Tegrity.AI GroupJUBAP.Net

Quantum Objects, Oracles, and Resource Accounting

Companion Paper II — version 2.1
July 2026 · Prepared for QAVA and research collaborators
Ivan Abril Palma · IMSV.org / tegrity.ai working group

Purpose

To define a technically defensible quantum research programme from two concrete sources: the regime-awareness programme’s open candidate-selection problem and the preserved xSeil production codebase. The note does not claim quantum advantage. It specifies the conditions under which such a claim could be tested, the classical baselines it must beat, and the resource costs that must be included.

This version consolidates and supersedes QAVA Quantum Sketch Note v4, Paper III drafts v0.2/v0.3, and the prior Resource-Accounting Note v5. It is designed to be read with Companion Paper I v2. The main corrections are summarized in Section 2.

Abstract

This note reformulates four candidate quantum work packages grounded in a formal regime-awareness programme and in the preserved source code of xSeil, a deployed logistics-planning system. The candidates are: (Q1) amplitude estimation for candidate-origin scores that are explicitly defined as expectations over uncertainty; (Q2) amplitude amplification for rare, implicit structural targets in xSeil’s concordance space; (Q3) amplitude estimation of rollback or cascade probabilities using a finite deterministic planner kernel extracted from the production code; and (Q4) a snapshot QUBO benchmark over a frozen route pool. The note separates ideal query complexity from end-to-end cost, corrects the crossover mathematics, distinguishes bifurcations from basin boundaries, and removes unsupported claims about market equilibrium, pre-armed catastrophic scenarios, identical simulation code paths, and exact quantum fit. The principal recommendation is to begin with an end-to-end resource audit. A negative result remains scientifically useful because it establishes which apparent quadratic speedups survive state preparation, reversible-oracle construction, output requirements, and comparison with strong classical methods.

Executive finding. The research direction holds, but only as a formulation-and-resource-accounting programme. Q2 is the cleanest first reversible-circuit study; Q3 has the highest potential operational value but the most difficult oracle; Q1 becomes valid only after the candidate score is defined as a bounded expectation; Q4 is a useful benchmark and negative control, not evidence of optimization advantage.

Document map

1. Purpose and research posture

The purpose is not to demonstrate that the regime-awareness mathematics or xSeil “belongs on a quantum computer.” The purpose is to turn general quantum language into explicit computational objects that a quantum-computing researcher can accept, reject, or resource-estimate. The document therefore treats quantum relevance as a hypothesis subject to four gates:

1. A precise classical task must exist, with finite inputs, outputs, error tolerance, and a strong classical baseline.

2. The task must admit coherent state preparation and a finite reversible oracle or Hamiltonian.

3. The ideal query reduction must survive state preparation, oracle execution, error correction, repeated shots, output requirements, and classical coordination.

4. The residual advantage, if any, must matter economically or scientifically for the stated decision.

The note makes no NP-hardness claim about the open candidate-selection problem, no production-scale quantum advantage claim for xSeil, and no assertion that all four formulations deserve implementation. The first result may be that one or more candidate windows are empty under any realistic overhead. That result would still be valuable.

2. Corrections incorporated in this version (carried from Resource-Accounting Note v5)

3. Formal programme: what is open and what would make it quantum-relevant

The regime-awareness programme describes a small exact layer—identities for selected history-dependent estimators, correction under an explicit contamination model, and local contraction of a reference operator inside a supplied basin. The relevant open problem is global candidate selection: choosing among a finite family of possible regime origins or reference basins. This note does not re-prove those results. It asks what additional structure is needed before the open problem becomes a candidate quantum task.

3.1 Candidate selection is not automatically amplitude estimation

Let C={c₁,…,c_m} be a finite candidate family. If each candidate has a deterministic, directly computable score s(c), then comparing candidates is an ordinary deterministic computation. Quantum amplitude estimation is not justified merely because two scores are close. A valid amplitude-estimation formulation requires a bounded random variable or stochastic subroutine, for example:

μ(c) = E_{ω ~ D}[ g(c, ω) ], with 0 ≤ g(c,ω) ≤ 1.

Here ω may represent uncertain histories, perturbations, bootstrap resamples, calibration uncertainty, or model ambiguity; D must be explicit. The computational task may then be to estimate μ(c), distinguish μ(c₁)−μ(c₂)=Δ, or identify a candidate within a declared tolerance. Without D and g, the phrase “1/Δ versus 1/Δ²” is only an analogy.

