The SPIRAYA Framework II: Twistor Cohomology, the Geometric Origin of the Standard Model, and Structural Dark Matter

In SPIRAYA I we developed a stochastic event dynamics framework in which quan-
tum information processing in a unitary (U-) phase and discrete actualization events in
an event (E-) phase are coupled via a holographic soft gate. Coarse-graining the resulting
event cloud produces an effective stress-energy tensor that sources a generalized unimodular
gravity (UG) kernel, leading to a traceless Einstein equation and a dynamical ledger field
Λeff that integrates the non-conserved event current. A key conclusion was the Irreducible
Process Theorem: in SPIRAYA, macroscopic geometry can only couple to time-asymmetric
dissipative flows of events, while static microscopic structures are filtered out by a double
mechanism (unitary insulation in the U-phase and algebraic vacuum degravitation in UG).
This quantitative framework is directly derived from the core SPIRAYA philos-
ophy. In this second paper we move from a “field + particle” viewpoint toward a twistor
and information-theoretic picture of the matter and gauge sector. We interpret particles and
fields as sitting in a hierarchy of twistor cohomology classes H1(O(N )), where the integer
N labels layers in a complex-geometric stack behind 4D spacetime. Standard Model (SM)
matter is treated as residing in deeper layers of the twistor cohomology stack, separated from
the gravitational ledger at Ngrav = 2 by a cohomological distance Ndiff ≡ Nmatter − Ngrav.
We introduce a specific structural conjecture Ndiff = 15 in Section 4.4, and we stress that
it is a conjecture only. The physical weakness of gravity relative to the electroweak scale is
then reinterpreted as a topological distance in this twistor hierarchy rather than as a finely
tuned cancellation of local loop integrals.
On top of this geometric backdrop we construct a Hilbert–Schmidt operator space of
collapse channels and classify them under the adjoint action of the Standard Model gauge
group GSM = SU (3)C × SU (2)L × U (1)Y . This leads to a fundamental split of collapse
operators into a radiative sector Lrad transforming in non-trivial representations of GSM and
a structural sector Lstruct forming the gauge-singlet subspace. Radiative events necessarily
excite gauge fields and export entropy to the holographic boundary (in particular through
the outer U (1) layer parameterised by the fine-structure constant α), while structural events
rearrange stress-energy without sourcing SM gauge flux. We interpret Lstruct as defining a
structural dark sector : cold, collisionless, and electromagnetically silent, yet fully gravitating
through the ledger mechanism of SPIRAYA I.
We then revisit the question of why the SM gauge group GSM = SU (3) × SU (2) × U (1)
appears at all. Rather than treating GSM as a random point in a large string-theoretic
landscape, we formulate a holographic packing problem: how can a universe bounded by
an area-scaling entropy capacity maximise bulk information processing while avoiding three
instabilities—a “volume catastrophe” from unconfined colour, a “thermal catastrophe” from
inefficient cooling, and an “interface catastrophe” from the absence of a chiral gateway be-
tween storage and radiation? Under explicit assumptions we show that SU (3)C , SU (2)L and
U (1)Y play three distinct functional roles in this architecture: SU (3)C realises high-density
storage with infrared confinement, U (1)Y /U (1)EM provides a linear radiation channel for
entropy export, and SU (2)L serves as a minimal chiral interface between storage and ra-
diation. In twistor language, these roles correspond to specific features of the cohomology
stack and its outer boundary: U (1) defines the ledger interface at N = 1, SU (2) implements
intrinsic chirality of twistor geometry, and SU (3) supports confining internal fibres for dense
coding.
We refine the geometric-leakage picture of the electroweak–Planck hierarchy into a lay-
ered attenuation mechanism. Matter degrees of freedom are treated as separated from the
gravitational ledger at Ngrav = 2 by a distance Ndiff ≡ Nmatter − Ngrav. We discuss a
specific conjecture Ndiff = 15 in Section 4.4 (conjecture only), while emphasising that the
structural-sector phenomenology and null predictions developed in this paper do not depend
on fixing Ndiff to a particular integer.
A simple layered-attenuation ansatz can be written as MEW/MP ∼ α Ndiff /2
⋆ , where
α⋆ < 1 is an effective per-step factor. If one adopts the conjectural value Ndiff = 15, the
implied α−1
⋆ is of order 102 (numerically close to α−1), but this numerology is not used in any
of the concrete predictions of this paper (e.g. the Structural Null Theorem and cross-section
scalings).
Subsequent sections develop the phenomenology of the structural dark sector, arguing for
a strict null prediction in non-gravitational direct-detection experiments within the minimal
SPIRAYA realisation. Finally, we discuss how the 2α link between microscopic electro-
magnetic structure and macroscopic ledger efficiency—derived in Paper I via a one-loop
EFT analysis—closes the loop between the effective field theory description and the present
twistor-informed architecture.