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REVIEW 3 major objections 5 minor 35 references

The paper constructs a large class of six-dimensional gauged-supergravity domain walls that, after type IIA uplift, describe D4-branes wrapped on constant-curvature four-manifolds and serve as holographic duals of supersymmetric quantum mec

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2026-08-02 22:20 UTC pith:BK5JM5WT

load-bearing objection A solid catalogue extension of wrapped-D4 domain walls with two analytic solutions, but the D4/SQM interpretation rests on a partial IIA uplift the authors admit is incomplete. the 3 major comments →

arxiv 2602.17113 v2 pith:BK5JM5WT submitted 2026-02-19 hep-th

Supersymmetric quantum mechanics from wrapped D4-branes

Parinya Karndumri , Patharadanai Nuchino This is my paper
classification hep-th
keywords supersymmetric quantum mechanicsholographic dualityD4-braneswrapped branesgauged supergravitydomain wallstopological twisttype IIA supergravity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper's aim is to establish that wrapped D4-branes can produce supersymmetric quantum mechanics through holography. It constructs a large family of domain walls in six-dimensional maximal gauged supergravity, sliced as time times a constant-curvature four-manifold, and argues that many of these, when lifted to type IIA string theory, have physically acceptable infrared singularities. A sympathetic reader would care because these are candidate gravity duals for renormalization-group flows across dimensions: from five-dimensional super Yang-Mills on the D4 world-volume down to one-dimensional supersymmetric quantum mechanics preserving two supercharges, or one in the SU(2)-twist cases. The construction covers spheres and hyperbolic spaces, products of two Riemann surfaces, and Kähler four-cycles, and it works for both CSO(p,q,5-p-q) and CSO(p,q,4-p-q)⋉R⁴ gauge groups. The physicality criterion is concrete: an infrared singularity is called physical when the time-time component of the type IIA metric does not diverge there; by that test, negative-curvature slicings mostly pass and many positive-curvature ones fail.

Core claim

On the paper's own terms, the discovery is that twisted compactifications of D4-branes on four-manifolds of constant curvature have explicit supergravity descriptions. The solutions are t×M4-sliced domain walls that interpolate between asymptotically locally flat domain walls—the gravity duals of five-dimensional maximal SYM—and singular infrared geometries which, after uplift, are interpreted as D4-brane configurations wrapping M4. The construction uses topological twists to cancel the spin connection of M4, reducing the supersymmetry conditions to first-order flow equations for the warp factors and scalar fields. Each infrared singularity is then classified by the behavior of the type-IIA

What carries the argument

The engine is the topological twist combined with the BPS flow equations. For each four-manifold M4, gauge fields are turned on so that their field strengths cancel the spin connection of M4, allowing radial Killing spinors and preserving between one and eight supercharges depending on the twist; the supersymmetry variations then reduce to first-order ordinary differential equations for the warp factors, the dilaton, and the remaining scalars. The second load-bearing piece is the uplift test: using partial consistent-truncation data, the authors compute the (00)-component of the ten-dimensional type-IIA metric, ĝ00, and classify an infrared singularity as physical exactly when this component

Load-bearing premise

The load-bearing premise is that the partial truncation data used to lift the six-dimensional solutions to ten dimensions come from genuinely consistent truncations; if the full ansätze contain additional fields, the computed ĝ00—and with it the physical/unphysical classification—could change.

