Safety of dynamical SUSY breaking and gaugino condensation in models of spontaneous CP violation

Norimi Yokozaki

REVIEW

Safety of dynamical SUSY breaking and gaugino condensation in models of spontaneous CP violation

Norimi Yokozaki

High Energy Physics - Phenomenology · Submitted 6 Oct 2026

Pith's verdict: A careful, internally consistent map of where dynamically generated scales can inject CP phases into Nelson-Barr models; the safe-class results hold, and the dangerous-class claims are honestly conditional.

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arXiv ID2610.08002 (version 2)

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CitationNorimi Yokozaki. "Safety of dynamical SUSY breaking and gaugino condensation in models of spontaneous CP violation." arXiv:2610.08002 (2026). https://pith.science/paper/UUWKDQKW

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Editor's note

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This paper does what it says: it checks, model by model, whether dynamically generated scales — gaugino condensation for the constant term, DSB for the F-term — reintroduce a strong CP phase when all UV couplings are real. The observation that such phases can arise even with a real Lagrangian, and that the VY/ADS family is safe only for N' = N_c − N_f in {1,2}, is the standard branch structure of SYM applied as a model-building criterion. That application is the new and useful bit.

The paper earns credit because it computes rather than gestures. The IYIT analysis via the (3,3) signature of η is a clean eigenvalue argument; the ISS degenerate-limit orientation mechanism is real; the 3-2 R-axion argument is careful; and the messenger-alignment second route with its floor at fixed gluino mass (Eq. 18) is genuinely new. The numbers I checked are consistent: the 0.063 anomaly-mediation coefficient, the keV gravitino bounds, c_Z = 1.04. An ancillary script covers the instanton integrals. And the paper flags its caveats instead of burying them: Eq. (30) is inserted by representation theory, the cluster-decomposition objection [44] is acknowledged, ISS higher loops and the IYIT large-|X| minimum are left open.

The soft spots are the acknowledged ones, and they sit at the edges of the dangerous-class claims, not the safe class. The "N' in {1,2}" exclusion assumes the branch vacua are degenerate states of one real Lagrangian with no dynamics selecting among them; if cluster decomposition genuinely fails, or if some mechanism picked the CP-even branch, the exclusion would lose its footing. The authors say exactly this (b186, b196), and I think the standard lore is on their side: the mass-deformation cross-check in Sec. 4.3 produces the same branch structure through cited Seiberg results without touching the contested instanton normalization. A referee should still push on this. The IYIT "roughly half" frequency claim is stated without a precise measure; it is plausible from the odd-permutation symmetry of the parameter space, but loose as written.

This is for SUSY model builders working on Nelson-Barr and gauge mediation. The safe-class results are useful; the dangerous-class claims are conditional but worth consolidating, not dismissing. Send it to referees — it should not be desk-rejected.

Referee report

Significance

If the central classification holds, the paper delivers a concrete and useful necessary condition for an important model-building class: a Nelson-Barr solution with dynamically generated constant term and DSB must use N' ∈ {1,2} and must avoid the degenerate-mass ISS limit and the purely-imaginary IYIT class. The paper is careful about its assumptions: it explicitly flags the branch-reality assumption as an open point (Sec. 4.2, Eq. (30), sentences b186 and b196), the cluster-decomposition issue [44], and the strong/weak-coupling instanton normalization discrepancy (footnote 7). The paper provides several machine-checkable ingredients: the 0.063 coefficient of Eq. (13), the keV bounds of Eq. (14), the algebra of Eqs. (18)-(19), and an ancillary Python script for the zero-mode and collective-coordinate integrals of Sec. 4.2. The model-by-model conclusions are quoted against published benchmarks (Seiberg, Finnell-Pouliot, Shih, ISS), and no parameter is fitted to data; the derived c_Z values and branch classifications are computed from explicit integrals.

