What question did this study set out to answer?

To identify and prove a structural invariant applicable to zero-cost co-production systems across various domains.

April 18, 2026Open Access

C1: A Structural Invariant in Zero-Cost Co-Production Systems

Key Points

To identify and prove a structural invariant applicable to zero-cost co-production systems across various domains.
Identified the gross value multiplier Φ through mathematical proofs.
Validated the model empirically across five domains using hardware and infrastructure combinations.
Proved the Intertemporal Synergy Theorem (IST) regarding net present value growth and cost dynamics.
Demonstrated a canonical value Φ_B = 26.6× with specific energy pricing conditions.
Established conditions A1–A4 that lead to increasing net present value under specific economic conditions.
Quantified the cost of inaction at 339 million euros for a one-year delay in a specific system configuration.

Abstract

This paper identifies and proves a structural invariant — the gross value multiplier Φ = Mₙet/p₀ — that holds across five independent physical domains of zero-cost co-production: hydroelectric curtailment (RAIDE), offshore wind, industrial waste heat recovery, solar curtailment, and geothermal. The canonical value ΦB = 26. 6× (Mₙet = 1, 221 €/MWh, p₀ = 46 €/MWh) emerges from global GPU compute pricing acting against locally stranded energy. Four structural conditions (A1–A4) are identified, and the Intertemporal Synergy Theorem (IST) is proved: any A1–A4 system exhibits Σ (t) > 1 strictly increasing, divergent NPV when shadow-price growth exceeds the discount rate, and strictly convex delay cost. The opportunity momentum coefficient M⁻ (Δt) quantifies the compounding cost of inaction, reaching 339 M€ for a one-year delay at Miranda do Douro (M4 configuration). Empirical validation covers 36 of 38 hardware × infrastructure combinations across five domains (Φₒps ∈ 8. 8×, 27. 0×; Φcan ∈ 11×, 105× at γ = 1), including NVIDIA H100/B200 and RISC-V Tenstorrent hardware. The invariance is demonstrated to be a structural consequence of global bit pricing against local electron stranding, not a feature of any particular technology. This paper is part of the RAIDE series: C1: A Structural Invariant (this paper) — DOI: 10. 5281/zenodo. 19558936 C2: A Four-Axiom Framework — DOI: 10. 5281/zenodo. 19558932 C3: RAIDE Atom — DOI: 10. 5281/zenodo. 19558933 C4: RAIDE Network — DOI: 10. 5281/zenodo. 19559468 C5: RAIDE at National Scale — DOI: 10. 5281/zenodo. 19559402

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Cite This Study

Daniel A. N. Silva (Wed,) studied this question.

synapsesocial.com/papers/69e3205140886becb653f60a https://doi.org/https://doi.org/10.5281/zenodo.19604391

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