What would settle it

Pick one solution with a claimed physical infrared singularity, such as the t×H4 flow with SO(4) twist in the SO(5) gauge group, and construct or obtain the complete consistent truncation ansatz from type IIA theory; if the exact ten-dimensional metric has ĝ00 diverging at the infrared endpoint where the partial formula does not, the central claim fails. A weaker but still decisive test is to verify that the truncated BPS equations imply all second-order field equations of the full six-dimensional theory, including those that were imposed rather than derived.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the central claim is right, five-dimensional maximal SYM on the D4 world-volume, when twisted and compactified on H4, H2×H2, H2×R2, or CH2, flows to one-dimensional supersymmetric quantum mechanics with two preserved supercharges, and the paper supplies explicit gravity duals for those flows.
  • The ĝ00 criterion gives a practical way to separate trustworthy wrapped-brane holographic duals from suspect ones: negative-curvature slicings generically pass, positive-curvature slicings generically fail.
  • The analytic solutions in the CSO(3,0,2), CSO(3,0,1)⋉R4, and CSO(2,0,2)⋉R4 gauge groups provide closed-form examples whose infrared singularities are either cleanly physical or cleanly unphysical, making them convenient starting points for further computation.
  • These constructions add a new class of gravity duals of supersymmetric quantum mechanics that do not come from D0-branes, broadening the domain-wall/QFT correspondence to (0+1)-dimensional field theories.
  • For each family considered, the paper records for which gauge groups, twist types, and parameter values the infrared singularity passes the criterion, giving a systematic catalogue of candidate quantum-mechanics duals from wrapped D4-branes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The authors leave open the full ten-dimensional uplift; if the missing consistent-truncation ansätze are constructed, the complete metric could shift the physical/unphysical split, so the tables are best read as provisional until that check exists.
  • The recurring pattern that negatively curved slicings pass while positively curved ones fail hints that curvature sign, not just topology, drives the infrared physics; testing intermediate cases such as lens spaces or mixed products would isolate that variable.
  • A sharper check of the physicality criterion would be a boundary observable—say the spectrum of the preserved supercharges or a holographic entanglement entropy in the proposed quantum mechanics—which the paper does not compute and which could decide whether 'physical singularity' corresponds to finite low-energy physics.
  • Because the same six-dimensional gauged supergravity also encodes D4-branes wrapped on two- and three-manifolds, this construction plausibly joins those families into a unified set of wrapped-D4 quantum-mechanics duals across dimensions; that unification is implicit but not stated in the paper.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies supersymmetric t×M4-sliced domain walls in six-dimensional maximal gauged supergravity with CSO(p,q,5−p−q) and CSO(p,q,4−p−q)⋉R4 gauge groups. It constructs topological twists for four-manifolds M4 that are either space forms, products of two Riemann surfaces, or Kähler four-cycles, derives first-order BPS equations from the fermionic supersymmetry variations, and presents numerical and a few analytic interpolating solutions between locally flat domain walls and singular IR geometries. The paper then uses the g00 criterion of [18] to label IR singularities as physical or unphysical after a partial type IIA uplift, and interprets the physical cases as holographic duals of supersymmetric quantum mechanics from twisted compactifications of D4-branes. The six-dimensional construction is standard and documented in detail; the central unresolved point is that the type IIA/D4-brane interpretation relies on incomplete truncation ansätze, as the authors themselves state in the Introduction.

Significance. If the higher-dimensional embedding is made fully consistent, this would be a substantial catalogue of holographic RG-flow candidates from 5D SYM to 1D SQM, including analytic branches (CSO(3,0,2) and CSO(2,0,2)⋉R4) and parameter regions for physical singularities. The systematic treatment of Bianchi identities, for instance around Eqs. (3.23)–(3.26), is careful and is a genuine strength. However, because only the (00)-component of the ten-dimensional metric is computed, the D4-brane interpretation is conditional. As it stands, the paper is best evaluated as a 6D supergravity classification; the advertised D4-brane/SQM interpretation is a plausible but not yet established corollary.