Major objections (7)

[Sec. 4.2, Eq. (30)] The load-bearing step for the dangerous-class classification is the identification of the realized vacuum with an arbitrary root e^{2πik/N'}. The paper itself states that Eq. (30) is 'inserted after the fact by the representation theory of the unbroken discrete symmetry, and is not itself directly computed' (sentence b186), and that cluster decomposition in the strong-coupling instanton computation has been challenged (sentence b196). This is an acknowledged open point, but the central conclusion that N' ≥ 3 is dangerous for gaugino condensation rests on it. If dynamics selected the CP-even k=0 branch, or if ⟨λλ⟩ does not factor from the N_c-point correlator, then 'every branch must be real' would not apply. I do not see a contradiction with the published literature in the branch analysis itself, so this is a correctness-risk concern rather than a demonstrable error; I would like the paper to state explicitly that the exclusion of N' ≥ 3 assumes the standard cluster/representation-theory input, and to discuss what direct test (e.g., lattice or R^3×S^1 computation) could settle the branch-selection question. The authors acknowledge this: “Consistency with the spontaneous breakingZ 2Nc→Z 2 induced by⟨λλ⟩̸= 0 therefore requires the form ⟨λλ⟩k = (γ0 Nc)1/NcΛ3e2πik/Nc, k= 0,...,N c−1,(30) but this is inserted after the fact by the representation theory of the unbroken discrete symmetry, and is not itself directly computed.”
[Sec. 3.2, Eq. (25) and Sec. 4.1] The paper classifies the ADS superpotential for N_f < N_c as carrying an (N_c−N_f)-fold branch, and hence dangerous for N_c−N_f ≥ 3. However, the derivation of Eq. (25) uses holomorphic decoupling from the Higgsed phase, whereas the direct strong-coupling computation of Sec. 4.2 applies to the unbroken theory. The paper acknowledges the mismatch in the coefficient (footnote 7), and notes that only the reality of γ_0^{N_c} matters for the phase. But the identification of N' distinct degenerate vacua is still imported from the low-energy effective description rather than derived within the computation. This is the same open point as in Sec. 4.2, and it should be stated as a unified caveat in Sec. 3 rather than only in footnote 7.
[Sec. 6, Eqs. (70)-(72)] The dangerous-class channel in ISS is identified with the magnetic gaugino condensation term W_dyn ∼ (det Φ)^{1/\tilde N_c}, which reproduces the N_c supersymmetric vacua of the electric theory. The paper correctly notes that this term vanishes/does not apply at the metastable vacuum, where the magnetic gauge group is completely Higgsed. However, the argument that the metastable vacuum remains Higgsed after the supergravity displacement of Φ (Eq. (75)) relies on δΦ ∼ m_{3/2}/h being far below |\bar\mu|. The bound m_{3/2} ≲ keV quoted in Eq. (15) is needed for the dangerous class, but for the ISS analysis the paper does not give the numerical range of m_{3/2} relative to |\bar\mu|. I recommend adding the explicit hierarchy condition to make the claim 'the magnetic gauge group stays completely Higgsed' quantitative.
[Sec. 2, Eq. (18)] The claim that the messenger-alignment contribution is a floor (cancellation of M_mess between the ⟨Z_eff⟩ shift and Λ_mess) is derived for the IYIT and ISS portals. The same parametric behavior is stated for the 3-2 model in Sec. 7, but the 3-2 portal is composite (W ⊃ X_1 f fbar / M_*^2) and the displacement of ⟨X_1⟩ by the R-axion fixing is controlled by the cos(2a/f_R) potential of Eq. (87) with a possible second-harmonic correction (sentence b416). The paper correctly flags the second-harmonic assumption, but the statement in the abstract that 'in all three' the messenger vacuum aligns with arg C should be qualified in Sec. 7 to include the harmonic-suppression assumption. The authors acknowledge this: “This suppression is a necessary input for what follows: a second harmonic larger than a quarter of the first and of opposite sign would move the minimum to a CP-conjugate pair of points away from the extrema below.”
[Sec. 5.1, Eqs. (45)-(52)] The 'roughly half of the real Yukawa parameter space gives purely imaginary meson VEV' claim relies on the signed eigenvalue distribution of N = H^{-1/2} η H^{-1/2}. The argument is sound for generic random λ, but the statement 'roughly equal probability' is heuristic. I would like a more precise characterization of the measure: e.g., whether the two classes are separated by a codimension-one surface and whether the claim holds for all real λ or only for a generic distribution over real 6×6 matrices. This is a minor gap but affects the abstract's summary of IYIT.
[Sec. 4.3, Eqs. (36)-(40)] The claim that the N_c-fold branch of the meson VEV is transmitted with the same k for all flavors is derived from the pure-SYM gaugino condensation of the mass-deformed theory. The identification of a single k per sector is reasonable, but the paper should note that this assumes the vacuum label is chosen once in the confining IR theory and does not discuss whether a superposition of branches could occur. The subsequent cancellation in det M (Eqs. (41)-(42)) is a clean algebraic identity, and I am not raising this as an error; it is a point where the presentation should be more explicit.
[Sec. 2, Eq. (13) and Eq. (14)] The numerical coefficient 0.063 is quoted as arising from g_3^2(TeV) ≃ 1.1 and the anomaly-mediation coefficient 3(g_3^2/16π^2). The conversion from Eq. (11) to Eq. (13) uses |M_3^{AMSB}| = 3(g_3^2/16π^2) m_{3/2}, and the ratio is then r_AMSB ≃ 3 m_{3/2}/M_3^{tot}. For M_3 = 2-20 TeV, the resulting m_{3/2} ≲ (3.7-37) keV is consistent with the 0.063 coefficient. This spot-check passes, but the paper should specify the running scale at which g_3 is evaluated in Eq. (13) and whether the same value is used in Eq. (14).

