Summary Information
of Texts
The following is a general overview and chapter-by-chapter summary of the unique physical knowledge
and data in
241 Mumbers - the
Definitive Data for Fundamental Physics and Cosmology, as well
a short overview of its auxiliary text
Projective
Geometry and its Regional Subgeometries.
In essence, these books establish a categorically consistent and complete system
of, or isomorphism between, `pure’
Mumbers
or
‘Membrane
Numbers,'
the deepest tenets of geometry and interfacing principles of cosmological
physics. As such, 241-Mumbers constitutes the only precise, predictive,
explanatory system defining nearly every fundamental parameter, and addressing
solutions to the major contemporary problems, in universal evolutionary physics.
241 Mumbers: The Definitive Data for Fundamental Physics and Cosmology:
Preface: The history of A. J. Meyer's model, the Millennium questions and the
'Monolithic' solution to Gross's
quandary concerning a "dimensionless physics" devoid of free-parameters. Some personal
reflections on religion, science and psychology are given with respect to
a predictable abreaction to pure numerical analysis; with hints from learning theory on transcendence of self-limiting beliefs
or assumptions. This lesson is augmented by a couple of objective tasks
similar to the chosen equations of our
Sample Data and Proofs.
Introduction to the Tautology of 241 Mumbers via a
Co-Derivation of Global Coupling Constants establishes an
exacting numeric invariance
for a dimensionless physics tied to a time-tested material metric of
the combined proton and electron mass. The derivation of the "Monolith
Number," the essential, multi-dual mumber, 'dimensionless scale,' constant
and cosmological field of the 241 system. Which subsequently also yields the
exact (inverse) electromagnetic fine-structure constant expressed as a 'pure' number;
discretely derived without any
reference to 'metric dimensions' of mass, length or time. By contrast, the 'Planck scale' of
'quantized gravitation' is connected to both the empirical metric of,
and a pure Planck scaling to, ordinary matter; allowing a categorically
complete and consistent co-derivation of the gravitational coupling constant as
well. The Monolithic Tautology thereby represents a definitive discrete, or quantified, unification of the three large-scale
fields and coupling constants representing a 'World-tensor' in an over-due
update of 5-Dimensional Kaluza-Klein/Einstein-Bergmann Space-Time.
The Monolith is
further essential for precise derivations of
Table I: The Fundamental Particulate Scale, as augmented by a supersymmetric Higgs mechanism that generates mass, with a special theoretical eye on the origin of baryon matter, together with ‘dark mass.’ So the first equations of this table determine the mass of, and relations between, the four Higgs bosons and its two vacuum doublets, as well as the two charge-less gauginos, the Wino
(or 'chargino'), and neutralino (or 'higgsino') basically the 'left-over' component of the extended SUSY Higgs spectrum equivalent to a stable, heavy charge-neutral
'Fermi dark mass.' With further derivations of the
W and Z
weak vector bosons and each of the six quarks; providing the first 'pudding'
proofs' of
the hard values of the Higgs field, gauge bosons and quarks, as witnessed the by
Z-boson derivation of the Sample Data. Which leads to calculations of a
few essential hadrons, concluding with preliminaries of neutrino sector
mixing that offers a precise value and definition of an axion as 'Bose dark
mass.' In any case, multiple approximations will often be used to illustrate or explore any number issues for strong or less secure parameters alike,
although
the best value for that parameter will generally be apparent in the
corresponding cell of Table-II. Which, however, is not necessarily applicable to
Table-I,
where some calculations are left 'potentially incomplete' as non-optimal values
and equations compared to improved or expanded renditions found in the second table.
For here the reader, with minor help, is left to their own devices to spot which
values may be left 'purposely,
incomplete' relative to other calculations that won't be modified at
all in
the extended table. This ambiguity is designed as a prod to provoke professors, students or interested
laymen alike to pursue additional hands-on home-study without reference to Table-II.