3.2 Decision boundaries, bifurcations, and separatrices

A bifurcation is a qualitative change in solutions or their stability as parameters vary. A separatrix is a boundary separating regions with different asymptotic behaviour, typically different basins of attraction. A bifurcation may create, destroy, or move a separatrix, but the concepts are not identical. The global regime-origin problem may involve a decision boundary; it becomes a basin-boundary or separatrix problem only after a dynamical representation defines states, attractors, basin membership, and an evolution map.

Permitted bridge. Both the formal candidate-selection problem and some xSeil stress tests may be studied as classification near decision boundaries. Under an explicitly defined dynamical model, a subset of those boundaries may correspond to basin separatrices. This is a modelling hypothesis, not a structural identity.

3.3 Why the open problem remains scientifically interesting

The open layer is valuable even if no quantum advantage exists. It raises three independently publishable questions: how candidate scores should be defined under uncertainty; how much candidate evaluations can share work; and whether the cost of resolving small differences is justified by downstream decision utility. Quantum methods supply one disciplined way to expose these quantities because they force precise definitions of state preparation, oracle access, error, and output.

4. xSeil as a code-preserved empirical substrate

xSeil is useful because the production repository preserves concrete classical primitives, not because its scale alone implies quantum advantage. The code establishes an offline route-combination layer, a persisted concordance relation, scenario-dependent nonlinear scoring, sequential allocation with in-loop re-pricing, bounded retry and search widening, and simulation-oriented planning paths. These objects can be translated into search, estimation, and optimization experiments.

4.1 Code-established architecture

4.2 Claims deliberately not carried forward

• The code does not establish that xSeil solved an explicit supply–demand equilibrium before each planning cycle.

• Nonlinear price curvature and threshold effects are not, by themselves, proof of a dynamical bifurcation or anticipatory regime detector.

• The 2016 saturation product and the later probability-based fragility formula share a broad multiplicative-pressure pattern but are not the same mathematical object.

• The repository does not yet establish an algorithm that pre-identifies catastrophic scenarios, orders clusters from stable to entangled, or materializes basin separatrices.

• Offline scheduling removes the real-time streaming requirement; it does not remove coherent data loading, state preparation, or total turnaround cost.

• Reported production cardinalities remain project-record claims unless reconstructed from surviving database counts or execution logs.

4.3 Correct architectural bridge

The valid bridge is narrower and stronger: xSeil separates expensive offline structure-building from online adaptive control. A future quantum experiment, if justified, would enrich an offline library or estimate a stress probability; the online route allocation, re-pricing, and pacing loops remain classical. This is a natural integration location—not proof of end-to-end benefit.

4.4 Classical functional preconditions and exclusion map

Companion Paper I and the functional-inventory study establish that route search is only one layer of xSeil. A quantum object is valid only after classical functions have produced a coherent snapshot, declared constraints, observable outcomes, and an authorized utility. The functions below are therefore inputs to quantum formulation, not candidates for quantum acceleration in their own right.

# Operational state vocabularies: a valid instance begins with governed state
STATUS_MANTTO_CHOICES = (('MNO','No set'), ('MAN','In maintenance'),
                         ('DIA','Up to date'), ('REA','Awaiting reschedule'),
                         ('MPR','Appointment upcoming'))
STATUS_DISPONIBLE_CHOICES = (('DIS','Available for planning'),
                             ('NDI','Not available'), ('PRI','Private service'))

# Simple but decision-relevant classical baseline: rental sizing
pax_estimated = confirmed_now * historical_final / historical_by_now
units_needed = (pax_estimated * occupancy_factor) / seats_per_unit

These mechanisms sharpen the comparison baseline. Quantum resource accounting must begin after their cost has been paid, but it cannot omit the cost of converting their outputs into coherent quantum inputs. A method that accelerates repeated candidate evaluation while assuming free entity reconciliation, state preparation, or event labeling has not established end-to-end advantage.

Exclusion rule. Master-data reconciliation, availability truth, boarding capture, SLA definition, and reassignment governance are semantic or observational problems. They may determine the value and input of a quantum task, but quantum search does not solve their underlying failure mode.

5. Q1 — Regime-candidate expectation estimation

Q1 belongs to the formal programme rather than directly to xSeil. It asks whether a candidate regime origin or reference basin can be scored as an expectation over uncertainty and, if so, whether ideal amplitude-estimation query savings survive the cost of preparing that uncertainty and evaluating the candidate.

5.1 Exact classical task

Input: candidate c ∈ C, uncertainty seed ω ∼ D, bounded evaluator g(c,ω) ∈ [0,1].

Target: μ(c)=E[g(c,ω)] and, for two candidates, Δ=|μ(c₁)−μ(c₂)|.