Minor objections (12)

[Sec. 1, Eq. (1)] The definition of theta-bar includes arg det m_q, but Eq. (3) later sets theta-bar = 3 arg M_3 after integrating out heavy states. The text explains the basis choice, but a reader may be confused by the two different expressions; a sentence clarifying that Eq. (3) is in the Nelson-Barr basis with real heavy masses would help.
[Sec. 2, Eq. (5)] The anomaly-mediation formula includes Kähler-dependent terms; the paper correctly states that they are subleading for ⟨K_i⟩ ≪ 1, but the notation K_i F^i is introduced without defining F^i as the auxiliary field of the SUGRA sector. A short definition would improve readability.
[Sec. 3.1, Eq. (21)] The VY superpotential is written with S = −(1/32π^2) tr W^α W_α, and the log term is justified by the R-anomaly. The phrase 'the log term is essential' is correct, but the paper should cite the original derivation of the normalization of S to avoid confusion with alternative conventions.
[Sec. 3.2, Eq. (24)] The matching relation Λ_low^{3(N_c−N_f)} = Λ^{3N_c−N_f}/det M is stated without a comment on the sign convention of Λ. The paper later discusses the coefficient normalization in detail; a cross-reference to that paragraph would be useful.
[Sec. 4.2, Eq. (31)] The Green's function is written with the index structure (G_{N_c}^{N_c})^{i_1...i_{N_c}}_{j_1...j_{N_c}}, but the text does not define the contraction convention for the epsilon tensors. The reader can infer it from Eq. (32), but it would be cleaner to state it.
[Sec. 4.2, Eq. (33)] The SU(4)_F covariance argument for N_c=2 gives ⟨\hat M_{ab}(x_1) \hat M_{cd}(x_2)⟩ = κ ε_{abcd} Λ^4. The text should note that the two-point function is constant only after the SUSY Ward identity is used for the combination of lowest components; Eq. (33) is a two-point function of chiral superfield lowest components, and the constancy follows from the Ward identity. This is implicit in the text but should be explicit.
[Sec. 5.1, Eq. (48)] The matrix η is real symmetric with signature (3,3), and the diagonalization by H^{-1/2} is used to prove the bound. The paper should mention that the orthogonal transformation O ∈ SO(6,R) exists for any real symmetric matrix N, which is standard but not stated.
[Sec. 6, Eq. (68)] The Kähler potential K = (1/β) Tr(q†q + qtilde†qtilde) + (1/α|Λ|^2) Tr M† M is written with positive α, β; the text says α, β ∈ R_{>0} by positivity of Hermitian bilinears. This is correct, but the normalization β=1 for the canonical variables is introduced only later; a footnote would avoid confusion.
[Sec. 7, Eqs. (82)-(85)] The minimization of the 3-2 model is quoted from Bagger-Poppitz-Randall [59]. The paper should state explicitly that Eq. (85) is a quoted result, not recomputed here; this is currently implicit in the text.
[Sec. 8, IYIT bullet] The conclusion 'the SU(2) theta angle enters this sector only through the phase of Λ^4 in Pf M = Λ^4' is a helpful summary, but the statement 'θ=0 and θ=π both give a real Λ^4, of opposite sign' deserves a sentence explaining the sign convention, since Λ^4 is usually defined positive in the text.
[Abstract and Sec. 2] The phrase 'the phase from the former can be diluted, but the phase from the latter is not diluted at all' is correct, but the paper should define 'diluted' as the suppression by r_AMSB in Eq. (10) before using the term in the introduction.
[Throughout] The paper uses 'safety' and 'safe class' extensively; a one-sentence explicit definition at the start of Sec. 2 would help readers who skip the introduction.

