PQuant Services Ltd · Research programme · Where the corpus points next
The open research programmes arising from the RiskCircuit / Risk Graph corpus, grouped by field and marked by what each needs before it can be answered.
A theory is worth the questions it leaves open. These are the ones the corpus has earned the right to ask — each with its status stated plainly.
Who
Founder · author of the RiskCircuit corpus
Civil Engineer (École Nationale Polytechnique), MBA, AACE Certified Cost Professional. Thirty years in project controls with Saudi Aramco, RasGas / QatarEnergy, Suncor Energy and Jacobs; graduate teaching at KFUPM. Author of the RiskCircuit corpus and founder of PQuant Services Ltd, Doha.
Publications
Posted for comment and not yet peer-reviewed.
The corpus
The volumes are password-protected. The password is available on request — write to the address below and it will be sent to you.
Canon editions of 28 August 2026. Cite as: Seddiki, B. (2026). [Title]. The RiskCircuit Corpus, Volume N. Doha: PQuant Services Ltd.
Empirical status
The corpus's central dynamical claim — that an activity's cost-performance trajectory follows a second-order response whose damping and natural frequency are fixed by the committed/consumed split of its budget — is being tested against real project records.
On the Ghent DSLIB library (231 projects, v3.4), the activity-level prediction cannot be resolved: only 19 of 1,681 cost-split activities have five or more in-progress observations, and on the fifteen that can be tested the predicted overshoot is not observed. At project level (10 usable projects) the predicted natural frequency ranks projects correctly but the predicted damping does not.
A replication on an independent Australian civil-construction dataset (Thiele et al., 2021) is under way, and further data are being sought. The report and its scripts are available on request.
The graph-theoretic and earned-value layers of the corpus do not depend on this result; the utility-theoretic derivation of damping does, and will be revised if the finding holds.
The programme
The programme below lists open and completed questions arising from the corpus, for readers who know it; the header above is the summary.
The corpus set out a formal account of project risk as a coupled dynamical system — activities as nodes, shared commitments and shared calendars as the couplings, precedence as the transport, the cost and schedule distortions as the state — and then tested on the public datasets that can carry it, with results summarised above.
That testing settled some things and opened many more, and along the way it borrowed instruments from circuit theory, control, spectral graph theory and dynamical systems that had never been pointed at a project register before. What follows is the research programme that results, grouped by field. Within each group the order is by maturity.
The programme below is stated in the corpus's own vocabulary. Five terms recur; the rest of the shorthand — the fit-out, the D-series, the ruled convention — names particular registers, experiment series and conventions defined in the volumes.
Realised overruns are organised by which activities share the calendar — shown on five hundred time-tracking projects and on the largest real register available, and surviving the size confound that killed its first version. Open: whether the effect varies by industry and project size; whether it is binary in the shared window, as two independent tests suggest, or graded; and whether the field's graph-smoothness is visible at the halfway point, which would turn a post-mortem into a monitoring signal. The deliverable is a calibrated prior for the correlation the schedule-risk upgrade needs.
Walk-forward backtests found the per-task distortion field forecasts failure at the halfway point and the register's geometry adds nothing on top. Next: which field statistics carry the forecast, at what horizon, and whether a graph network with the register as its known weights beats a plain model on the field — the corpus predicts it cannot, because the learnable component is the graph-smooth tide and the alarms live in the rough band. A field-baseline-versus-geometry comparison settles what the application should compute.
Two corpora agree that a quarter to a half of activities finish exactly on plan, that a project tool's "fixed cost" is a data-entry category rather than an economic one, and that four registers in five never record the committed/consumed split at all. The behavioural study of when these artefacts appear and what they do to every downstream statistic has not been written, and its findings are what a recording standard should be designed around.