The functional substrate supplies candidate consequences that can enter g: SLA breach, extra-rental requirement, unserved demand, route-sheet instability, or a bounded governance-approved action cost. Possible g functions include normalized fit under bootstrap histories, probability that a candidate yields a stable local contraction under perturbation, expected action utility under a bounded scenario family, or probability that the candidate remains admissible under calibration uncertainty. Each interpretation produces a different research problem and must be fixed before resource accounting.

5.2 Quantum object

For a fixed candidate c, define a state-preparation operation A_c and bounded-value encoding U_g such that the probability of a designated ancilla state equals μ(c). Iterative or maximum-likelihood amplitude estimation can then estimate μ(c) without requiring the original phase-estimation implementation. The ideal query comparison is O(1/ε²) classical samples versus O(1/ε) coherent oracle uses for additive error ε, under the standard access assumptions [1–3].

5.3 Gating questions

• What exactly is D, and can samples be generated from finite seeds?

• Is g bounded, deterministic given (c,ω), and side-effect free?

• Can A_c, U_g, and their inverses be implemented coherently at lower total cost than the classical sample reduction?

• Is additive error appropriate, or is the decision controlled by relative error, ranking confidence, or regret?

• Does resolving a smaller Δ change the authorized action, or would abstention/satisficing remain rational?

Q1 status. Conceptually relevant but not yet instantiated. The first deliverable is a complete stochastic score definition, not a quantum circuit.

6. Q2 — Rare implicit structural search in the xSeil concordance space

Q2 is the cleanest first quantum-computing study because the production code contains an explicit pair-construction mechanism and cheap structural predicates. The useful task, however, cannot be “find hermanas” after the flag has already been materialized and indexed. The target must be an implicit property evaluated over a pair space that the classical system has not already stored.

6.1 Classical primitive and corrected target

The repository groups routes by shared non-base stop, enumerates co-occurring pairs, deduplicates them, accumulates shared-stop metadata, and classifies special relations. Let P be a duplicate-free index of concordant pairs. A valid new target T might be:

• a pair that remains jointly feasible under a declared stress vector σ;

• a pair whose combined frozen-state score exceeds θ while satisfying a structural diversity constraint;

• a pair that provides a specified coverage or redundancy pattern not already materialized;

• a witness that violates or satisfies a newly introduced policy predicate.

6.2 Quantum object and task variants

mark_T(j) = 1 iff pair(j) ∈ P satisfies target T.

Classical witness search: O(1/p). Ideal amplitude amplification: O(1/√p), p=M/N.

The formulation is appropriate for finding one witness, testing existence, approximate counting, minimum/maximum finding under an oracle score, or a bounded top-k task. It does not imply an advantage for materializing all M marked pairs; outputting all results already costs Ω(M). Fixed-point search or an unknown-M schedule may be used where the marked fraction is not known [1,4].

6.3 Binding resource problem: coherent pair indexing

The classical code obtains P through shared-stop grouping, within-group pair enumeration, and deduplication across stops. A quantum algorithm needs a reversible, duplicate-free map j↦pair(j) and access to route attributes. This is likely more important than the Boolean comparator itself. Two implementation families should be compared:

1. Pre-indexed loading: prepare a superposition over a classically materialized pair index. This may remove the original construction cost from the quantum experiment and therefore measures only search over an already built relation.

2. Coherent reconstruction: derive pair(j) from route–stop incidence data. This is closer to replacing the classical construction but may consume the entire theoretical gain.

6.4 Classical baselines

• The deployed PostgreSQL group-and-combine construction with indexes and batching.

• Modern sparse incidence joins and conflict-graph construction.

• Stratified or importance-guided classical sampling when a full materialization is unnecessary.

• Classical top-k or branch-and-bound when the target includes a score.

Q2 status. Best first reversible-oracle study. Its publishable question is whether a duplicate-free concordance state can be prepared cheaply enough for the quadratic rarity reduction to survive.

7. Q3 — Rollback and cascade probability estimation from an extracted planner kernel

Q3 has the closest relationship to quantum risk analysis: estimate the probability that a declared perturbation causes a retry, deep search escalation, unserved demand, or another operational failure event. It also has the largest implementation barrier because the production planner is a database-backed, mutable, variable-length program rather than a reversible oracle.

7.1 Event and distribution

Frozen state z₀; perturbation seed ω ∼ D; deterministic kernel F(z₀,ω); event f(z₀,ω) ∈ {0,1}.

Candidate events include: retry count at or above k; advanced-search depth at or above d; residual unserved passengers above u; frozen-score loss above τ; or a route-board saturation event. The event must be declared before the experiment and captured in a structured record rather than inferred from informal logs.

