hequ.ai/ discovery
AI Review Board

Three minds,
one verdict.

Claude Opus 4.6 · OpenAI GPT-5 · Gemini 2.5 Pro vote independently on every candidate. Unanimous APPROVE promotes to PROVED; any REJECT demotes.

Records produced this run: 13 Board members: Claude Opus 4.6 · OpenAI GPT-5 · Gemini 2.5 Pro

Board verdicts were collected via the protocol in framework/ai_review_board.py §12. Every vote appears verbatim in the ledger; the Markdown below is a human-readable digest.

Outcome: **PROVED** (1)

`EQ-NEWTON-II` ↔ `EQ-WORK-ENERGY` — `m` ↔ `m`

Board rationale: Unanimous APPROVE from the AI review board.
claude-opus-4-6: approve — The coupling identifies the inertial mass parameter m in Newton's second law (F = ma) with the same inertial mass m appearing in the work-energy theorem (W = ½mv_f² − ½mv_i²). Both semantic descriptors specify the identical QUDT quantity kind (Mass), the same object of interest (rigid body), the same context (inertial frame), and no additional constraints, connected via an identity transfer function. This is a textbook-level tier-1 equivalence: the work-energy theorem is derived directly from Newton's second law by integrating F·ds along a path, so the mass parameter is literally the same physical quantity in both equations. The physical-constraint filter returning all not_applicable is expected, since mass is a scalar parameter rather than a bond-graph port variable, and neither equation is a linear transport law. The emergent Buckingham π groups are dimensionally consistent: F⁻¹·a·m is trivially unity by F=ma, while the groups involving v_f and v_i reflect the nondimensionalization of velocities against (F/a)^(1/2) · W^(-1/2), which is physically sensible. No spurious emergent properties are claimed. This is a well-justified, physically correct coupling.
openai-gpt-5: approve — The variables represent the same physical quantity (the rigid body’s inertial mass) in both Newton’s second law and the work–energy theorem within an inertial frame, so an identity mapping at tier-1 equivalence is appropriate. The physical-constraint checks are correctly marked not applicable because mass is a parameter, not an effort/flow variable, and this does not indicate any inconsistency. The listed dimensionless groups are reasonable (duplication aside) and do not suggest spurious emergent behavior. Overall, the coupling is physically plausible and semantically sound.
gemini-2.5-pro: approve — The proposed coupling is physically fundamental, as the work-energy theorem is a direct integral consequence of Newton's second law. The inertial mass 'm' is definitionally identical in both equations when applied to the same rigid body. The semantic descriptors correctly and identically capture this context. The physical constraint filter's inability to provide a positive verdict is a reflection of its current limited scope, not a flaw in the proposed coupling, as this relationship does not fit the specific forms (e.g., transport laws, bond graph ports) that the available automated checks are designed to analyze.

Outcome: **REJECTED** (12)