The corpus derives an activity's duration from its committed-to-consumed ratio and the settling-time identity. On thirty-six real projects the asserted duration is negatively correlated with that ratio and no project agrees with the law; the mechanism is that consumed cost rises faster with duration than committed cost does. Either planners disagree with the model systematically, or the law's direction is backwards — the fork is open and volume-level. Beside it sits the empirical transducer found in the data, duration premium proportional to cost distortion with a project constant near two-thirds, whose provenance is unknown. Both need a register whose consumed cost is recorded from effort rather than derived from the plan.
The central untested claim. The one real test dissolved into calendar overlap; the semi-synthetic study showed the mechanism is not identifiable on any public register structure even when present, becoming visible only with many small committed lines of unequal weight, across roughly a dozen projects. The question is now exactly posed and its data requirement exactly stated.
The common-mode coefficient was estimated at 0.58 with an interval excluding zero and could not be certified: second moments cannot identify direction. An event-based estimator using single-mover periods and dated events restores attribution and is calibrated synthetically; it needs the event log and status transitions the Standard asks for.
The identification of committed and calendar couplings jointly, y = (I + αFEF + ατEτ)δ, is specified with disjoint supports giving edge-domain identifiability, and the deconvolution θ̂ = (I − K)ε is unlocked. Both wait on concurrent contention; both can first be validated in the semi-synthetic harness, which is the immediately runnable part.
Under an honest ledger the consumed-channel radius is unity by theorem, so the exposure closure does not exist there; every published consumed-channel figure owed its margin to a double count. What constitutes private consumed cost on a register where all labour is pooled is an open ruling with consequences for every V-channel result, and the crew-sharing test that found the consumed channel to be a scheduler rather than a conduit was underpowered.
Tellegen's theorem holds on the register at machine precision, including the strong form across two different sets of element values on one topology. Two of the three energy ledgers are state functions auditable from balance-sheet snapshots; the settlement ledger — the only money actually spent — is path-dependent and must be metered along the trajectory. Open: closure as a structural audit of a register independent of every estimate; whether a shared budget line (contingency across activities) should put off-diagonals in the stiffness operator, a coupling channel never modelled.
Two dual representations exist — activity as branch with resources as nodes, or activity as mesh with resources as shared branches — related by Kron reduction: the pool-clique assembly is the star–mesh transform of the interface graph, the fundamental cut-sets are the resource pools exactly, and coupling is rhythm-dependent because L(ω) = A Y(ω) Aᵀ routes slow disturbances through the committed channel and fast ones through the budget channel. The multi-pool activity, the shunt branch for resources that stand idle, and the mesh–interface dictionary need one consolidated treatment.
A passive register makes Blackman's formula trivial; a management policy is the dependent source that makes it bite, and the two theorems are one Sherman–Morrison identity distinguished only by symmetry of the update. Verified to machine precision on three registers, they gave four results the corpus did not have: the firewall proved rather than assumed; a closed-form null condition explaining why some pools cannot move the radius at all; the finding that raising a pool's scalar is a rank n − 1 update, so the scalar extra-element theorem is wrong by up to eighty per cent and Woodbury is required; and a degeneracy of the ratio form exactly when an element creates a path that did not exist. Open: the MIMO return-ratio generalisation for policies acting on several activities; cross-transfers, which are Middlebrook's territory; the units of the policy gain; and the redistribution identity that gives the whole velocity vector under a policy from two vectors, which belongs in the engine.
With the sanction identity X = F + V every uncoupled activity pole lies on the circle |s + 1| = √2; overdamped pairs obey a product rule about it; assembly does not preserve the identity unless the budget line is assembled too, in which case the slow modes disappear. The schedule axis has no locus — its pole is a repeated real root — and the circle fixes the schedule-to-cost conversion V/X = ρ/(1+ρ), which yields the trade nobody had stated: an activity designed to settle fast is maximally exposed to slip. Which convention is canon, and what the locus implies for pole placement, are open.