Empirical calibration (v2.1). Recovered SOX reservation exports for two complete 2017 service days give the late-demand perturbation family a measured anchor: 7-10% of reservations were captured on the service day itself (326 and 270 reservations on 4 and 6 July 2017), and date-level capture resolution bounds demand visibility at the 18:00 planning cut between 31-37% and 90-93%. The declared distribution D for demand-burst and late-arrival perturbations should be fitted to these artifacts rather than assumed; executed route sheets for 1-8 August 2017 additionally supply observed multi-trip and multi-destination structure for event definitions. One matched demand-to-plan day (a SOX export for any date in 1-8 August 2017) remains the highest-value missing artifact.

7.2 Required extraction before quantum compilation

1. Freeze all database inputs into immutable arrays or records.

2. Represent every stochastic perturbation through a finite seed ω.

3. Remove persistence, transactions, external I/O, logging side effects, and non-deterministic iteration.

4. Bound loop counts, memory, numeric precision, and failure modes.

5. Produce a classical side-effect-free function f(z₀,ω)→{0,1} and validate it against the original planner on a frozen test set.

6. Only then estimate reversible gate count, logical qubits, ancilla cleanup, and fault-tolerant overhead.

7.3 Error model

For a rare probability p, additive error ε may be operationally meaningless. A relative-error target η is normally more informative. Under ideal coherent access, classical Monte Carlo requires approximately O(1/(pη²)) samples in the rare-event regime, while amplitude-estimation error bounds motivate O(1/(η√p)) coherent uses up to constants and algorithmic conditions [1–3]. The end-to-end comparison must multiply those query counts by the full kernel and state-preparation costs.

7.4 Classical baselines

• Crude Monte Carlo with exact confidence intervals.

• Importance sampling with a pre-declared proposal family.

• Subset simulation or adaptive multilevel splitting.

• Stratified sampling over time bands, destinations, burst magnitude, or outage duration.

• Surrogate-assisted rare-event estimation, reported separately from exact-simulator methods.

Q3 status. Highest potential operational value and lowest current implementability. Its near-term contribution is a rigorous classical-kernel extraction and fault-tolerant resource estimate, not execution on current hardware.

8. Q4 — Frozen-state QUBO benchmark over the route pool

Q4 is retained because it provides a conventional optimization benchmark and makes the limits of static quantum formulations explicit. It is not an exact mapping of the deployed allocator. xSeil recalculates occupancy, scarcity, and total score as assignments are made, so the deployed reward is S_r(z), not a single immutable coefficient S_r.

8.1 Snapshot route-selection relaxation

Freeze the operational state z=z₀ and compute a static route score S̄_r=S_r(z₀). Let x_r indicate whether route r is selected, A_nr whether route r covers demand group n, u_n an optional unserved-demand slack, and C a set of incompatible route pairs. One benchmark Hamiltonian is:

H = −Σ_r S̄_r x_r + λ_cov Σ_n (1 − u_n − Σ_r A_nr x_r)²

+ λ_conf Σ_(r,r′)∈C x_r x_r′  +  λ_u Σ_n c_n u_n.

This is a static route-selection benchmark. It omits endogenous re-pricing and may omit vehicle identity unless the conflict graph fully captures resource compatibility.

8.2 Fleet-aware alternative

A closer representation uses y_{r,v}=1 when vehicle v executes route r, plus compatibility and temporal-conflict constraints. It is much larger and must represent vehicle type, base, route timing, multi-trip sequencing, and overlap. The note should not claim fleet fidelity while reporting the logical-variable count of the simpler x_r model.

8.3 Penalties and algorithms

A generic condition λ>max|S̄_r| is not sufficient to guarantee feasibility because one violation can enable several profitable selections. Penalty bounds must dominate the maximum objective improvement obtainable through each violation, or a feasibility-preserving mixer/encoding should be used. QAOA is an approximate depth-dependent algorithm [5]; annealing and QAOA have no assumed production-scale advantage here. Q4 must be evaluated through empirical solution quality and time-to-target, not through the estimation frontiers of Section 9.

Q4 status. Useful as a controlled benchmark and negative result. It is lower priority than Q2 and lower potential value than Q3.

9. Corrected economics and formulation-specific frontiers

All costs below must be expressed in a common unit—time, energy, money, or normalized utility—and must include the full coherent subroutine, not only the number of oracle calls. Define B as the total quantum cost per effective oracle use, including state preparation, inverse preparation, reversible evaluation, error correction, and hardware execution. B is formulation-specific.

9.1 Expectation or discrimination frontier

C_c(Δ)=a/Δ², C_q(Δ)=B/Δ.

Equality: Δ_x=a/B. Quantum cost is lower only when Δ<a/B.