major comments (3)
  1. [Introduction, p.4; App. B] The D4-brane/SQM interpretation is the headline claim, but it rests on incomplete higher-dimensional truncations. The paper states that complete type IIA/11D truncation ansätze on H^{p,q}×R^{4−p−q} and H^{p,q}×R^{5−p−q} have not been worked out, and only g00 is obtained from partial results in [33,34]. Tables 1–11 base all physical/unphysical verdicts on this single component. If the actual consistent truncation contains additional fields, or if the partial ansatz does not extend to a full embedding, g00 can be corrected and the classification can change. This is not a demonstrated error, but it is load-bearing. Please either provide the complete truncation, prove that the singlet sector used here is a consistent truncation, or explicitly state that the D4-brane interpretation is conjectural and not established by the present equations. The abstract should match that caveat.
  2. [§3.1, Eqs. (3.27)–(3.30); cf. §3.2, §3.3, §4] The first-order BPS systems are introduced with 'we find', and the claim that they satisfy all bosonic field equations is asserted with phrases such as 'It can be verified that these equations satisfy all bosonic field equations'. Since every numerical solution in the paper is a solution of these first-order equations rather than of the second-order field equations, this verification is not a formality: it is what makes the flows actual supergravity solutions. Please include an explicit check for at least one representative case in each family, and indicate whether the remaining cases follow by identical algebra. Without this, the reader cannot distinguish an actual solution from a solution to a truncated but inconsistent set.
  3. [§4, Eqs. (4.11)–(4.12)] For the CSO(p,q,4−p−q)⋉R4 gaugings, all tensor fields are set to zero and the Bianchi identity is satisfied by requiring the term proportional to H∧H to vanish. This is a structural restriction, and it is not shown that the resulting subspace is a consistent truncation of the full six-dimensional theory. The text says 'we are not able to find a consistent set of BPS equations with non-vanishing two-form fields'; this is an explicit open consistency question. Please provide an independent consistency argument for the scalar/vector sector used in §4, or discuss whether the omitted tensor fields could become nonzero once the BPS equations are embedded in the full theory.
minor comments (5)
  1. [Throughout] There are many typos and grammatical errors, e.g., 'gemetries', 'interpretrations', 'Upon uplifted', 'topological twits'. A careful proofread is needed.
  2. [Table 11 caption] The caption says 'obtained from SO(3) twist', but Section 4.2.2 is about an SO(2) twist. Please correct.
  3. [Figures 1–65] No numerical integration details are given: no method, tolerances, boundary conditions, or error estimates. Given the extensive parameter-space claims, adding reproducibility information or code would materially strengthen confidence in the numerical classification.
  4. [§3.3.1 and §4.2.1] The analytic solutions include integration constants C0 and C1. A short statement of which constants are physical moduli and which can be absorbed by coordinate rescalings would help.
  5. [References] Some arXiv identifiers are incomplete or malformed, e.g., ref [2] 'hep-th/9802.109' and ref [15] '250315954'. Please standardize.

Circularity Check

0 steps flagged

No circularity: the BPS equations are derived from the 6D SUSY variations with explicit twist projectors, and the acknowledged incomplete uplift is a support gap, not a circular step.

full rationale

The derivation chain is not circular. The first-order equations (e.g. (3.27)-(3.30)) are obtained by imposing δψ=0 and δχ=0 in the known fermionic supersymmetry variations (2.28)-(2.31) together with explicit twist/projector conditions (3.18)-(3.21), and are then integrated numerically; no parameter is fitted to a target physicality verdict. The [18] criterion is applied after constructing the solutions to classify singularities, not used to define the ansatz. The paper itself states the main limitation: "complete truncation ansatze for both type IIA theory on H^{p,q}×R^{4-p-q} or eleven-dimensional supergravity on H^{p,q}×R^{5-p-q} have not been worked to date" and that only ĝ00 can be computed from partial results [33,34]. This is an acknowledged support gap: if the full truncation is inconsistent or corrects ĝ00, the D4-brane/SQM interpretation could fail, but this is not equivalent-by-construction to the inputs. Reliance on the authors' prior papers [28-31] for notation, flat-domain-wall asymptotics, and analogous wrapped-brane solutions is ordinary extension of prior work, not a self-citation chain that forces the conclusion. The claim that BPS equations imply all field equations is asserted rather than shown, but that is an unverified check, not circular reasoning.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

No new particles, forces, or dimensions are postulated. The four-form field strengths, magnetic two-form potentials, and shift scalars used to satisfy Bianchi identities are all components of the known supergravity multiplet. What the reader must buy upstream is the supergravity framework itself plus the two interpretive assumptions (truncation consistency and the [18] criterion).