Likewise, the first objective task given at the end of the Preface refers to a parameter
and equations in one of the expanded table's most prominent cells: so an ideal set-up {tailored cheaply to e-subscribers}1a,b
is designed to discourage a peek before one can venture an answer without a
cheap cheat. Which then either A: serves as a test to bolster confidence in
one's intuitive perception and logical competence as an 'open
skeptic' and 'seriously interested learner;' or B: serves to test a 'closed skeptics' fixation on mechanical
measure and collective opinion or interpretation; as manifested with utter focus on one's self-perceived role, problems,
given status or job in maintaining this system of institutional
belief0,1c
by slowly adjusted, incremental refinements involving many researchers and
departments. But, as note-1b reiterates, the latter hub is only weakly conducive
to a
broader 'paradigm shift' required for a so-called 'Theory of Everything' (TOE),
although it's highly conducive to easy contemporary reference {research, peek,
then repeat even minor references} or rote habit.1c
Still, just as reference is an inevitable facet of scientific inquiry, taking the
easiest path is not only an endemic of part of human nature, but serves the better purposes
of scientific inquiry if it cuts through to endless details and
formality to get a meaningful solution to the problems at hand - but certainly not
if used just a guise for an inability to investigate what isn't diligently sought
with open curiosity, honest interest and the meaningful intent of one's own
reasoning.1b-c,2
Table II: The Extended SUSY and Standard Particle Spectrum:
the full table covering the entire swamp of mass-derivations and loose theoretical briefs
augmenting the above parameters. In addition to the Higgs fields and gauginos, the
'sparticles' includes the gluino, all six squarks,
charged sleptons, their sneutrinos, and a photino. With essential details
of strong gluino and heavy squark decays to lighter ones that subsequently
undergo gaugino mediated transformations resulting in the creation of baryon
matter; along with the Fermi component of the heavier neutralino, in addition to
the Bose element of axion dark mass.
Which also offers the solution to the
'flavor hierarchy' or 'generation-inverted SUSY' problem, as well as clues to super-symmetry breaking
as a prelude to electro-weak symmetry breaking, culminating in
a precise derivation of the Fermi
Energy of the Weak coupling constant. The format of
a descending mass-scaled data-table accordingly provides a succinct
forum for a working comprehension of the deepest theory (saving an expository
discussion for the Summary subsection), which conversely is
naturally encoded into equations that largely utilize ordinary arithmetic
to define each mass-parameter of the complete particle spectrum.
Likewise, each equation encapsulates revelations of
often multiple, and/or indisputable, physical principles, in addition to
the crucial precision of
numeric invariance that mirrors the Monolith Mumbers' fundamental 2-based exponential
tautology, which 'sets' the invariantly strongest, most immutable, or definitive parameters such as
the mass of the Heavy Higgs scalar. Which furthermore provides numerous mathematical, theoretical and empirical
cross-confirmations of not only the (already) definitive mass-values for all six
quarks, as well as equally definitive
supersymmetric precepts and values for sparticle masses such as squarks
and gauginos, by comparison with
derivations and values of a relatively well-established standard particle spectrum
ranging from the Z and W gauge bosons
to over 50 hadrons. Thus, once an individual masters the basic tautology, system
and equations, they
can
confirm
the derived mass-values of weak gauge bosons or hadrons themselves by a similar empirical imperative for hands-on
learning2 - by comparison
with their measured
values, most of which are given and downloadable from the
particle data group site at
http://pdg.lbl.gov/pdg.html (for the
sake of invariant consistency all basic parameters are in accord with the PDG and NIST
http://nist.gov/ measurements of 2000: so gather
these first from their archives). In any case, each parameter is evaluated by a
uniquely annotated, starred system of confidence that is pragmatic, instructive
and entertaining; serving as a central forum for a compact, often witty,
commentary. (The wise will find the multiplicity of dark humor and pointed poetic asides are
not only core to a short-hand for rating arguments in a creative system of
learning, but also serves as a mnemonic prep for a higher theory that is not to be
ignored. Yet such word-play will also serve to make others walk right out the
first door: a main reason Notable Rants is included as a
rudely blunt, 'purposely off-setting' X-rated sampling.0-1a)
Beginning with a determined value of the Upsilon-4s or B-B
resonance, calculations are given for various bottom flavored bosons
down to the neutral (bd-bar) and charged (u-) B-mesons; which gives extended
support for our 2nd
Sample Proof, b-mesons being
dominate products of Zo (or toponium) decay. Likewise, calculations
of
b-baryons range from a unique SuSy based prediction for the Omega-bss down to a
highly determined Lambda-b mass,
with hard theoretical deductions, calculations, and 'proofs'
for
intervening values of
both charge and spin mass states of the b-Sigma's,
as well as yet unmeasured masses for the -charged and neutral Xi-b. Table II moves to charmed
hadrons, beginning with unprecedented predictions for the ccc-Omega and three cc-Xi's;
with calculations that similarly serve as demonstrative proofs based on interrelations between the SUSY sCharm/sTop differential, quark derivations conforming to other higher states of
charmed flavors of positive charge and spin and logical comparison of decays of the W++-ccc
into a ucc-X++,
or of the spin 3/2 ucc-X++ into
a dcc-X+
and a +pion. (Which all in all accounts for a set of quite nuanced
proofs, though these value presently are largely unavailable as empirical
measures of pudding in the sense that the '04-6 pdg-listings only
gives the ccd mass; as editors at lbl were apparently baffled by rather convincing SELEX
data for the two ccu-Xi spin states. So though our comparative calculations fit
cc-Xi data too well not to recognize there's piles
of pudding on the table - the initial reaction to the
data in the general physics community was absolute surprise, owing to a novel large gap between the cc-Xi's
containing the up quark and the one with down; which misses some major points).