This corrected direction is essential: increasing quantum overhead decreases the range in which a quadratic query reduction can be economic.

Utility proportional to the gap

If U(Δ)=cΔ, then U/C_c=cΔ³/a and U/C_q=cΔ²/B; both tend to zero as Δ→0.

When near-degenerate scores imply near-degenerate consequences, increasingly precise ranking becomes uneconomic for both technologies. Abstention, satisficing, or a coarser decision rule may dominate.

Utility floor

Classical viability: Δ ≥ √(a/u₀). Quantum viability: Δ ≥ B/u₀.

Quantum-only interval: B/u₀ ≤ Δ < √(a/u₀), non-empty iff B < √(a u₀).

This is the corrected stakes-versus-overhead condition. It does not prove that xSeil or the regime-origin problem lies in this interval; a, B, and u₀ must be estimated for a defined instance family.

9.2 Rare marked-state search frontier

C_c(p)=a/p, C_q(p)=B/√p, p=M/N.

Quantum cost is lower only when p < (a/B)².

This applies to a witness/existence/counting-style output. It does not include the cost of outputting every marked item or the cost of building a pair index that the quantum routine assumes.

9.3 Rare-event relative-error frontier

Classical: O(1/(pη²)). Ideal amplitude estimation: O(B/(η√p)).

The constants and exact bound depend on the chosen amplitude-estimation method. The dominant Q3 question is whether B—driven by the reversible planner kernel and distribution loading—overwhelms the reduction in the number of event evaluations.

9.4 No generic QUBO frontier

QAOA and annealing are not assigned a universal 1/Δ law. Q4 must report approximation quality, feasibility rate, time to target, embedding or compilation cost, shot count, classical parameter-optimization effort, and end-to-end wall-clock cost against strong classical solvers.

10. Proposed research programme and decision gates

Phase 0 — Define the classical objects

• Freeze the candidate family, uncertainty distributions, xSeil data schemas, and event definitions.

• Build strong classical baselines and measure actual sample cost, variance, rarity, and output requirements.

• Establish anonymized or synthetic instances with reproducible seeds and frozen splits.

Phase 1 — Kernel extraction and reversible accounting

• Q1: implement the bounded evaluator g(c,ω) as a deterministic finite function.

• Q2: specify and prototype duplicate-free pair indexing and the target predicate T.

• Q3: extract and validate f(z₀,ω) from the planner.

• Q4: generate both snapshot and fleet-aware interaction graphs and derive defensible penalty ranges.

• Produce logical qubit, Toffoli/T-count, depth, ancilla, and repeated-query estimates under declared fault-tolerance assumptions.

Phase 2 — Frontier and benchmark paper

• Insert measured classical constants and resource-estimated B values into the separate frontiers of Section 9.

• Report empty and non-empty windows with sensitivity analysis, not a single optimistic point estimate.

• Compare result quality and cost against the named classical rare-event and optimization baselines.

Phase 3 — Hardware experiment only if justified

• Run small, fully reproducible instances whose input loading and classical preprocessing are included in the report.

• Use hardware results to validate resource models, not to extrapolate production advantage without evidence.

11. Publication logic and usefulness to QAVA

The package is useful to QAVA because it provides code-preserved industrial primitives and an open mathematical selection problem that can support rigorous positive or negative results. The strongest first publication is not a claim of quantum advantage. It is an end-to-end taxonomy and resource audit that determines which formulations survive basic scrutiny.

This programme also gives QAVA a valuable falsification role: identifying that an attractive quadratic query result is erased by state preparation or reversible simulation is not a failure of collaboration. It is the result the note is designed to make measurable.

12. Conclusion

The corrected quantum case is narrower than the earlier notes and more valuable. The formal programme supplies an open global candidate-selection problem, but Q1 requires a stochastic score definition before amplitude estimation applies. xSeil supplies code-defined pair relations, dynamic scoring, and stress events, but it does not by itself establish a quantum speedup, a formal market equilibrium, or a basin-separatrix architecture. Q2 is the best first circuit-level study; Q3 is the highest-value long-term formulation; Q4 is a benchmark and control. The immediate joint research question is therefore:

Recommended first joint question. For each concrete task, does the ideal quadratic reduction in oracle uses survive coherent input preparation, reversible evaluation, output requirements, strong classical baselines, and decision utility?

Annex A — xSeil code-evidence register

Repository snapshot reviewed: Xseil-master, dated 2018-04-21 in the supplied archive. Line numbers refer to that snapshot and may shift in later copies.

