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REVIEW 2 major objections 5 minor 45 references

Snakes climb vertical walls by balancing force across many extra contacts and reshuffling that network every time a new foothold is added.

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2026-07-11 07:17 UTC pith:MCHXHZSE

load-bearing objection Solid multi-contact force data on limbless vertical climbing: redundant balance, null-space redistribution, and ascent contacts that do positive work beyond a passive baseline. the 2 major comments →

arxiv 2607.06239 v1 pith:MCHXHZSE submitted 2026-07-06 physics.bio-ph

Redundant contacts and force redistribution stabilize limbless vertical climbing

Calvin A. Riiska , Michelle Lee , Yonatan Nemenman , Gauge Thacker , Joseph R. Mendelson III , Jennifer M. Rieser This is my paper
classification physics.bio-ph PACS 87.19.lu87.85.gj45.40.Ln
keywords limbless climbingforce redistributionredundant contactsquasi-static balancecornsnakepassive frictionserpenoid wavevertical locomotion
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.

Cornsnakes can climb a smooth vertical wall studded with sparse posts even though they have no feet and cannot wrap the surface. They do it by holding five to sixteen contacts at once—far more than the three needed for force and torque balance—and by treating the whole set as a reconfigurable network. A simple computer model and an open-loop robot show that a traveling body wave plus ordinary sliding friction is already enough to go up and down. Live snakes, however, systematically leave that passive baseline: on the way up they generate positive mechanical work at many contacts, and every new contact triggers a rapid, stereotyped redistribution of force that stays almost entirely inside the space of balanced solutions. The paper therefore argues that limbless climbing on nearly flat surfaces is not a matter of isolated footholds but of managing a redundant, balance-preserving contact network, a principle that both explains how climbing evolved repeatedly in snakes and supplies design rules for agile robots.

Core claim

Cornsnakes climb quasi-statically by dynamically balancing forces across a highly redundant network of 5–16 simultaneous contacts; whenever a new contact is engaged they execute a stereotyped, system-wide force redistribution that remains largely inside the null-space of the three quasi-static balance constraints, while ascending snakes actively generate positive tangential work at contacts beyond passive Coulomb friction.

What carries the argument

Balance-preserving force redistribution (the null-space component of Δf after each new contact): the excess contacts open a high-dimensional space of force configurations that all satisfy net Fx = 0, Fy = Mg and torque = 0, allowing the animal to reassign load without ever leaving quasi-static equilibrium.

Load-bearing premise

That the measured positive tangential power on ascent is an animal-specific active strategy rather than an inevitable geometric side-effect of the body wave interacting with the posts under the paper’s contact-centroid and velocity-threshold definitions.

What would settle it

If an open-loop robot whose body wave and post geometry exactly match those of the snakes produces the same fraction of positive-power contacts as the live animals, the claim of systematic active deviation collapses; conversely, if snakes still generate positive work after the contact-classification thresholds are varied over a wide range, the claim is strengthened.

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

If this is right

  • Redundant contacts are not wasteful overhead but the mechanical resource that lets a continuous body absorb contact gain and loss without falling.
  • Passive body-wave + friction robots can already climb sparse vertical arrays; adding local force redirection at new contacts should raise reliability on shorter or sparser posts.
  • The same null-space redistribution principle supplies a biomechanical explanation for why climbing evolved repeatedly in limbless lineages that lack specialized attachment organs.
  • Gait switches (lateral undulation versus concertina) can be understood as different ways of sampling the same balance space when contact density changes.

Where Pith is reading between the lines

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

  • The same null-space logic should apply to any multi-contact soft robot or organism that must remain balanced while contacts appear and disappear, including soft grippers and multi-legged walkers on irregular terrain.
  • If force redirection is accomplished by local skin–rib musculature rather than global neural feedback, then distributed tactile sensing along the ventral surface becomes the key missing hardware for snake-like climbing robots.
  • Kingsnakes that fail on the same wall may simply lack the ability to keep rearrangements inside the null-space, offering a comparative test of the redundancy hypothesis.

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

2 major / 5 minor

Summary. The manuscript reports that cornsnakes ascend and descend a smooth vertical wall instrumented with force-sensing posts by maintaining a highly redundant network of 5–16 simultaneous contacts, far above the three contacts required for planar force/torque balance. Climbing is quasi-static (net Fx ≈ 0, Fy ≈ Mg, torque about CoM ≈ 0; accelerations small). A prescribed-serpenoid computational model with passive Coulomb friction and an open-loop robotic climber both succeed with only 3–4 contacts, establishing a minimal passive baseline. Snakes systematically deviate: descents are largely dissipative (effective µ ≈ 0.22), while ascents produce positive tangential contact power (Pt = Ft · vt > 0) at >40 % of dynamic contacts. New-contact onset triggers a stereotyped, largely null-space force redistribution that preserves whole-body balance, with amplitude and spatial pattern depending on post length and spacing.