The shared-activity push rule, the series-EMF trap, the two-rail rule and the Wheatstone configuration the roofing bridge creates are documented on the fit-out; the zeros of the register transfer function have never been computed, and the graph reading of them via Schur complements is the open item.
On the two-axis register the schedule block has twelve distinct poles for thirty states because durations repeat; a single input can never separate identical modes. Observability is cheap — per-activity SPI gives full rank, aggregate SPI a third — but controllability needs five independent effort channels, more coupling does not help, and even at full rank the delay margin against real reporting latency is two weeks against four to eight. The decision rule that fell out — concentrate recovery effort on one of two slipping activities sharing a resource, because their combined response is differential — is a testable prescription. The programme is the control-authority audit made general: which levers move which poles on which registers.
The two-axis system is block-triangular with both blocks Hurwitz, so stability is guaranteed by construction and a certificate is vacuous; what is not guaranteed is the transient — max‖eAt‖ = 2.48 at week 4.45 on the fit-out, manufactured by resource coupling feeding the schedule-to-cost path, in a direction that names the same activity pair three independent methods named. Whether transient amplification predicts where real projects overshoot is an empirical question on any register with per-activity tracking.
Gating makes the register a switched system; a common quadratic Lyapunov function across the planned modes certifies arbitrary switching where it exists, and the closed-loop no-runaway proof depends on it. Where re-allocation is periodic, frozen-time spectra do not determine stability: a register healthy in every snapshot goes unstable under resource rotation near twice a modal frequency, after a transient that makes early reports look better than ever, with the re-allocation term as the pump in the energy law. The fit-out is parametrically safe by a factor of four; the hazard profile is lightly damped modes under two-to-five-week rotation. Believed novel in the project-controls literature; the paper is queued.
Three regimes need three toolkits — slow variation permits frozen tracking of connectivity and radius, piecewise-constant variation is switched-system theory, periodic variation demands Floquet — and the channel matters: falling connectivity on the committed channel is relief, on the consumed channel fragility. Quantifying "slow" against modal periods on real registers, and stating the fractional-gate extension, are open.
The activity algebra of the first volume is the network algebra of the third at one eigenvalue — θ ↔ K, ε = θ/(1−θ) ↔ E = K(I−K)⁻¹, the geometric series ↔ the hop expansion — so every activity identity lifts by functional calculus. The (ε, ε̇) phase-plane treatment, the γ-absorption result that risk appetite acts on the activity and not on a channel, and the free-decay test that separates the three readings of ψ are consequences awaiting a consolidated derivation.
A constitutive law φ from distortion to slip closes the loop between the cost state and the gate; the hybrid system, the no-runaway condition and the dwell-feedback gain are drafted. Whether real slip obeys any such law is the same question as the transducer of §1.4.
Amplification lives with the Perron vector of the coupling operator, the chokepoint with the Fiedler vector of its Laplacian, and on real registers they rank differently — sometimes sharing none of the top five. Which a manager should act on, the dwell-ratio severity proposals, the observation that a levelled plan forces the live graph into a matching so the Fiedler apparatus earns its place only as-built, and the requirement that gating re-assemble rather than mask, are all testable on DSLIB's as-built traces.
Decomposing the tracking film into modes and reading each against the graph Fourier basis gave a law and a correspondence: increments are graph-rough while the accumulated field is graph-smooth — risk arrives privately and accumulates collectively — and a mode's persistence in time anti-correlates with its graph-frequency centroid. The standing field also grows genuinely rougher than chance as a project ages, mechanism unknown. Open: the mechanism of that fossilisation; DMD on more than one real film; whether the burn-down clock being the calendar mode generalises; and the monitoring consequence that low-pass learners are structurally blind to the alarm band.
Only the binding pool moves the radius; splitting pools into their concurrent groups lowers it at no cost; below that floor spend is effective only until it ties the next block. But the damping convention ruling reversed the free lever's damping benefit into a trade-off, because splitting removes shared dissipation as well as shared inertia. The general co-liveness rule, the tie rule and the η-versus-damping trade need re-derivation under the ruled convention before they are procedure.