Provenance addendum (v2.1). A second archive exists: a third-party containerization dated 2023-01-28 (SHA-256 c2de31a8…54edd2 versus 77bc819a…586ce786 for the 2018 snapshot). All files cited in E1-E14 are byte-identical across both archives, so every register entry stands. The 2023 port introduces at least three semantic divergences – a schema-rename defect that breaks calcular_concurrencias at runtime, an exception-propagation change (raise replaced by logging) that alters retry semantics, and a reversed transfer-admissibility inequality in the hotel-transfer builder – and must therefore never be used as the kernel-extraction source for Q3 or as any replay baseline without a defect audit. Its divergences are candidates for the semantic-repair arm of the replay programme.

Selected verbatim excerpts

# Concordance source groups (combinaciones.py:217–223)
SELECT ARRAY_AGG(id_combinacion_id ORDER BY id_combinacion_id) AS combinaciones_concordantes,
       id_parada_id, p.politica_transbordos
FROM xsail_combinacionparadas
JOIN x_cat_puntos_parada p ON p.id = id_parada_id
WHERE orden > 0
GROUP BY id_parada_id, p.politica_transbordos;

# Pair emission and deduplication (crear_combinaciones_concordantes.py:53–82)
for concordancias in list_concordancias:
    for combinacion1, combinacion2 in combinations(concordancias["combinaciones_concordantes"], 2):
        key = (combinacion1, combinacion2)
        obj = self.list_concordancias_pair.get(key) or CombinacionesConcordantesTmp(...)
        obj.paradas_coincidentes.append(concordancias["id_parada_id"])

# Scenario values and nonlinear exponents (calcular_puntuaciones_pickups_pd.py:196–207)
valor_politicas = self.__escenario.valor_politicas
valor_puntualidad = self.__escenario.valor_puntualidad
...
exp_valor_politicas = (valor_politicas / 300) + 1
exp_valor_puntualidad = (valor_puntualidad / 300) + 1

# Dynamic total-score recalculation (planeacion.py:727–731)
row['puntuacion_total_final'] = (row['puntuacion_total']
    + row['puntuacion_directos_final'] + row['puntuacion_aislamiento']
    + row['puntuacion_lleno'] + row['puntuacion_escasez_unidades'])
pickups_franjas.set_value(Index, 'puntuacion_total_final', row['puntuacion_total_final'])

# Feasible route growth and bounded construction (crear_combinaciones_pd.py)
iterator = start_num_paradas
while True:
    obj_len = Combinaciones.objects.filter(num_paradas=iterator).count()
    if obj_len == 0: break
    for offset in range(0, obj_len, BATCH_SIZE_SELECT):
        self.__pool_main.add_task(self.make_combinaciones_by_batch, ...)
    self.__pool_main.wait_completion(); iterator += 1
    if iterator > NUM_PARADAS_COMBINACIONES: break
...
if _fecha_b < _fecha_a: return
if _combinacion.tiempo > self.TIEMPO_MAXIMO_PICKUP: return

Already-materialized sister flags: predicate example, not primary target

are_sister = paradas_c1[:1] == paradas_c2[:1] if are_sister: if base_c1.politica_transbordos == ‘CT’ or base_c2.politica_transbordos == ‘CT’: new.hermanas_ct = True if base_c1.politica_transbordos != ‘CT’ and base_c2.politica_transbordos != ‘CT’: new.hermanas = True new.puntuacion_combinacion1 = new.puntuacion_combinacion2 = 0.8

# Retry and bounded advanced search expose candidate stress events
ret = CONST_REINTENTAR
while ret == CONST_REINTENTAR:
    ...
    for page in range(self.__pargeneral.limite_paginacion_planeacion):
        if page == 1:
            self.logger.warn('Modalidad: busqueda avanzada')
        ...
    ret = self.crear_rutas_by_franjas(...)

# Functional state: admissibility is encoded before optimization
STATUS_MANTTO_CHOICES = (('MNO','No set'), ('MAN','In maintenance'),
                         ('DIA','Up to date'), ('REA','Awaiting reschedule'),
                         ('MPR','Appointment upcoming'))
STATUS_DISPONIBLE_CHOICES = (('DIS','Available for planning'),
                             ('NDI','Not available'), ('PRI','Private service'))

# Rental sizing: a production baseline quantum methods must beat end-to-end
pax_estimated = confirmed_now * historical_final / historical_by_now
units_needed = (pax_estimated * occupancy_factor) / seats_per_unit