Significance. If the measurements and null-space analysis hold, the work supplies a concrete biomechanical mechanism—redundant multi-contact force sharing plus balance-preserving redistribution—for limbless climbing on low-curvature surfaces that cannot be encircled or braced. The dual passive baselines (simulation + physical robot) cleanly separate mechanical sufficiency from the animal’s active strategy, and the open data/code repository strengthens reproducibility. The results are directly useful for both evolutionary biomechanics (repeated evolution of arboreal climbing) and the design of limbless robots for unstructured vertical terrain. The energetic (rather than neural) definition of “active” and the planar sensing limitation are acknowledged and do not overturn the central multi-contact claims.

major comments (2)
  1. Results (contact-power analysis) and SI S5: classification of contacts as dynamic/active rests on a 3 mm/s velocity threshold and a distance-weighted contact centroid φ. While the open-loop robot and passive model produce predominantly dissipative contacts under comparable geometry (Fig. 3q, SI Fig. S7), a brief sensitivity check on the threshold (or an alternative sliding criterion) would confirm that the ascent–descent sign reversal of Pt is robust rather than threshold-dependent. This is not fatal to the central claim but would tighten the “systematically deviate” language.
  2. SI S4 and main-text footnote 2: out-of-plane forces were measured on only a single post and found small (∼1–5 % body weight). The claim that the snake remains below the static-friction limit and that planar balance is sufficient therefore rests on limited sampling. A short statement quantifying how large an unmeasured Fz would have to be to violate the quasi-static planar constraints would close this residual uncertainty.
minor comments (5)
  1. Fig. 2 legend and panels f–h: the phrase “center near balance” is qualitative; adding the numerical means ± s.d. (or the few-percent figures already stated in the text) would make the quasi-static claim immediately quantitative.
  2. Methods (Quasi-static climbing model): the penalty stiffness K and the precise serpenoid parameters (κ m, λ s, nw) used for the “best-matching” waveform are not tabulated; listing them (or pointing to the code repository values) would aid exact reproduction.
  3. Fig. 5e–g: fit-parameter uncertainties are described as “overlapping”; showing the hierarchical bootstrap distributions (already performed in SI S7) as error bars or violin plots would make the trade-off between α and β visually clearer.
  4. Abstract and Conclusions: “fault-tolerant network” is used without a direct perturbation experiment (e.g., sudden post removal). Softening to “redundant, balance-preserving network” would keep the claim strictly within the data.
  5. SI Movie captions: post spacings are listed as “50 cm” and “100 cm” in several places; these should be 50 mm / 100 mm to match the main text.

Circularity Check

0 steps flagged

No significant circularity: central claims rest on direct multi-contact force/kinematic measurements compared to independent passive baselines

full rationale

The paper's load-bearing results are (i) measured contact counts (5–16) exceeding the three quasi-static constraints of Eq. 1, (ii) direct observation that net force/torque remain near balance, (iii) contact-power sign reversal (Pt = Ft · vt) on ascent versus descent, and (iv) stereotyped null-space force rearrangements after new-contact onset (Fig. 5, SI S6). The computational model and open-loop robot establish only a passive baseline (prescribed serpenoid wave + Coulomb friction) that succeeds with 3–4 contacts and predominantly dissipative contacts; they are not fitted to force the snake's positive-power or redistribution results. µ ≈ 0.22 is extracted from descent data solely for comparison and is not used to construct the ascent observation. Waveform parameters are chosen to approximate observed shapes and speeds, but the models are not claimed to predict the animal-specific force patterns. No uniqueness theorem, self-citation chain, or definitional identity reduces any central claim to its inputs. The work is self-contained experimental + modeling comparison against independent passive controls.