Anyway, we go on to derive masses of the J/psi and eta cc-mesons
before moving to singly charmed c-baryons, with charmed Omega,
Xi's and Sigma's of
both J= 3/2 and 1/2 spins, the double-charged cuu-Sigmas constituting a third
state of slightly higher mass (due to more repulsive q-charge) than the neutral cdd
in both cases. These heavier c-baryons are scaled with respect to differentials
to the base state c-Lambda+
- whose mass is determined by a calculation from a Wino and/or its decay - which
contrasts with the following equations to provide the most nuanced set of
demonstrative proofs and broad supersymmetric correspondence in this table. The case in point involves
strikingly
instructive derivations of
the charming D+ cs
and cd mesons utilizing
appropriate SUSY modifications of a similar equation as a function, and main
decay product, of a (by convention, positively charged) W-boson (and goes on to define the tau
lepton mass by an equally
revealing modification). Two auxiliary calculations not only give a precise
correspondence for the cd-D+ mass within an order of about 1/10,000,000 parts,
the most important being a direct derivation from the given c and d quarks that serves as a
proof for the neutral D as well - the real pudding here being the multiple
calculations and correspondences, the multiple accurate correlation with measure being
here only a
little cherry on top, marinated by the chef in a sherry wine2b. In
any case, the hadron table next moves on to
strange
baryons, all calculations, except for the
sud-Lambda per se, being determined by a different route that the differential
of charmed Omega, Xi's and Sigma's to a
c-Lambda
- as multiples of the strange mass, with appropriate modifications involving combinations of the down and up. We
then go on to give the derivation of the time parameter for beta-decay of a free
neutron to a proton, electron and an antineutrino, completing the equation given as the
4th example of Sample Data. Which serves as a
perfect introduction to a precise derivation of neutron mass as a ratio to our
basic p+e-gauge. Having exhausted baryons, we
finalize analysis with a review of the strange K and pi mesons
developed in the first table. We proceed to list the
various combinations of first generation quarks composing the basic light baryons
and mesons, the same mass differential in each class of hadron constituting our 3rd,
and Best Proof in theory, application or pudding. This hadron schematic is
supported by equally precise, and revealing, electroweak derivations for the tau
lepton and
muon, that together with the measured mass of an electron produced in
W-mediated weak beta-decay, compose the three types of charged lepton that
may be created, along with a respective flavor of neutrino, in a direct
decay of a ('non-virtual') W-boson. The attendant scaling in sum provides clues to the
time-decay parameters for the tau or muon into neutrinos, which, in addition to
the given
t-parameter for neutron decay
into a proton, electron and e-antineutrino, supplies an
exacting framework for analysis of neutrinos as having a definitive weak mass at
the moment of creation. Yet thereafter they can oscillate to another mass-value by
virtue of 'flavor mixing' - where, for instance, we give a precise calculation
for the 'e-mu mixing angle'
that accords with its experimental value,
further also accounting for the suppressed 1/3 ratio of electron neutrinos to
theoretical estimates of massless ones. Which must then also
determine the `base-value' of the electron {or
analogously, a tau or mu} neutrino
mass,
as a function of its very definition as a fermion conforming to the
monolithic tautology of mumbers, as specifically compared to a relatively stable dark mass
that defines an axion as a boson - with respect to a common scale representing
what can be called a "broken charge-, or 'charge-neutered',
symmetry."
Mumbers and the Monolith Numbers: I:
The broader, more philosophical underpinnings of our Introduction's Tautology
on significance of the Monolith Number to not
only a dimensionless physics, but a
number of other pertinent Strings 2000 `Millennium Questions’ as well.