`EQ-FICK-DIFFUSION` ↔ `EQ-FOURIER-HEAT` — `D` ↔ `k`

Board rationale: 1 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: approve — The coupling correctly identifies the well-known structural analogy between Fick's law of diffusion (J = -D ∇C) and Fourier's law of heat conduction (q = -k ∇T). Both are linear, first-order transport laws of identical mathematical form, and the mapping D ↔ k under variable renaming is the canonical textbook analogy. The semantic descriptors honestly label distinct but structurally analogous quantities (diffusion coefficient vs. thermal conductivity) rather than claiming they are the same physical quantity; the transfer function is 'identity' in the sense of structural role equivalence, not dimensional equality, which is consistent with the dimensional mismatch correctly noted in the Tellegen check. The Onsager reciprocity check appropriately passes for a 1×1 trivially symmetric transport coefficient. The Buckingham π groups are dimensionally consistent within each domain. No spurious emergent properties are claimed. This is a legitimate tier-2 structural similarity coupling that reflects genuine physics (irreversible thermodynamic transport phenomena sharing the same linear-response framework).
openai-gpt-5: reject — D (mass diffusion coefficient) and k (thermal conductivity) are distinct transport coefficients with different physical dimensions and meanings; equating them via an identity map is not physically plausible. The semantic descriptors refer to DiffusionCoefficient vs ThermalConductivity, not the same quantity nor a named transform; the correct cross-domain analogue for Fick’s/heat equations is D ↔ thermal diffusivity α = k/(ρ c_p), not k itself. The physical-constraint filter’s Onsager pass is trivial and does not address the dimensional mismatch (indeed dim_a ≠ dim_b appears in the evidence), so it does not validate the proposed identity. The listed π groups are tautologies of the constitutive laws, not genuine emergent properties. Therefore the coupling should be rejected.
gemini-2.5-pro: approve — The proposal correctly identifies the canonical mathematical analogy between Fick's law of diffusion and Fourier's law of heat conduction, a classic and valid example of a cross-domain structural similarity. While the 'identity' transfer function is physically invalid due to the dimensional mismatch between the diffusion coefficient (D) and thermal conductivity (k), the discovery of this isomorphism is valuable for the ledger. The physical constraint filter correctly passes the relevant checks for such linear transport laws and its evidence logs the dimensional inequality, providing the necessary context for this Tier 2 similarity coupling.

`EQ-FICK-DIFFUSION` ↔ `EQ-FOURIER-HEAT` — `J` ↔ `q`

Board rationale: 1 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: approve — This is a well-known and physically legitimate structural analogy between Fick's law of diffusion (J = -D ∇C) and Fourier's law of heat conduction (q = -k ∇T). Both are linear, first-order transport laws of identical mathematical form, and the coupling correctly identifies J (molar flux) and q (heat flux density) as the analogous flow variables in their respective bond-graph representations. The semantic descriptors are honest: they do not claim dimensional equality but rather structural correspondence, and the Tellegen pairing check correctly notes that dimensions differ while accepting the analogy at the structural level. The Onsager reciprocity check is trivially satisfied for single-flux laws. The transfer function is listed as 'identity,' which is appropriate for a structural (syntactic) mapping rather than a numerical one, and the sieve reason explicitly states this is a rename-level bijection. The Buckingham pi groups are the standard dimensionless forms of each law. No spurious emergent properties are claimed. The only caveat — that any downstream numerical coupling must supply a transducer coefficient — is properly noted in the evidence. This is a textbook example of a valid cross-domain transport analogy.
openai-gpt-5: reject — While Fick’s and Fourier’s laws are structurally isomorphic, J (molar flux) and q (heat-flux density) are distinct quantities with incompatible dimensions; equating them via an identity transfer function is not physically meaningful. The filter’s flow–flow pass only supports a structural analogy, not numerical identity, and a valid cross-domain link would require an explicit, unit-bearing transduction (e.g., enthalpy-per-mole relating convected heat to mass flux, or named Soret/Dufour cross-coefficients). The reported π-groups are tautologies of the base laws, not genuine emergent properties. Hence the proposed identity coupling is not acceptable for the ledger.
gemini-2.5-pro: approve — The proposed coupling represents a classic, physically sound analogy between heat and mass transport, as both are governed by structurally identical linear flux-gradient laws. The semantic descriptors are accurate, correctly identifying the distinct physical nature of molar flux and heat flux density. The physical constraint filter's assessment is robust, appropriately treating the coupling as a structural analogy (akin to a bond-graph flow-flow pairing) and correctly verifying the Onsager symmetry. The emergent property analysis is non-artefactual, further confirming the validity of this fundamental cross-domain mapping for inclusion in the discovery ledger.