Axiom & Free-Parameter Ledger

6 free parameters · 4 axioms · 0 invented entities

The experimental claims rest on standard quasi-static mechanics and Coulomb friction plus a small set of measurement and modeling choices (contact thresholds, serpenoid wave parameters, penalty stiffness). No new physical entities are postulated; the “active” label is an energetic classification, not a new force law.

free parameters (6)
  • kinetic friction coefficient µ_k = ≈0.22
    Extracted from dissipative descent contacts (≈0.22) and used as the passive baseline against which ascent forces are compared.
  • serpenoid wave parameters (κ_m, λ_s, v_c, n_w)
    Chosen to approximate observed body shapes and center-of-mass speed in both the computational model and the robot.
  • contact penalty stiffness K
    Sets the magnitude of the repulsive spring force that enforces non-penetration in the quasi-static model.
  • dynamic-contact velocity threshold = 3 mm/s
    3 mm/s cutoff used to classify contacts as dynamic versus static for power analysis.
  • contact distance threshold = 17 mm
    17 mm body-to-post distance used to declare a contact for force attribution and kinematics.
  • force detection threshold = 0.21 g
    0.21 g (3× sensor noise) used to mark contact onset.
axioms (4)
  • domain assumption Climbing is quasi-static: net force and torque about the center of mass remain approximately zero at every instant (Eq. 1).
    Supported by measured Fx,net ≈ 0, Fy,net ≈ Mg, τ_net ≈ 0 and small accelerations, but remains an idealization used throughout the analysis.
  • domain assumption Contact forces obey kinetic Coulomb friction opposing local sliding plus a unilateral normal reaction.
    Standard dry-friction model used for the passive baseline and for interpreting positive Pt as non-passive.
  • standard math Three independent balance constraints (Fx, Fy–Mg, τ) define a null-space of admissible force redistributions.
    Linear algebra of planar rigid-body equilibrium; used to decompose Δf into balance-preserving and residual parts.
  • ad hoc to paper Body shape can be prescribed as a traveling serpenoid wave without solving internal muscle dynamics.
    Simplifies the computational and robotic models to open-loop kinematics; sufficient for the minimal-baseline claim but not claimed to be the animal’s control law.

pith-pipeline@v1.1.0-grok45 · 24945 in / 2965 out tokens · 26126 ms · 2026-07-11T07:17:36.533941+00:00 · methodology

0 comments
read the original abstract

Animals navigating complex vertical environments must secure stable footholds, a challenge for species without feet. While arboreal climbing has evolved repeatedly in snakes, the physical mechanisms they use to scale broad, nearly flat surfaces remain poorly understood. By measuring three-dimensional body kinematics and per-contact forces on a smooth vertical wall with protruding posts, we show that cornsnakes climb by dynamically balancing forces across a highly redundant network of 5 to 16 simultaneous contacts--far exceeding the three contacts minimally required for physical stability. Using a computational model and a robotic climber, we demonstrate that while simple body undulations and passive friction are mechanically sufficient to climb this terrain, snakes systematically deviate from this passive baseline. While downward climbing relies primarily on friction, ascending snakes actively generate positive mechanical work at their contacts to propel themselves. Furthermore, we found that whenever a snake engages a new contact, it triggers a stereotyped, system-wide redistribution of force that seamlessly integrates the new foothold without disrupting whole-body balance. These results reveal how a continuous, flexible body can transform sparse environmental features into a robust, fault-tolerant network. This mechanism provides a biomechanical framework for understanding the repeated evolution of limbless climbing and offers physical principles for designing agile robots for unstructured terrain.

Figures

Figures reproduced from arXiv: 2607.06239 by Calvin A. Riiska, Gauge Thacker, Jennifer M. Rieser, Joseph R. Mendelson III, Michelle Lee, Yonatan Nemenman.

Figure 1
Figure 1. Figure 1: A force-sensing wall resolves body kinematics and per-post forces [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Across substrates, snakes have variable kinematics but maintain force balance. All panels are probabil￾ity densities pooled across trials, for ascent and descent in three post configurations (leg￾end, a). (a) Center-of-mass speed: simi￾lar up and down, slower on shorter posts. (b) Body curvature κ: similar across con￾ditions. (c) Number of simultaneous con￾tacts: more on closely spaced posts, fewer when wi… view at source ↗
Figure 3
Figure 3. Figure 3: Computational and robotic models reveal the minimal requirements for [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Downward climbs have mostly dissipative interactions at con￾tacts while upward climbs are active. (a) Heatmaps of Ft and vt with quadrants marked “A” and “D” respectively indicate active and dissipative contacts respectfully. Dissipation in downward climbs matches sim￾ulated predictions while upward climbs, in￾cluding the trial that the model was based on (red “x”) involve active contacts. Distri￾butions o… view at source ↗
Figure 5
Figure 5. Figure 5: Force redistribution is stereotyped and balance-preserving. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

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