Separability falsification — is one IBM job really one quantum system?

The primary architecture claim for QPC: when K objective contextures run coupled in one circuit, the measurement statistics show cross-context correlation that K independent IBM jobs cannot reproduce. This page explains the task, the math in plain terms, and every IBM Fez result from June 2026.

Plain English

What this test is: Separability falsification — compare one coupled IBM job (transjunctions ON) against the same objectives run as independent jobs (transjunctions OFF).
Why we did it: An external AI review challenged whether “QPC” was just stacked layers or true parallel contextures. ICC is the proposed falsification: joint structure only the coupled arm can show.
What QPC computed: ICC (inter-context correlation) from raw shot counts at each context boundary — same readout pipeline on both arms; only wiring differs.
Headline result: Toy instance 3/3 pass (gaps 0.052–0.106) · Cerrado real data gap 0.088 · part of JSC levels L1–L3 with public job IDs.
What we claim — and do not: Claim: coupled runs show measurable joint structure on IBM Fez. Do not claim: ICC formula is public IP — verification is via our published job IDs and outcome tables.

The task (no jargon)

Build a quantum circuit with three objective blocks (e.g. carbon, biodiversity, social).
Coupled arm: connect blocks with transjunction gates → submit one job to IBM.
Control arm: run each block alone (no transjunctions) → submit three jobs, then pair samples as if they were independent.
Ask: does the coupled run show extra correlation between adjacent objectives that the control cannot match?

If yes → QPC is doing something quantum-joint, not “three cloud jobs + Python merge.”

This test does not ask who got the best portfolio score. Optimization is a separate benchmark.

How we score separability

We compare coupled (one IBM job, transjunctions on) vs separable control (independent jobs, samples paired as if uncoupled). A proprietary inter-context correlation (ICC) witness is computed from shot statistics on aligned decision qubits at each context boundary. Both arms use identical readout and post-processing — only coupling differs.

Public pass criteria (outcomes only)

Coupled ICC materially exceeds separable control on the same backend
ICC gap meets pre-registered thresholds on toy and Cerrado instances
At full Heron width: per-boundary reporting when mean gap is below pilot threshold

Exact ICC formula, readout schedule, and morphogram depth are proprietary. Independent verification uses published IBM job IDs below.

Toy soft-objective instance (15Q coupled, ibm_fez)

Synthetic three-contexture instance — fixed seeds for reproducibility. 4096 shots each.

Seed	ICC gap	Coupled ICC	Pass	Coupled job ID
7	0.106	0.114	✓	`d8i3vdtv8cos73f549cg`
11	0.052	0.062	✓ (rerun)	`d8i429dv8cos73f54e60`
42	0.104	0.112	✓	`d8i3vu66983c73drmk10`

Strong pass: 3/3 seeds.

Cerrado real data (Goiás carbon portfolio)

Same open dataset as Ribeiro 2026 (arXiv:2602.09047). Three objective contextures in one 156Q Heron layout when noted.

Instance	Layout	Depth	Mean ICC gap	Verdict	Job ID
n=8, k=3	shared	~500	0.088	Pass	`d8i4065v8cos73f54a8g`
n=12, k=4	shared	474	0.088	Pass	`d8i42ic2upec739loi50`
n=28, k=7	full width	1883	0.025	Mean fail	`d8i43g42upec739loja0`
n=28, k=7	full width	1329	0.031	Heron pass*	`d8i44rc2upec739loktg`

*Heron pass = per-boundary, not mean:

Transjunction boundary	Coupled ICC	Separable ICC	Gap	Per-boundary pass
carbon ↔ biodiversity	0.005	0.010	−0.005	✗
biodiversity ↔ social	0.110	0.012	0.098	✓
social ↔ carbon	0.003	0.001	0.001	✗

Honest read at full Heron width: NISQ depth washes two of three boundaries; the biodiversity↔social bridge still shows strong non-separability. More shots did not help (8192-shot gap 0.010).

What this demonstrates (value for reviewers)

Falsifiable architecture claim with IBM job IDs, not simulation-only.
Separates architecture from optimization — you can pass ICC and still score near greedy; both numbers are reported.
Independent review loop — external AI challenge → corrected parallel definition → proposed test → we ran it.
Negative results included — mean ICC at n=28, readout boost failure, Antenna closed (see architecture program page).