Hong's bound transfers as a weighted Frobenius audit, tight on near-regular cliques and useless on paths; Hamiltonian and Eulerian structure fits the interface audit and little else; the weighted Laplacian family with F, V and X as three non-blendable weightings closes under the dynamics through the generalised and quadratic eigenproblems. A min-degree refinement of the bound and a formal statement of the family are open.
The register is itself a graph-convolution operator with measured self-loops; the corpus's position is that a learned network should be initialised at it and judged against it, and that if a learned coupling beats the operator the physics is missing something. The known-weight comparison on the field-level tasks that survived the D-series is the experiment.
State-dependent coupling, where a pool's coupling strengthens as its members drift, with its energy consequences and a free-decay discriminating test; and the management-reserve extension X = F + V + x₀ with its reserve-fraction law and an open modelling fork. Each has a candidate law and needs the pilot register.
The semi-synthetic study showed a Ford–Sterman rework loop is cleanly separable from every corpus mechanism by a within-activity signature. Running the adjudication blind on real films — which world does a real project resemble — is the sharpest external test available and a direct engagement with the system-dynamics literature the prior-art audit positioned against.
Sensing at one activity and acting at another, the firewall, the de-crowding prescription, the concentration rule: correct as algebra, unreachable by observation. A designed comparison within a portfolio or a forensic reconstruction of interventions actually taken is the only route, and the second connects to the dispute practice.
Risk tolerance as energy in a Schrödinger-type equation with distortion as position, the three tolerance regimes as bound states. A formal proposal with no empirical content; worth a paper, presented as such.
Draws correlated by co-liveness through exact CPM; merge bias dominated the one register piloted and yielded a triage rule — sparse registers are merge-bias-dominant, dense ones earn the correlation. Validating the triage across register types and benchmarking against commercial simulators is applied research.
As-built critical-path reconstruction from tracking data, the discovery that a real baseline was resource-levelled invisibly in the logic, and the question of which analysis method a register's structure favours in a dispute. Each engagement is also a Standard-recorded register.
The asset nobody else has: projects recorded with the cost split, the pooled lines at the granularity contention needs, the events and the cadence. Designing the Standard to be cheap to comply with, publishing it as a citable versioned document, and assembling the corpus through pilots and engagements is a programme in itself, and the benchmarks it yields are the durable output.
Table 1
| Field | Runnable now | Pilot-blocked | Theory / speculative |
|---|---|---|---|
| 1 · Empirical laws | co-exposure at scale; field vs geometry; recording artefacts | duration law and transducer | — |
| 2 · Register circuit | estimators in the harness | contention; attribution; two-channel identification | private consumed cost |
| 3 · Circuit theory | nodal/mesh zeros; premium-balance audit | — | interface representation; Blackman/EET MIMO; sanction locus |
| 4 · Control and dynamics | transient amplification; Floquet on real cadences | — | control authority; switched and time-varying registers; state space; closed loop |
| 5 · Spectral and modes | two bottlenecks as-built; DMD on real films; known-weight networks | — | optimisation under the ruled convention; bounds and the weighted family |
| 6 · Extensions and rivals | — | rework adjudication; interventions | nonlinear register; quantum attitudes (speculative) |
| 7 · Applied | SRA triage; forensic ABCP | — | the Standard and the corpus (building) |
"Pilot-blocked" means fully specified and waiting only on a register recorded to the Standard; the number of projects each such question needs comes from the semi-synthetic power study.
Contact
Data received from partners is used for research only, is not redistributed or incorporated into commercial products, is stored on PQuant systems with access limited to the named researchers, and is cited to its source in every output.
Derived tables and results are shared with the data owner before publication; acknowledgement or co-authorship is offered as the owner prefers. A written data-use agreement is available on request.