`EQ-FICK-DIFFUSION` ↔ `EQ-FOURIER-HEAT` — `dC_dx` ↔ `dT_dx`

Board rationale: 2 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: approve — The coupling between Fick's law of diffusion and Fourier's law of heat conduction is a textbook example of structural analogy between linear transport equations: J = -D·(dC/dx) maps to q = -k·(dT/dx) under a consistent variable renaming. The concentration gradient and temperature gradient play identical structural roles (driving forces in their respective flux laws), and the tier-2 similarity classification with an identity transfer function accurately reflects this isomorphism rather than claiming the two quantities are literally identical. The Onsager reciprocity check correctly notes that a 1×1 coupling matrix is trivially symmetric, and the other constraint checks are properly marked not applicable. The Buckingham π groups are dimensionally consistent within each equation. No spurious emergent properties are claimed. This is a well-established and physically meaningful cross-domain analogy in irreversible thermodynamics.
openai-gpt-5: reject — Despite the structural similarity of Fick’s and Fourier’s laws, dC/dx (ConcentrationGradient) and dT/dx (TemperatureGradient) are different physical quantities with incompatible dimensions; an identity transfer function is therefore not physically plausible and is not supported by the semantic descriptors. A meaningful cross-domain link would require a named transform (e.g., nondimensionalization or phenomenological cross-coefficients such as Soret/Dufour relating appropriate forces/fluxes), not direct equality of the gradients. The physical-constraint filter’s Onsager “pass” concerns symmetry of transport matrices and does not validate variable identity, and the reported π-groups are trivial restatements of the base laws rather than genuine emergent properties.
gemini-2.5-pro: reject — The proposed coupling incorrectly equates a concentration gradient with a temperature gradient via an identity transfer function. While Fick's Law and Fourier's Law are structurally analogous and describe phenomena that are physically coupled in nature (e.g., thermodiffusion), a concentration gradient is not a temperature gradient. They are distinct physical quantities with different dimensions. This proposal confuses a valid mathematical analogy with an invalid physical identity, and as a result, no genuine emergent properties are discovered.

`EQ-FICK-DIFFUSION` ↔ `EQ-HOOKE` — `D` ↔ `k`

Board rationale: 3 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — The proposed coupling maps a diffusion coefficient (dimensions L²/T) to a spring stiffness (dimensions M/T²) via an identity transfer function. These quantities are dimensionally incompatible, physically unrelated, and belong to entirely different phenomenological domains (irreversible transport vs. conservative mechanics). The syntactic similarity between Fick's first law (J = -D dC/dx) and Hooke's law (F = -kx) is superficial: both are linear proportionality relations, but the operands carry fundamentally different physical meaning. The physical constraint filter passed no checks (all returned not_applicable), which means there is zero physical evidence supporting the coupling—the 'all_not_applicable' status should not be interpreted as permissive but rather as indicating the absence of any validating physics. The claimed emergent Buckingham pi groups are trivially the dimensionless ratios already implicit in each law individually and do not represent genuine cross-domain insight. This coupling is an artefact of syntactic pattern matching on linear constitutive equations and has no physical justification.
openai-gpt-5: reject — Equating the diffusion coefficient D from Fick’s law with the spring stiffness k from Hooke’s law via an identity map is not physically plausible: they describe unrelated material responses and have incompatible dimensions (L^2/T vs M/T^2). The semantic descriptors clearly denote different properties (DiffusionCoefficient vs Stiffness) with no named transform linking them. The physical-constraint filter did not pass and its dimensional mismatch aligns with basic dimensional analysis. The claimed structural similarity stems only from both being linear proportionalities and does not justify parameter identification; the reported Pi groups are trivial rearrangements of each separate law, not genuine cross-domain emergent properties.
gemini-2.5-pro: reject — The proposed coupling is rejected as it is based on a superficial mathematical analogy between two physically unrelated phenomena. It equates the diffusion coefficient (D, a parameter in a dissipative transport law with dimensions L²/T) with a spring constant (k, a parameter in a conservative mechanical law with dimensions M/T²). These quantities are dimensionally inconsistent and semantically distinct, making the 'identity' transfer function physically meaningless. While the structural similarity is noted, it does not imply any valid cross-domain physical relationship, a conclusion supported by the physical constraint filter's inability to apply any validation checks successfully and its noting of the dimensional mismatch.

