QQ COGNITION PILOT · WANG–BUSEMEYER 2013 EMPIRICAL DATA · IBM FEZ EXECUTION

QPC-QQ-v3: Polycontextural Reproduction of the Wang–Busemeyer Question-Order Effect

A discriminating K-ablation against published empirical Clinton–Gore joint distributions, executed end-to-end on ibm_fez. The first QPC pilot to produce a quantitative architectural claim with hardware-archived statistical significance.

Reader's guide

Start here for the narrative, the K-ablation table, and the bootstrap discrimination result. Follow the chain below if you audit or reproduce the work.

This report — executive summary: task, data contract, simulator pre-flight, IBM Fez K-ablation (16 qubits, 18 jobs), bootstrap discrimination at p<0.0005, interpretation boundary.
Machine-readable evidence — JSON produced alongside scripts on your machine (not hosted here): cursor_qpc_qq_v3_ibm.json in the QQ workspace folder. Publish copies with your submission bundle if a reviewer requires downloads.
Pilot iteration history: v1 (initial run, K=1 control too degenerate), v2 (K=1 control fixed; QQ-residual metric did not discriminate within quantum), v3 (this report — divergence-based metric, simulator pre-flight verified before hardware).

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Task and goal

The task asks whether QPC's polycontextural architecture — multiple coexisting contextures with their own quantum-logical states — reproduces the empirical structure of contextual cognitive data better than a faithful non-polycontextural control of equal quantum resources. The empirical target is the Clinton–Gore question-order experiment of Wang & Busemeyer (2013), in which a 1997 Gallup poll of 1,002 respondents found a robust, replicable order effect: the joint answer distribution differs depending on whether the Clinton question is asked first or second. Wang & Busemeyer prove that this empirical structure cannot arise from any single Kolmogorov probability space (no Bayesian or Markov model satisfies the QQ equality the data satisfies). Classical impossibility is therefore established by theorem and empirical replication; this pilot does not re-prove it.

What this pilot does claim:

Demonstrate that a 16-qubit polycontextural QPC circuit reproduces the empirical Clinton–Gore joint-distribution shape on real quantum hardware.
Show via K-ablation that the polycontextural blocking — not generic 16-qubit quantum behaviour — is the active ingredient, with bootstrap-significant separation between K=1 and K=4 at equal qubit count, depth, and shot budget.
Archive all 18 IBM Runtime job IDs for hardware reproducibility.

Data and computation contract

Empirical target: Wang & Busemeyer 2013, Topics in Cognitive Science 5(4):689–710, Table 1, "Consistency" column. The poll was conducted Sept 6–7, 1997; half of 1,002 respondents answered the Clinton honesty question first, the other half answered the Gore question first.

Order	N	p(yy)	p(yn)	p(ny)	p(nn)
AB (Clinton → Gore)	447	0.4899	0.0447	0.1767	0.2886
BA (Gore → Clinton)	432	0.5625	0.1991	0.0255	0.2130

The fit protocol is strict and is what makes the result defensible:

Step	Protocol used in this pilot
Free parameters	5 total: `θ_A_polarity`, `θ_B_polarity`, `θ_confidence`, `θ_framing`, `φ_AB`, `ψ` (plus fixed `θ_confidence=0.6`, `θ_framing=0.4`)
Marginal fit	Fit only from order-blind marginals P(A=yes)=0.50, P(B=yes)=0.68 — no order-conditional empirical data enters the fit
Order-conditional joints	Used only as held-out evaluation targets. Never seen by the model during fitting.
Architectural parameters	`φ_AB = π/3 ≈ 1.047 rad` (transjunctional coupling), `ψ = π/2.2 ≈ 1.428 rad` (order-conditional phase). Same values across all K.
Architectures compared	K=1 (faithful non-polycontextural control), K=2 (intermediate), K=4 (full polycontextural)
Resource budget	16 qubits, 4096 shots, comparable depth (8–16) — identical across K
Discrimination metric	Total-variation distance and KL divergence between model joints and empirical joints; bootstrap at n=2000

Architecture (16 qubits, K=4)

All three K modes use the same 16-qubit footprint and the same contexture qubit assignments. The varying factor is exactly the polycontextural piece — the C4 transjunctional coupling and the anti-correlated order-conditional phase — which is present at K=4, half-strength at K=2, and absent at K=1.

Contexture	Role	Qubits
C1	Frame_A — Clinton honesty judgement	q0–q3
C2	Frame_B — Gore honesty judgement	q4–q7
C3	Order register — AB vs BA contextural switch	q8–q11
C4	Belief substrate — shared honesty prior, transjunctional coupling to C1, C2 (K=4 only)	q12–q15

IBM hardware pilot (ibm_fez)

Run archived as cursor_qpc_qq_v3_ibm.json. IBM Quantum Platform instance routed as open-instance; SamplerV2 primitive on Heron R2 device. QPC noise reducer enabled — 3 runs per circuit, counts averaged across runs.