# Isolation as a structure-preserving PostgreSQL containment join
WITH q AS (
  SELECT ARRAY_AGG(DAP.id_destino_agrupadores_id) agrupadores, DAP.id_pickup_id
  FROM xsail_PickUpsPlaneacion P
  JOIN xsail_DestinoAgrupadoresPlaneacion DAP ON P.id_pickup_id=DAP.id_pickup_id
  WHERE P.posible_lleno IS TRUE GROUP BY DAP.id_pickup_id)
SELECT A.id_pickup_id, count(*)-1 AS num_concurrencias
FROM q A JOIN q B ON B.agrupadores <@ A.agrupadores
GROUP BY A.id_pickup_id;

# Pacing control: observable event and bounded field directive
track['indice_saturacion_unidades'] = track.num_unidades / track.andenes_max
track['indice_saturacion_pasajeros'] = track.pax_franja / track.pax_max
track['indice'] = (track['indice_saturacion_pasajeros']
                   * track['indice_saturacion_unidades'] * track['indice_franja'])
mask = (track.indice_saturacion_unidades > 1) | (track.indice_saturacion_pasajeros > 1)
...
hoja.status_hruta = INCREMENTAR_VELOCIDAD if row.velocidad == up_speed else DISMINUIR_VELOCIDAD

Annex B — Formal oracle and Hamiltonian interfaces

B1. Q1 candidate expectation

Inputs: candidate c ∈ C finite uncertainty seed ω ∈ Ω with declared distribution D Classical kernel: g(c, ω) -> fixed-precision value in [0,1] Quantum interfaces: A_c |0> -> Σ_ω sqrt(D(ω)) |ω>|0>|workspace> U_g |c>|ω>|0> -> |c>|ω>|enc(g(c,ω))> Output: estimate μ(c)=E[g(c,ω)] to declared error/confidence Required audit: finite precision, reversible cleanup, cost of A_c and A_c†, comparator/ranking policy.

B2. Q2 rare implicit pair search

Inputs: duplicate-free pair index j ∈ {0,…,N-1} pair map pair(j)=(r1,r2) over implicit concordant pairs P target descriptor T Classical kernel: mark_T(r1,r2) -> {0,1} Quantum interfaces: A_P |0> -> (1/sqrt(N)) Σ_j |j>|pair(j)> O_T |j>|pair(j)> -> (-1)^{mark_T(pair(j))}|j>|pair(j)> Permitted outputs: one witness; existence; approximate count; bounded top-k; min/max under score oracle Excluded inference: no automatic advantage for outputting all marked pairs.

B3. Q3 planner-event kernel

Inputs: frozen operational state z0 perturbation seed ω ∈ Ω, ω ~ D Classical extraction: F(z0,ω) -> bounded deterministic planner result f(z0,ω) -> 1 if preregistered event E occurs, else 0 Quantum interfaces: A_D |0> -> Σ_ω sqrt(D(ω)) |ω>|0>|workspace> U_f |z0>|ω>|b> -> |z0>|ω>|b XOR f(z0,ω)> Required audit: equivalence to frozen original planner; loop/memory bounds; fixed precision; ancilla cleanup; no I/O.

B4. Q4 snapshot QUBO

Frozen inputs: static scores Sbar_r=S_r(z0) coverage A_nr conflict set C Variables: x_r ∈ {0,1}; optional slack u_n ∈ {0,1} Hamiltonian: H = -Σ_r Sbar_r x_r + λ_cov Σ_n (1-u_n-Σ_r A_nr x_r)^2 + λ_conf Σ_(r,r’)∈C x_r x_r’ + λ_u Σ_n c_n u_n Status: frozen-state route-selection relaxation; not the exact sequential xSeil allocator.

Annex C — Corrected derivations

C1. Additive-error or score-gap crossover

a/Δ² = B/Δ ⇒ a = BΔ ⇒ Δ_x = a/B.

C_q < C_c ⇔ B/Δ < a/Δ² ⇔ Δ < a/B.

The earlier expression B/a was dimensionally and directionally inconsistent: increasing B would have expanded, rather than reduced, the quantum region.

C2. Utility-floor interval

a/Δ² ≤ u₀ ⇒ Δ ≥ √(a/u₀).

B/Δ ≤ u₀ ⇒ Δ ≥ B/u₀.

Quantum viable while classical is not: B/u₀ ≤ Δ < √(a/u₀).

Non-empty iff B/u₀ < √(a/u₀) ⇔ B < √(a u₀).

C3. Rare-search crossover

B/√p < a/p ⇔ B√p < a ⇔ p < (a/B)².

C4. Relative-error rare probability

For Bernoulli event probability p and relative error η, crude Monte Carlo variance gives an order of 1/(pη²) samples for fixed confidence in the rare-event regime. Standard amplitude-estimation error bounds contain a leading √p/M term; setting this term to ηp gives M of order 1/(η√p), subject to coherent access and constant factors. This ideal comparison is only the query layer.