`EQ-FICK-DIFFUSION` ↔ `EQ-HOOKE` — `J` ↔ `F_spring`

Board rationale: 3 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — The coupling identifies molar flux (J, a flow variable with dimensions [substance]/[length]²/[time]) with spring force (F_spring, an effort variable with dimensions [mass]·[length]/[time]²) via an identity transfer function. These are dimensionally incompatible and represent fundamentally different physical quantities — one is a transport flux in a diffusive medium, the other is a restoring force on a rigid body. The physical constraint filter correctly flags this as a failed Tellegen pairing: these are bond-graph duals (flow vs. effort), not equivalent quantities. The syntactic similarity between Fick's first law (J = -D·dC/dx) and Hooke's law (F = -k·x) is a superficial algebraic resemblance (both are linear proportionalities with a negative sign), not a genuine physical coupling. The emergent Buckingham π groups are trivially the dimensionless forms of each equation individually and reveal no new physics from the proposed coupling. This is a classic artefact of structural pattern-matching without physical grounding.
openai-gpt-5: reject — The proposed identity coupling maps molar flux (a flow variable with dimensions [substance]/[L]^2[T]) to mechanical force (an effort variable with dimensions [M][L]/[T]^2), violating dimensional consistency and effort–flow role matching; the semantic descriptors do not denote the same quantity nor a recognized transform. The physical-constraint filter’s tellegen_pairing failure is correct and aligns with standard bond-graph analogies (J ↔ flow, F ↔ effort). The claimed structural identity is a superficial algebraic resemblance (y = −Kx) that does not confer physical equivalence, and the listed π-groups are trivial restatements of each equation rather than genuine cross-domain emergent properties.
gemini-2.5-pro: reject — The proposed coupling is physically implausible as it equates Molar Flux with mechanical Force, quantities that are dimensionally, conceptually, and semantically distinct. This identification is based on a superficial syntactic similarity between the two equations and is correctly flagged as invalid by the physical constraint filter, which notes the dimensional mismatch and the fundamental error of equating a 'flow' variable (flux) with an 'effort' variable (force). No genuine emergent properties are generated; the coupling is a physically meaningless algebraic artifact.

`EQ-FICK-DIFFUSION` ↔ `EQ-HOOKE` — `dC_dx` ↔ `x`

Board rationale: 3 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — This coupling equates a concentration gradient (dimensions [substance]·[length]⁻⁴) with a displacement/position (dimensions [length]) via an identity transfer function, which is dimensionally inconsistent and physically meaningless. The semantic descriptors clearly identify entirely different quantities — a spatial derivative of concentration in a diffusing medium versus a displacement from equilibrium of a rigid body in a spring system. The fact that Fick's law and Hooke's law can be made syntactically identical under variable renaming (both being linear proportionality relations) is a trivial algebraic observation, not a genuine physical coupling. All physical constraint checks returned 'not_applicable,' meaning no filter actually validated the coupling — this should not be interpreted as passing. The claimed emergent pi groups are simply restating each equation's own dimensionless ratio and do not constitute emergent cross-domain physics. This is an artefact of purely syntactic pattern matching with no physical basis.
openai-gpt-5: reject — The proposed identity mapping dC_dx → x is not physically or semantically defensible: concentration gradient (a driving gradient/thermodynamic force with dimensions [substance]/L^4) is not the same type of quantity as mechanical displacement (a state with dimension L), and no named transform is provided to relate them. The claimed structural identity between Fick’s first law (J = −D∇C) and Hooke’s law (F = −kx) is merely formal; an appropriate analogy would pair flux with force and gradient with displacement over length/strain, not gradient with displacement itself. The physical-constraint filter offered no supporting checks (all not applicable), and the listed π-groups are trivial restatements of each constitutive law rather than genuine emergent properties. Therefore the coupling lacks physical plausibility and semantic alignment.
gemini-2.5-pro: reject — The proposed coupling is rejected due to a fundamental physical implausibility. It equates a concentration gradient with a mechanical displacement, which are quantities with incompatible physical dimensions and distinct semantic meanings. This coupling appears to be an artefact of a superficial syntactic similarity between the linear forms of Fick's law and Hooke's law, rather than a representation of a genuine physical interaction. The claimed emergent property is a trivial algebraic rearrangement of one of the original equations, not a novel feature arising from the coupling.