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The paper

The paper claims

Even with all couplings real and all θ-angles zero, spontaneous-CP SUSY models can still produce a θ-bar phase, because the dynamical scales they need come from multivalued superpotentials on complex vacuum branches.

The reading

The paper asks whether spontaneous CP violation can still solve the strong CP problem when the two scales a supersymmetric Nelson-Barr model needs—the constant term of the superpotential and the SUSY-breaking F-term—are generated dynamically instead of being put in by hand. Its answer is that dynamic generation is not automatically phase-safe: even with every coupling real and every $\theta$-angle zero, the multivalued Veneziano-Yankielowicz / Affleck-Dine-Seiberg superpotential can sit on a branch carrying the phase $e^{2\pi i k/N'}$, and because the Lagrangian does not determine which degenerate branch is realized, safety requires every branch to be real. That requirement holds only for $N'\in\{1,2\}$; for a condensing sector with $N'\ge 3$, the phase of the constant term reaches the gluino mass through anomaly mediation and forces a gravitino below a few tens of keV. Each DSB model must be checked separately: the 3-2 model introduces no phase, ISS is safe for non-degenerate quark masses but can give an $O(1)$ phase in the degenerate limit, and IYIT produces a purely imaginary F-term for roughly half of its real Yukawa couplings. A complex constant term also reaches $\bar\theta$ through the messenger mass by a second route that lowering the messenger scale cannot remove.

What carries the argument

The load-bearing object is the $N'$-fold branch structure of the Veneziano-Yankielowicz / Affleck-Dine-Seiberg superpotential, $C=N'\Lambda^3 e^{2\pi i k/N'}$: the branch label $k$ labels degenerate vacua of one real Lagrangian, so every branch must be real, which holds only for $N'\in\{1,2\}$. The argument is organized around a three-part safety criterion—the superpotential fixes the gauge-invariant quantity single-valuedly, the effective potential selects a real vacuum, and holomorphic matching leaks no phase—and around two phase channels to the gluino mass: anomaly mediation, which carries $\arg C$ and can be diluted by the ratio $r_{\mathrm{AMSB}}$, and gauge mediation, which carries the DSB F-term phase undiluted. A third mechanism completes the picture: in IYIT, ISS and the 3-2 model the messenger-coupled vacuum is displaced along $\arg C$, so a complex constant term enters $\bar\theta$ through the messenger mass as a floor that survives any messenger-scale choice.