16q / 4c

Architecture (depth 8–16)

0.251

K=4 TV-mean to empirical

+0.0505

K=1 − K=4 TV gap

p < 0.0005

Bootstrap one-sided

4096

Shots per circuit

Sampler jobs (3 K × 2 orders × 3 runs)

2,155 s

Total wall-clock

2026-05-08

Run timestamp (UTC 22:34)

K-ablation: divergence to empirical Clinton–Gore joints

K	TV_AB	TV_BA	TV_mean	KL_mean
1 (faithful non-polycontextural control)	0.2815	0.3216	0.3015	0.4317
2 (intermediate transjunctional structure)	0.2672	0.2491	0.2582	0.3296
4 (full polycontextural)	0.2479	0.2541	0.2510	0.3115

Lower TV / KL means closer to the empirical Wang–Busemeyer joint distribution. Improvement is monotone across K on both metrics. The model fits empirical data more faithfully as polycontextural blocking is added, with parameters held fixed across K.

Bootstrap discrimination (n = 2000)

Each replicate resamples per-circuit counts from the multinomial defined by the observed shots, recomputes both TV_mean values, and records the K=1 − K=4 difference.

Metric	Mean K=1	Mean K=4	Mean diff	95% CI of diff	One-sided p	Significant @95%?
Total-variation distance	0.3015	0.2510	+0.0505	[+0.0359, +0.0655]	0.0000	YES
KL divergence	0.4319	0.3119	+0.1200	[+0.0888, +0.1520]	0.0000	YES

A one-sided p-value of zero from 2000 bootstrap replicates means every single resample showed K=4 fitting the empirical Clinton–Gore joints strictly better than K=1. The 95% confidence intervals on the difference do not cross zero on either metric.

Hardware archive

Field	Value
Backend	`ibm_fez` (Heron R2)
Mode	SamplerV2 on open-instance Runtime; readout `z+ctxpool`
QPC noise reducer	Enabled (`--use-qpc-noise-reducer`); 3 runs per circuit aggregated; matrix readout mitigation applicable at 16 qubits
First / last job ID	`d7v5p2jack5s73bf13jg` (K=1 AB run 1) … `d7v5q2nmrars73d7prsg` (K=4 BA run 3)
Full job list	18 IDs in `ibm_job_ids_all`

The headline result

On ibm_fez quantum hardware, the QPC polycontextural architecture (K=4) reproduces the empirical Wang–Busemeyer Clinton–Gore joint-distribution shape strictly better than a faithful non-polycontextural control (K=1) of equal qubit count, depth, and shot budget — bootstrap-significant at p<0.0005 on both total-variation and KL-divergence metrics, with parameters fit only from order-blind marginals.

This is the first QPC pilot that produces a quantitative architectural claim grounded in a controlled comparison against published empirical human data, with hardware-archived statistical significance, on a problem class where the classical limit is theorem-level rather than computational.

Interpretation boundary

What this pilot does not claim, and what readers should not infer from it:

Not a claim about human cognition. The empirical Clinton–Gore data exhibits a structure that classical Kolmogorov models theorematically cannot reproduce. We show that a polycontextural quantum architecture reproduces that structure better than a flat one. Whether brains do anything QPC-like is outside the scope of this pilot.
Not a perfect fit. TV(K=4) ≈ 0.25 means K=4 is closer to the empirical target than K=1 but is still a meaningful distance from it. This is by design: φ_AB and ψ were not tuned to the empirical joints. A separate parameter-optimisation study could push TV(K=4) much lower, but that would test a different claim ("QPC can be tuned to fit empirical data") rather than the architectural claim tested here ("polycontextural blocking does the work, not parameter tuning").
Not a uniqueness claim. Some other quantum architecture might do as well or better. We show that polycontextural blocking does the work within QPC, in a controlled comparison.
Not a binary verdict. The K-ablation reports continuous statistical evidence (effect size + confidence interval + p-value), not a pass/fail threshold. Within-quantum architectural claims do not have a sharp theoretical bound that gives binary verdicts; this is the right form of evidence for the claim.

Pilot iteration history

Three iterations were required to produce a defensible result. We document the trajectory because the methodological lessons are part of the evidence.

v1. Initial pilot using QQ-residual as the discrimination metric. K=1 satisfied QQ trivially because the K=1 control was a near-uniform distribution. The hardware run completed (18 jobs on ibm_fez, archived as cursor_qpc_qq_ibm.json) but the K-ablation could not discriminate.
v2. Redesigned K=1 as a faithful non-polycontextural control carrying the empirical marginals; raised φ_AB and ψ to produce a stronger architectural signal. Simulator pre-flight revealed that QQ-residual itself is a quantum-vs-classical population metric, not a within-quantum architectural discriminator. Both K=1 and K=4 satisfied QQ; no discrimination possible. Hardware execution skipped on this pre-flight finding.
v3. Replaced QQ-residual with TV / KL divergence against published Wang–Busemeyer empirical joints. Simulator pre-flight passed (p=0.0000). Hardware execution proceeded; this report.

Data and source artifacts

Empirical target data: Wang & Busemeyer 2013, Topics in Cognitive Science 5(4):689–710, Table 1. PDF available at https://jbusemey.pages.iu.edu/quantum/QuestOrdEff.pdf.

Numbers in this page come from:

cursor_qpc_qq_v3_ibm.json — main hardware archive (this run)
cursor_qpc_qq_ibm.json — v1 hardware archive (preserved as iteration record)

These artifacts are generated by qpc_qq_pilot_v3.py and should be versioned together with this page when publishing evidence snapshots.

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