`EQ-FOURIER-HEAT` ↔ `EQ-HOOKE` — `dT_dx` ↔ `x`

Board rationale: 3 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — This coupling maps a temperature gradient (dimension [temperature]/[length]) to a displacement/position (dimension [length]) via an identity transfer function, which is physically nonsensical — an identity map requires dimensional compatibility, and these quantities differ by two fundamental dimensions. The coupling is based purely on a syntactic bijection between the canonical forms of Fourier's law and Hooke's law, which, while structurally interesting, does not establish a physically meaningful relationship between these specific variables. The physical constraint filter passed no checks (all returned not_applicable), meaning there is zero physical evidence supporting this coupling. The claimed emergent pi groups are simply restating the original equations' dimensionless forms and do not arise from any genuine cross-domain interaction. A legitimate analogy between these two linear constitutive laws does exist (thermal resistance ↔ spring compliance), but it would require a properly defined analogical transfer function with explicit dimensional scaling, not an identity map between a gradient quantity and a positional state variable.
openai-gpt-5: reject — Although Fourier’s law (q = -k dT/dx) and Hooke’s spring law (F = -k x) share a linear form, mapping a temperature gradient to a mechanical displacement via identity is not physically or dimensionally meaningful (K/m vs m) and the semantic descriptors do not denote the same quantity; a valid analogy would pair gradient with strain (∂u/∂x) or temperature/force-like potentials under a named transform, not identity. The physical-constraint filter’s non-applicability outcomes and failure to pass are consistent with this mismatch, and the cited Buckingham-π groups are trivial restatements of the constitutive relations rather than genuine emergent properties.
gemini-2.5-pro: reject — The proposed coupling is physically nonsensical as it equates a temperature gradient (dT_dx) with a displacement (x). These quantities possess fundamentally different physical dimensions ([temperature]/[length] versus [length]), rendering a direct identity mapping a violation of dimensional analysis. The noted structural similarity between Fourier's Law and Hooke's Law is a purely mathematical analogy, not representative of a valid physical cross-domain interaction. Consequently, the coupling lacks physical plausibility, and any claimed emergent properties are merely artifacts of this invalid algebraic substitution.

`EQ-FOURIER-HEAT` ↔ `EQ-HOOKE` — `k` ↔ `k`

Board rationale: 3 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — The coupling maps thermal conductivity (W·m⁻¹·K⁻¹) to spring stiffness (N·m⁻¹) via an identity transfer function, despite the two quantities having fundamentally different physical dimensions and representing entirely different physical properties. The only basis for the coupling is a superficial syntactic coincidence: both equations are linear and both use the symbol 'k' as a proportionality constant. The physical-constraint filter passed vacuously (all checks not applicable), providing no affirmative evidence for the coupling. The claimed emergent Pi groups are simply the standard dimensionless forms of each equation individually and do not represent any genuine cross-domain insight. There is no physical mechanism, analogy, or dimensional consistency that would justify equating or directly transferring thermal conductivity and mechanical stiffness. This is a symbol-collision artefact, not a meaningful physical coupling.
openai-gpt-5: reject — Equating Fourier’s thermal conductivity with Hooke’s spring stiffness via an identity map is not physically plausible: the semantic descriptors refer to distinct quantity kinds with incompatible dimensions (kg·m·s⁻³·K⁻¹ vs kg·s⁻²), and no named transform (e.g., geometry-based conductance/stiffness relations) is provided to relate them. The physical-constraint filter did not pass and its dimensional evidence aligns with this mismatch. The purported equation-level structural similarity is a superficial algebraic analogy, not a valid parameter identification, and the listed Pi groups are intra-equation tautologies rather than genuine cross-domain emergent properties.
gemini-2.5-pro: reject — The proposed coupling is physically implausible. The two variables, thermal conductivity (k) from Fourier's Law and spring stiffness (k) from Hooke's Law, are fundamentally different physical quantities with incompatible dimensions ([M][L][T]^-3[Θ]^-1 vs. [M][T]^-2). The 'identity' transfer function is therefore invalid, and the semantic descriptors for the properties correctly identify them as distinct, contradicting the proposed equivalence. The coupling is based on a purely superficial syntactic similarity between the two equations and does not represent a valid physical relationship or analogy.

