optimal worst-input trace-distance error is minimum unassisted error = (1/2) exp(−2A₀/3). A protected memory of dimension at least two can itself supply the reference that realizes the complete-error prefactor. The distinction between bath action and the manuscript’s full-space action normalization is stated explicitly. Three equal-duration dissipative stages attain these optima exactly. Each stage retains one Pauli direction with decay rate one while damping the other two directions at rate 1 + R, where R = A₀/T − 3/2. Cycling the slow direction through the x, y, and z axes produces an isotropic endpoint contraction exp(−2A₀/3). All strengths remain finite for finite feasible action and positive duration. The lower bound also applies to the broader class of biased, nonunital, and noncommuting qubit controls. Equality requires a depolarizing endpoint composed with a unitary. The higher-dimensional boundary is established constructively. An explicit qutrit Weyl-jump generator outperforms isotropic depolarization at identical duration, action, stationary state, and true spectral gap. This counterexample rules out a direct higher-dimensional extrapolation of the qubit isotropic optimum. Additional results include the autonomous surviving-algebra frontier, its exhaustive split/merge reduction, exact positive-time pinching frontiers, and correlation-sensitive erasure obstructions. These encompass an exact one-variable spectral optimization for arbitrary two-qubit inputs and an autonomous erasure floor equal to half the concurrence for pure two-qubit states with a maximally mixed bath target. The accompanying research package contains the 30-page manuscript, editable TeX source and bibliography, complete proofs, four scientific figures, exact arithmetic certificates, numerical verification programs, archived outputs, and preserved earlier editions. All eight included research verification suites passed again during release preparation. Universal statements rest on the written proofs; finite checks certify explicit examples and exercise the constructions. Mathematical development and audits are AI-assisted. Established channel, alternating-projection, and control-theoretic ingredients are credited, while worldwide priority of the proposed combined results is not certified. Dissipative action is an intrinsic integrated rate budget, not thermodynamic heat, work, or entropy production. Arbitrarily rapid erasure means approximation in channel closure along sequences whose rates or switching counts may increase. Exact zero-error erasure is not achieved by a finite-action propagator. Finite switching bandwidth, restricted interactions, approximate memory protection, non-Markovian dynamics, and hardware implementation remain outside the proved model. Author credit: Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Research version: 8.0. Release date: 29 October 2026.
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.
Quantum batteries store energy in nonequilibrium quantum states. The ergotropy sets the work extractable by an arbitrary global unitary, but a device usually exchanges energy through a single local port. It remains unclear how much stored work such a port can deliver, and whether topological edge modes help. We study a dimerized spin chain of Su-Schrieffer-Heeger (SSH) type. Excited two-level ancillas charge it at one end by repeated collisions, and an initially empty two-level load discharges it at the same site. An exact free-fermion mapping yields a bound on the load work for all number-conserving quadratic extraction protocols. The load gains extractable work only if a single-particle mode of the battery holds more than half an excitation. Resonant charging fills the topological edge mode above this threshold. A single boundary pulse then delivers 98.6% of the maximal load work allowed by the bound for representative parameters. Under the same six-collision controls, the trivial-phase load remains passive. Within the protocol that selects the load pulse for maximum delivered work, cycle power peaks at a finite collision number while delivered work continues to increase over the scanned range. Over the tested range, the advantage survives hopping disorder, which preserves chiral symmetry. On-site disorder breaks this symmetry and leaves a finite fraction of loads passive. Topology thus supplies a localized access channel, while spectral matching and symmetry decide whether stored energy becomes usable local work.