free parameters (4)
  • gauge coupling g = scanned values 0.1–4.04, signs chosen per gauge group
    Labels one-parameter families of numerical solutions. A genuine parameter of the gauged theory, scanned to map where IR singularities become 'physical', not fitted to a target result.
  • twist charges z1, z2 and magnetic charges p, p_ij, p1, p2 = scanned over e.g. (z1,z2)∈[-10,10], p1∈[-4,4]
    These select members of each solution family; the physical-region boundaries in (z1,z2) and p1 spaces are the classification output, so surviving subfamilies are defined by them.
  • integration constants C0, C1 in analytic branches = C1 = 0 vs C1 ≠ 0
    In the CSO(3,0,2) and CSO(2,0,2)⋉R4 analytic solutions the choice C1=0 selects the branch with g00 → 0 (declared physical). Standard constants of the general solution, but the branch selection is where the 'physical' label enters.
  • embedding-tensor signs p, q, κ, λ = κ, λ ∈ {0,±1}; p+q+r = 5 (or 4)
    Choose which CSO group is gauged; they enumerate the landscape of cases rather than being fitted.
axioms (6)
  • standard math Maximal 6D N=(2,2) supergravity with embedding-tensor formalism (from [27]) as the starting action
    The Lagrangian, supersymmetry transformations, and duality relations are imported from the cited construction; standard machinery in the subfield.
  • standard math The gaugings CSO(p,q,5-p-q) and CSO(p,q,4-p-q)⋉R4 embed in SO(5,5) as specified by Ymn and U^{np,m}
    Used to build all coset representatives and BPS equations; follows the established [28] decomposition.
  • domain assumption Consistent truncations of type IIA/11D on H^{p,q}×R^{...} exist and the partial results of [33,34] determine type-IIA g00
    The D4-brane interpretation and singularity classification depend on it; the paper explicitly states the complete ansätze are unavailable (p.4). This is the most exposed premise.
  • domain assumption Maldacena-Nuñez criterion [18]: non-divergence of g00 near the IR singularity suffices to call the singularity physical
    Every table's 'physical IR singularity' column is decided by this single test; no independent field-theory check is made.
  • domain assumption DW/QFT correspondence maps these singular domain-wall flows to RG flows ending in supersymmetric quantum mechanics
    The title's 'supersymmetric quantum mechanics' is never constructed on the field-theory side; its existence is inferred from the dictionary.
  • domain assumption The BPS equations imply the full set of bosonic field equations
    Asserted ('It can be verified', after (3.30), (3.59), (3.94)) without the verification being shown.

pith-pipeline@v1.3.0-alltime-deepseek · 93080 in / 18398 out tokens · 154376 ms · 2026-08-02T22:20:24.757017+00:00 · methodology

0 comments
read the original abstract

We find a large class of holographic solutions describing D4-branes wrapped on 4-manifolds $\mathcal{M}_4$ with constant curvature leading to gravity duals of supersymmetric quantum mechanics in the IR via twisted compactifications. The manifolds $\mathcal{M}_4$ considered here are four-dimensional spheres and hyperbolic spaces, products of two Riemann surfaces, and Kahler four-cycles. The solutions are obtained from the maximal gauged supergravity in six dimensions with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)\ltimes \mathbb{R}^4$ gauge groups. These gauged supergravities can be embedded in type IIA theory via consistent truncations on $H^{p,q}\times \mathbb{R}^{5-p-q}$ and $H^{p,q}\times\mathbb{R}^{4-p-q}\times S^1$, respectively. The solutions take the form of $t\times \mathcal{M}_4$-sliced domain walls interpolating between locally flat domain walls and singular geometries in the IR. Upon uplifted to type IIA theory, many solutions admit physical IR singularities and could holographically describe supersymmetric quantum mechanics arising from twisted compactifications of D4-branes on $\mathcal{M}_4$.

Figures

Figures reproduced from arXiv: 2602.17113 by Parinya Karndumri, Patharadanai Nuchino.