`EQ-FOURIER-HEAT` ↔ `EQ-HOOKE` — `q` ↔ `F_spring`

Board rationale: 2 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — The coupling maps heat flux density (a flow variable with dimensions [mass]/[time]³) to spring force (an effort variable with dimensions [mass]·[length]/[time]²) via an identity transfer function. The physical constraint filter correctly identifies that these are bond-graph duals, not equivalent quantities, and the Tellegen pairing check fails because their dimensions are incompatible. While Fourier's law and Hooke's law share a superficial syntactic similarity (both are linear proportionality relations between a response and a driving gradient/displacement), this structural analogy does not constitute a physically meaningful coupling. The identity transfer function is dimensionally inconsistent, the semantic descriptors identify fundamentally different physical quantities (heat flux density vs. mechanical force), and the claimed emergent pi groups are simply restating each equation's own dimensionless form rather than revealing any genuine cross-domain insight. This is an artifact of syntactic pattern matching, not a real physical coupling.
openai-gpt-5: reject — The proposed identity coupling maps heat flux density (q) to mechanical force (F) despite fundamentally different physical roles (thermal flow vs mechanical effort) and incompatible dimensions, so it is not physically plausible. The semantic descriptors identify distinct quantity kinds without a named transform linking them. The physical-constraint filter’s Tellegen pairing and dimensional checks correctly fail, aligning with standard bond-graph conjugacies (thermal: T/heat flow; mechanical: force/velocity). The listed Buckingham Pi groups are trivial rearrangements of each law individually, not genuine cross-domain emergent properties. Consequently, the coupling should not enter the discovery ledger.
gemini-2.5-pro: error — HTTP 503 from https://generativelanguage.googleapis.com/v1beta/models/gemini-2.5-pro:generateContent?key=REDACTED: {

"error": { "code": 503, "message": "This model is currently experiencing high demand. Spikes in demand are usually temporary. Please try again later.", "status": "UNAVAILABLE" } }

`EQ-NEWTON-II` ↔ `EQ-OHM` — `F` ↔ `V`

Board rationale: 1 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: approve — The coupling correctly identifies the well-known force–voltage analogy between mechanical and electrical domains. Both F (force) and V (voltage) occupy the effort slot in their respective bond-graph representations, and the structural isomorphism between F = m·a and V = I·R under variable renaming is a textbook result. The physical-constraint filter appropriately flags that dimensions differ while accepting the mapping as a structural effort-analogy, and it correctly notes that a transducer coefficient would be needed for any numerical composite. The Buckingham π groups are dimensionally consistent within each domain. The emergent properties are modest and not overclaimed. This is a legitimate tier-2 structural analogy with no artefactual claims.
openai-gpt-5: reject — The proposal equates force and voltage via an identity transfer despite them being different physical quantities with incompatible dimensions; the descriptors confirm Force vs ElectricPotentialDifference with no named transducer or transform to relate them. The physical-constraint filter’s pass rests only on a structural bond‑graph effort analogy, which cannot justify numerical identity. With no genuine emergent properties and a missing transduction coefficient (e.g., motor/piezo constant), the coupling is not physically plausible as stated.
gemini-2.5-pro: error — HTTP 503 from https://generativelanguage.googleapis.com/v1beta/models/gemini-2.5-pro:generateContent?key=REDACTED: {

"error": { "code": 503, "message": "This model is currently experiencing high demand. Spikes in demand are usually temporary. Please try again later.", "status": "UNAVAILABLE" } }