Extended reading notes

Core claim

The central claim is that the strong-coupling dynamics used to explain the scale hierarchy is itself the source of a CP phase, so the reality of all UV couplings and the vanishing of all bare $\theta$-angles are insufficient for a safe SCPV construction. In pure $SU(N_c)$ super Yang-Mills, the instanton computation fixes only the real, $Z_{2N_c}$-invariant product $\langle\lambda\lambda\rangle^{N_c}$, which survives one instanton, real coefficient, per the direct computation; extracting the condensate of a single field requires an $N_c$-th root, producing $N_c$ degenerate vacua of one and the same real Lagrangian, with the realized branch undetermined by the dynamics. The constant term inherits this phase, $C=N_c\Lambda^3 e^{2\pi i k/N_c}$, and it flows into $\bar\theta$ through anomaly mediation unless diluted by gauge mediation with $m_{3/2}\lesssim(3.7\text{--}37)$ keV; the same structure applies to the ADS family, which is safe only for $N'\equiv N_c-N_f\in\{1,2\}$. For the DSB sector, the paper shows that the $N_f=N_c$ quantum moduli constraint is branch-free, yet IYIT still admits purely imaginary meson vacua for roughly half of real couplings; ISS is real for non-degenerate masses but the degenerate limit permits a complex vacuum orientation; and the 3-2 model at $N'=1$ is safe once the real constant term fixes the R-axion at one of two CP-conserving points.

Load-bearing premise

The load-bearing premise is that the $N'$-fold branch structure is physically real—the vacua labeled by $k=0,\dots,N'-1$ are degenerate states of one real Lagrangian, and the realized branch is undetermined by the dynamics—so safety forces every branch to be real; for pure SYM the $N_c$-th root phase is inserted after the fact by representation theory of the unbroken discrete symmetry rather than computed, and a dynamical branch selection or a modified condensate coefficient would undo the dangerous-class classification.

Editorial extensions

If this is right

Gaugino condensation and ADS-type sectors are safe only for $N'\equiv N_c-N_f\in\{1,2\}$; any other confining sector that supplies the constant term must be accompanied by $m_{3/2}\lesssim(3.7\text{--}37)$ keV or it reintroduces $\bar\theta$.
Choosing gauge mediation does not by itself protect the Nelson-Barr mechanism: it dilutes the anomaly-mediated phase but leaves the DSB F-term phase undiluted.
Among the DSB models, the 3-2 model is safe, ISS is safe for non-degenerate quark masses but precarious in the nearly degenerate limit, and IYIT gives a purely imaginary F-term and an O(1) gluino phase for roughly half of real Yukawa couplings.
In IYIT and ISS the second route is a floor: at fixed gluino mass the $C$-induced displacement of the messenger-coupled vacuum is independent of the messenger scale, so lowering $M_{\mathrm{mess}}$ cannot remove the $\bar\theta$ contribution from $\arg C$ (Eq. (18)).
The $N_f=N_c$ quantum moduli constraint is branch-free because $\Lambda^{2N_c}$ enters linearly with a real instanton coefficient; only the vacuum-selection condition can fail there, as it does in the imaginary-meson class of IYIT.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the branch-degeneracy picture is correct, the practical design rule for SCPV model building is to restrict strongly-coupled sectors to $N'\in\{1,2\}$ with chiral matter content, which would steer constructors away from vector-like DSB sectors unless quark masses are kept non-degenerate.
The analysis singles out a decisive computation: evaluating the condensate phase without assuming cluster decomposition, for instance on $\mathbb{R}^3\times S^1$ as in the literature the paper cites, would directly confirm or undermine the dangerous class for $N_c\ge 3$.
The ISS degenerate-mass result extends as a caution to any composite construction with an approximate flavor degeneracy: near-degenerate sectors combined with antisymmetric portal couplings are a latent $O(1)$ phase source that the non-degenerate limit entirely hides.
Because both routes end in the same observable $\bar\theta$, a future measurement could not by itself identify which phase channel was active; only correlations with the gravitino mass and the messenger-scale dependence predicted here could separate them.