Figure 1
Figure 1. Figure 1: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The behavior of ˆg00 along the RG flows given in figures 1 and 2 respec￾tively for Σ4 1 = S 4 and Σ4 −1 = H4 in SO(5) gauge group. We now move to another class of solutions with asymptotic behaviors given by a locally flat domain wall with SO(4) symmetry of the form U ∼ V ∼ − 1 5 ln  − 5gρ √ 2  , φ ∼ −ϕ ∼ 1 25 ln  − 5gρ √ 2  . (3.35) 17 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
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Figure 5. Figure 5: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
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Figure 6. Figure 6: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
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Figure 7. Figure 7: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
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Figure 8. Figure 8: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
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Figure 9. Figure 9: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
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Figure 10. Figure 10: Regions (yellow) in the parameter space ( [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
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Figure 11. Figure 11: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
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Figure 12. Figure 12: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
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Figure 13. Figure 13: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
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Figure 14. Figure 14: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
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Figure 15. Figure 15: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p029_15.png] view at source ↗
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Figure 16. Figure 16: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p030_16.png] view at source ↗
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Figure 17. Figure 17: Numerical solutions interpolating between the locally [PITH_FULL_IMAGE:figures/full_fig_p031_17.png] view at source ↗
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Figure 18. Figure 18: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p032_18.png] view at source ↗
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Figure 19. Figure 19: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
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Figure 20. Figure 20: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p033_20.png] view at source ↗
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Figure 21. Figure 21: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p033_21.png] view at source ↗
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Figure 22. Figure 22: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p034_22.png] view at source ↗
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Figure 23. Figure 23: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p037_23.png] view at source ↗
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Figure 24. Figure 24: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p038_24.png] view at source ↗
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Figure 25. Figure 25: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p038_25.png] view at source ↗
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Figure 26. Figure 26: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p039_26.png] view at source ↗
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Figure 27. Figure 27: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p039_27.png] view at source ↗
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Figure 28. Figure 28: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p040_28.png] view at source ↗
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Figure 29. Figure 29: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p040_29.png] view at source ↗
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Figure 30. Figure 30: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p041_30.png] view at source ↗
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Figure 31. Figure 31: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p041_31.png] view at source ↗
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Figure 32. Figure 32: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p042_32.png] view at source ↗
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Figure 33. Figure 33: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p047_33.png] view at source ↗
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Figure 34. Figure 34: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p048_34.png] view at source ↗
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Figure 35. Figure 35: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p049_35.png] view at source ↗
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Figure 36. Figure 36: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p049_36.png] view at source ↗
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Figure 37. Figure 37: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p054_37.png] view at source ↗
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Figure 38. Figure 38: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p055_38.png] view at source ↗
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Figure 39. Figure 39: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p055_39.png] view at source ↗
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Figure 40. Figure 40: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p056_40.png] view at source ↗
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Figure 41. Figure 41: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p057_41.png] view at source ↗
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Figure 42. Figure 42: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p057_42.png] view at source ↗
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Figure 43. Figure 43: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p058_43.png] view at source ↗
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Figure 44. Figure 44: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p058_44.png] view at source ↗
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Figure 45. Figure 45: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p059_45.png] view at source ↗
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Figure 46. Figure 46: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p061_46.png] view at source ↗
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Figure 47. Figure 47: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p061_47.png] view at source ↗
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Figure 48. Figure 48: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p066_48.png] view at source ↗
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Figure 49. Figure 49: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p066_49.png] view at source ↗
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Figure 50. Figure 50: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p067_50.png] view at source ↗
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Figure 51. Figure 51: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p068_51.png] view at source ↗
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Figure 52. Figure 52: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p068_52.png] view at source ↗
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Figure 53. Figure 53: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p069_53.png] view at source ↗
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Figure 54. Figure 54: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p069_54.png] view at source ↗
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Figure 55. Figure 55: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p070_55.png] view at source ↗
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Figure 56. Figure 56: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p073_56.png] view at source ↗
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Figure 57. Figure 57: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p074_57.png] view at source ↗
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Figure 58. Figure 58: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p075_58.png] view at source ↗
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Figure 59. Figure 59: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p075_59.png] view at source ↗
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Figure 60. Figure 60: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p079_60.png] view at source ↗
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Figure 61. Figure 61: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p080_61.png] view at source ↗
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Figure 62. Figure 62: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p080_62.png] view at source ↗
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Figure 63. Figure 63: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p081_63.png] view at source ↗
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Figure 64. Figure 64: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p081_64.png] view at source ↗
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Figure 65. Figure 65: Interpolating solutions between the locally [PITH_FULL_IMAGE:figures/full_fig_p082_65.png] view at source ↗

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Reference graph

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