`EQ-NEWTON-II` ↔ `EQ-OHM` — `a` ↔ `I`

Board rationale: 1 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: approve — This coupling represents a well-known structural analogy between Newton's second law (F = ma, so a = F/m) and Ohm's law (V = IR, so I = V/R). Both equations share the same algebraic form (response = driving quantity / resistance parameter), and the mapping of acceleration to current is consistent with the standard mechanical–electrical analogy where both serve as 'flow' variables in their respective bond-graph domains. The transfer function is labeled 'identity,' which is appropriate at the structural/syntactic level — the sieve correctly identifies this as a rename-level isomorphism. The physical constraint filter appropriately notes that dimensions differ and flags the need for a transducer coefficient in any numerical application, which is honest and correct. The Buckingham π groups are legitimate dimensionless groupings from each equation. No spurious emergent properties are claimed. This is a textbook-quality cross-domain analogy and is suitable for the discovery ledger as a tier-2 structural similarity.
openai-gpt-5: reject — The proposed identity mapping a ↔ I is not physically or semantically sound: in bond-graph terms the mechanical flow variable is velocity, not acceleration (which is a time-derivative of flow), whereas current is a flow. Newton’s second law (F = m a = m dv/dt) corresponds to an inertial element (analogous to an inductor), not to a resistive law (V = R I). A valid Ohm-like mechanical analog would be viscous damping F = b v with v ↔ I (mobility analogy), not a ↔ I. The semantic descriptors (Acceleration vs ElectricCurrent) do not represent the same quantity nor a named transform, yet an identity transfer is claimed. The physical-constraint filter’s Tellegen check misclassifies acceleration as a flow and overlooks the dimensional mismatch; accepting it as a “structural flow-analogy” is inconsistent with standard cross-domain analogies. The listed π-groups are merely tautologies of the individual laws, not emergent cross-domain properties.
gemini-2.5-pro: approve — This coupling correctly identifies the well-established force-voltage (or mobility) analogy between mechanical and electrical systems. The mapping of acceleration ('a') to electric current ('I') is valid within this framework, as both serve as 'flow' variables in their respective domains. The semantic descriptors honestly represent the distinct physical quantities, and the physical constraint filter's reasoning is sound, correctly classifying this as a structural analogy where dimensional differences are expected. The emergent property analysis is consistent with a direct structural mapping, reinforcing the validity of this Tier 2 similarity.

`EQ-NEWTON-II` ↔ `EQ-OHM` — `m` ↔ `R`

Board rationale: 2 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
claude-opus-4-6: reject — While Newton's second law (F = ma) and Ohm's law (V = IR) share a syntactically identical trilinear algebraic structure, the proposed coupling maps mass (m) to resistance (R) via an identity transfer function, which is physically unjustified. Mass and resistance have incompatible dimensions ([mass] vs. [mass·length²·time⁻³·current⁻²]), and the identity mapping between them is dimensionally inconsistent. The analogy between these equations is a well-known purely formal/structural one (inertia as 'resistance to acceleration' paralleling electrical resistance to current), but a formal structural isomorphism does not constitute a genuine physical coupling. The physical constraint filter passed no checks (all returned not_applicable), providing no supporting evidence. The emergent pi groups are simply the trivially dimensionless restatements of each equation independently and reveal no new cross-domain insight. This is an artefact of algebraic pattern matching, not a physically meaningful coupling.
openai-gpt-5: reject — Despite a superficial algebraic similarity (both laws are linear proportionalities), mapping Newton’s mass m to electrical resistance R via an identity transfer is physically and semantically invalid: Mass (inertial, energy-storing) and resistance (dissipative) are different quantities with incompatible dimensions and roles; in standard analogies mass corresponds to inductance, not resistance. The semantic descriptors (Mass vs Resistance) do not identify the same quantity nor a justified transform. The physical-constraint filter flags unequal dimensions and offers no supporting reciprocity/energy checks. The listed Pi groups are per-equation tautologies, not emergent from the coupling. Therefore the proposed coupling is not physically plausible.
gemini-2.5-pro: error — HTTP 503 from https://generativelanguage.googleapis.com/v1beta/models/gemini-2.5-pro:generateContent?key=REDACTED: {

"error": { "code": 503, "message": "This model is currently experiencing high demand. Spikes in demand are usually temporary. Please try again later.", "status": "UNAVAILABLE" } }