Original abstract

Solving the strong CP problem with spontaneous CP violation (SCPV) in SUSY requires that the constant term of the superpotential and the SUSY-breaking F-term be real to high accuracy. When both are generated dynamically, by gaugino condensation and by dynamical SUSY breaking (DSB), their phases need not vanish even if every theta-angle vanishes and every coupling is real; e.g., the multivalued non-perturbative superpotential may sit on a branch with a complex phase. In fact, gaugino condensation, in pure SUSY Yang-Mills theory and in its Affleck-Dine-Seiberg generalization, is safe only for N_c - N_f in {1,2} (N_c = 2 for pure SYM); otherwise the phase of the constant term reaches the gluino mass through anomaly mediation. The SUSY-breaking F-term is the main source of the MSSM soft masses, including the gluino mass, so its phase reaches theta-bar as well. In the framework of global SUSY, the 3-2 model introduces no phase. The ISS model is safe in that sector as long as the quark-mass splittings exceed the messenger-loop corrections; when they fall below, a complex vacuum orientation can generate an O(1) phase. The IYIT model can generate a purely imaginary F-term: for half of the real Yukawa parameter space, the meson VEV is purely imaginary and CP is spontaneously broken. In all three, the vacuum of the field coupled to the messengers is aligned with the constant term, so a complex constant term generates a strong CP phase through a second route, separate from anomaly mediation.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-07: 1 request, 6,621 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.54 · compares with prior results 0.32 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Solving the strong CP problem with spontaneous CP violation (SCPV) in SUSY requires that the constant term of the superpotential and the SUSY-breaking F-term be real to high accuracy. When both are generated dynamically, by gaugino condensation and by dynamical SUSY breaking (DSB), their phases need not vanish even if every theta-angle vanishes and every coupling is real; e.g., the multivalued non-perturbative superpotential may sit on a branch with a complex phase. In fact, gaugino condensation, in pure SUSY Yang-Mills theory and in its Affleck-Dine-Seiberg generalization, is safe only for N_c - N_f in {1,2} (N_c = 2 for pure SYM); otherwise the phase of the constant term reaches the gluino mass through anomaly mediation. The SUSY-breaking F-term is the main source of the MSSM soft masses, including the gluino mass, so its phase reaches theta-bar as well. In the framework of global SUSY, the 3-2 model introduces no phase. The ISS model is safe for non-degenerate quark masses in that sector; in the degenerate (or nearly degenerate) limit, however, a complex vacuum orientation can generate an O(1) phase. The IYIT model can generate a purely imaginary F-term: for roughly half of the real Yukawa parameter space, the meson VEV is purely imaginary and CP is spontaneously broken. In all three, the vacuum of the field coupled to the messengers is aligned with the constant term, so a complex constant term generates a strong CP phase through a second route, separate from anomaly mediation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Solving the strong CP problem with spontaneous CP violation (SCPV) in SUSY requires that the constant term of the superpotential and the SUSY-breaking F-term be real to high accuracy.	background 1.00	0.12	0.17	asserted 1.00
s1	When both are generated dynamically, by gaugino condensation and by dynamical SUSY breaking (DSB), their phases need not vanish even if every theta-angle vanishes and every coupling is real; e.g., the multivalued non-perturbative superpotential may sit on a branch with a complex phase.	background 0.50	0.19	0.14	hedged possibility 0.61
s2	In fact, gaugino condensation, in pure SUSY Yang-Mills theory and in its Affleck-Dine-Seiberg generalization, is safe only for N_c - N_f in {1,2} (N_c = 2 for pure SYM); otherwise the phase of the constant term reaches the gluino mass through anomaly mediation.	result 0.91	0.35	0.25	asserted 0.98
s3	The SUSY-breaking F-term is the main source of the MSSM soft masses, including the gluino mass, so its phase reaches theta-bar as well.	background 0.61	0.20	0.09	asserted 1.00
s4	In the framework of global SUSY, the 3-2 model introduces no phase.	result 0.94	0.31	0.04	asserted 1.00
s5	The ISS model is safe for non-degenerate quark masses in that sector; in the degenerate (or nearly degenerate) limit, however, a complex vacuum orientation can generate an O(1) phase.	result 0.93	0.32	0.07	asserted 0.98
s6	The IYIT model can generate a purely imaginary F-term: for roughly half of the real Yukawa parameter space, the meson VEV is purely imaginary and CP is spontaneously broken.	result 0.96	0.28	0.05	asserted 0.90
s7	In all three, the vacuum of the field coupled to the messengers is aligned with the constant term, so a complex constant term generates a strong CP phase through a second route, separate from anomaly mediation.	result 0.85	0.46	0.24	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from argument 0.64.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Discussion

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