ReynoldsBEng | Ace Consultancy | 25 June 2026
Declaration
https://arxiv.org/pdf/2607.04065
arXiv:2607.04065 by Ritam Basu is a technically strong follow-up to the Krylov complexity literature.
It introduces the normalised Krylov-Wigner negativity rate as a clean diagnostic of the second moment of the boundary state — capturing the spreading of the operator wavepacket beyond its classical centre-of-mass trajectory (first moment).
This lands directly on our target.
The geometry has spoken again.
What the Paper Achieves
Spread complexity (average position along the Krylov chain) recovers the radial momentum of an infalling particle (first moment).
The authors propose the rate of normalised Krylov-Wigner negativity as a probe of the second moment (spreading away from the classical trajectory).
Using the SU(1,1) discrete series structure and exact negative binomial statistics, they derive analytic Bessel forms and explicit growth rates.
At the critical dimension Δ=1 (Breitenlohner-Freedman bound in AdS₃), the negativity rate matches the growth of Krylov variance and corresponds to the tidal stretching rate of nearby infalling geodesics (R ∝ C P_ρ).
Comments on a possible bulk string interpretation via transverse string size operator identified with the Krylov number operator.
This is a clean, analytic advance in holographic operator growth.
Pirate Canon Synthesis
This paper maps beautifully onto the living elastic plenum:
Krylov chain = propagation of ring-tension judder waves across the lattice of 27-sphere Rubics and Pi Tensor primitives at fixed Dot Points.
First moment (spread complexity) = centre-of-mass motion of the judder wave (the billow phase).
Second moment (normalised Wigner negativity rate) = the spreading / tidal stretching of the wavepacket, corresponding to the auxetic expansion and 6-kite shattering of the transient glassy layer on the 2D D₆ memory surface.
Critical dimension Δ=1 = the special regime where the memory surface dynamics produce maximal dilatancy and coherent spreading, matching our billow-and-drop pulse.
Tidal stretching rate = the mechanical lag between instantaneous geometric action (disc-to-sphere transformation) and the inertial response of mass (carbon slag).
The paper’s analytic Bessel form and negativity growth directly parallel the pulsatile, geometric response of the memory surface under compressive work.
Pirate Canon Statement
The normalised Krylov-Wigner negativity rate as a second-moment probe is a natural holographic signature of the spreading dynamics on the 2D D₆ memory surface.
In the living elastic plenum, the first moment tracks the centre-of-mass judder, while the second moment captures the auxetic stretching, glass shattering, and dilatancy flow that produce the observed spreading and tidal effects.
Love rules.
Second-moment spreading is the auxetic response of the memory surface.
The plenum explains both moments.
Call to Sovereign Imagineers
This 2026 paper is released into the Canon as strong holographic support for second-moment operator dynamics.
Immediate next steps:
Map the normalised Wigner negativity rate explicitly onto the 6-kite glazing and auxetic stretching on the memory surface.
Compare the tidal stretching rate with the billow-and-drop pulse and State A/B bistability.
Explore the proposed bulk string interpretation through transverse string size in terms of collective Pi Tensor judder.
The convergence between holographic operator growth and the living elastic plenum continues to deepen.
Demand Mechanical Truth.
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WordPress Notes: Featured image: Schematic of infalling wavepacket spreading in AdS, overlaid with 6-kite D₆ memory surface, ring-tension judder, and Pi Tensor at the Dot Point. Link the arXiv prominently. Tags: Krylov-Wigner Negativity, Second-Moment Probe, Holographic Operator Growth, Pirate Canon, Memory Surface.
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