Annex D — Benchmark and preregistration protocol

Minimum report per formulation

• A complete classical algorithm and measured runtime/sample profile.

• A complete access-model diagram identifying every invocation of A, A†, and the oracle.

• Resource estimates at several logical error rates and a transparent mapping to physical assumptions.

• A break-even plot with uncertainty bands, not one crossover number.

• A decision statement: proceed, remain theoretical, or reject the formulation for the declared instance family.

Annex E — Claim-status ledger

Annex F — Functional-precondition matrix for reproducible instances

Recommended reproducibility package: schema dictionary; anonymized or synthetic instance generator; frozen instance manifests; source-to-kernel equivalence tests; classical baseline implementations; oracle/Hamiltonian specifications; logical resource reports; physical assumptions; and a claim ledger linking every result to the access model actually used.

Annex G — Selected references and source documents

Quantum algorithms and resource framing

[1] G. Brassard, P. Høyer, M. Mosca, A. Tapp. “Quantum Amplitude Amplification and Estimation.” arXiv:quant-ph/0005055. https://arxiv.org/abs/quant-ph/0005055

[2] A. Montanaro. “Quantum speedup of Monte Carlo methods.” Proceedings of the Royal Society A 471 (2015). https://arxiv.org/abs/1504.06987

[3] D. Grinko, J. Gacon, C. Zoufal, S. Woerner. “Iterative quantum amplitude estimation.” npj Quantum Information 7, 52 (2021). https://arxiv.org/abs/1912.05559

[4] T. J. Yoder, G. H. Low, I. L. Chuang. “Fixed-point quantum search with an optimal number of queries.” Physical Review Letters 113, 210501 (2014). https://arxiv.org/abs/1409.3305

[5] E. Farhi, J. Goldstone, S. Gutmann. “A Quantum Approximate Optimization Algorithm.” arXiv:1411.4028. https://arxiv.org/abs/1411.4028

[6] C. Dürr, P. Høyer. “A quantum algorithm for finding the minimum.” arXiv:quant-ph/9607014. https://arxiv.org/abs/quant-ph/9607014

[7] A. Carrera Vazquez, S. Woerner. “Efficient State Preparation for Quantum Amplitude Estimation.” arXiv:2005.07711. https://arxiv.org/abs/2005.07711

[8] R. Srikant. “Quantum Estimation of Delay Tail Probabilities in Scheduling and Load Balancing.” arXiv:2602.09059, 2026. https://arxiv.org/abs/2602.09059

[9] D-Wave Quantum Inc. Advantage2 system release notes and Zephyr topology documentation, accessed July 2026. https://docs.dwavequantum.com/

[10] L. Grover, T. Rudolph. “Creating superpositions that correspond to efficiently integrable probability distributions.” arXiv:quant-ph/0208112. https://arxiv.org/abs/quant-ph/0208112

Internal research and evidence sources reviewed

• Paper I — Large-Scale Multi-Trip Vehicle Routing Under Fully Committed Demand: The xSeil System (2016–2017) and a Decade of Practice, draft v0.3.

• Paper II — Pre-Agentic Orchestration: Closed-Loop Logistics Control Before the Agent Era, draft v0.2. Several claims are corrected by this note.

• Paper III — Candidate Quantum Formulations for a Deployed Large-Scale Routing System, drafts v0.2 and technical v0.3. The economics and formulation boundaries are superseded by this note.

• QAVA Quantum Sketch Note v4. Superseded by this technical version.

• Xseil-master source repository, supplied archive, snapshot dated 2018-04-21.

• Minimalistic Regime-Aware Early Warning Systems: Complete Integrated Version.

• Companion Paper I v2 — Mission-Critical Routing Under Fully Committed Demand: xSeil Architecture and Functional Substrate.

• Paper IV — Functionally Rich, Technologically Minimal, draft v0.2, and Technical Code Annex v1.

• Anexo Técnico 1 (October 2016), contractual component taxonomy and deliverables.

• Recovered operational artifacts (2026): SOX reservation exports for service days 4 and 6 July 2017; executed operation route sheets for 1–8 August 2017; contemporary design-document corpus (62 files); production benchmark workbook. Private; the exports contain personal data and require anonymization before circulation.

• Second repository archive (containerization port), dated 2023-01-28. Provenance and divergence audit in Annex A.

Public programme sources

https://tegrity.ai

https://jubap.net/jubap-net-xseil-whitepaper/

https://jubap.net/case-studies/

https://www.latinoempresa.com/en/post/experiencias-xcaret-xseil-pre-agentic-logistic-intelligence-before-ai-mainstream-by-tegrity-ai

Companion Paper II v2 | July 2026 |