The
Unified Universal Meta-Physics of Monolith Mumbers: from Socrates to Oskar & Felix Klein,
and Beyond
begins with a few reflections on the unfinished business of synthetic dialectical discourse from the Socratic school
unto the 'formal simplicity' F. Klein perceived could serve as a final basis for Einstein's
extension of the (O.) Klein-Kaluza unification. We then briefly demonstrate how
debates in religion, science and politics can consistently be linguistically resolved within a
synthetic and 'holistic' natural philosophy, beginning with a firm geometric, numeric
and meta-logical basis for One 'Wholistic' Unified Physical Theory.3 Which
leads to a discussion of the significance of such issues to the development of a dimensionless monolithic meta-physics, a finite, sentential Hilbert algebra and multiple
(Godelian) meta-mathematical (numeric-geometrical-logical) 'mappings' for an 11-dimensional physical membrane.4
II: Initial-State Quantum Gravitation:
minimal entropy and the significance of an initial-state, antisingular
Planck-Motz 'primaton' to Creation. With exacting equations and illustrations that demonstrate how an initial-state
anti-singularity/wormhole theorem gives rise through quantum gravitation to
an internal 6-dimensional
manifold of superstring spin-replications that evolve unto a classical de Sitter Era of
Cosmic Creation. III:
Which leads back to a discourse on the basic meaning of
The Monolith Number as a
'Multi-Dual' Cosmic Constant, primordially represented by Meyer's
precise derivation of the `conserved,' or so-called 'critical,' Universal Mass! With the history and
introductory comments about this constant, followed by an overview of the
evolutionary substages of de Sitter Inflation mapped with respect to a `dimensional reduction' and `projective sectioning'
framed with respect to an increasing subscale of the monolithic space-time membrane.
Summary Flow of Cosmological Eras, Parameters and Geometries: An
review and extended description of the spatial stages, temporal eras and parameters
defining universal creation, inflation, the post-inflationary era and
latter cosmic evolution extending from the big bang to our present era, unto the
end of time. Twenty more pages are devoted to the Extended Era of de Sitter
Inflation, as co-driven by supergravity - with radii,
mass-densities and superluminal velocities at various stages up to its
termination. Which is followed by an extended discussion of Table II's deductions
concerning
the
Super-Symmetry
Era and the Origin of Baryon Matter and Dark Mass. Beginning with a few speculations about a dual role
of supergravity in the pre and post inflation eras, we review the resultant theory
(that serves as a prelude to this subsection's conclusions), with additional specifics of sparticle decays outlined in the extended table. A detailed explanation of strong gluino and first generation squark
decay follows: resulting in a multiplication of 2nd and 3rd
generation
squarks, as accompanied by a progressive co-production of a gluon (or massive 'glue-ball like' ) plasma
and a relatively co-stabilized or mass-conserving axion field -
which at least also furthers a concise derivation of the parameter
(measured in GeV)
representing the coupling constant associated with axion decay into photons (in
the presence of a strong magnetic field). The discussion then proceeds unto the
latter stages of the SuSy era representing gaugino mediated conversion of
these lighter squarks - resulting in baryogenesis, with an accordant explanation
for the origin of neutralino dark mass as well. Though this solution for the
origin of baryon matter is a revolutionary affront to, or (supersymmetric) upturning, of certain
common assumptions, it at once accommodates and accounts for standard theory or
interpretation - for example, it allows the exact determination of the two `CP-violating' decay modes
of the neutral K-meson into pions, which provokes some remarks about similar reasoning
involved in determining our final value for the Ko mass per se. This
subsection concludes (as it began) with a comparison of the hypervelocity at the
terminal inflation radius to a necessary highly conserved mass, so maximal gravitational field, during and up
to Super Symmetry Breaking
- that specifies its
space-time parameterization
as well. Which proceeds to compare the mechanisms of, and review the
mass-energies at which, the respective Super and Electro-Weak Symmetries are Broken,
concluding with a discussion of glue-balls that decay as mesons, deriving the
most likely candidate from a neutrally modified version of what we define
as a `base glue-ball' utilized in another context for a 'left over mass of a
glue-ball like binding mass-energy for the component quarks (or as if they are
removed) - a principle that holds for mesons or baryons alike - especially with
respect to our base p+e-gauge..
Which very naturally leads to a shorter subsection giving precise
Critical Mass
Percentages of baryon
matter, neutralino antimatter (oops!), as well as axion
dark mass. Which can interpreted in three manners: as a percentage of Planck
mass, a percentage relative to the 'critical
universal mass' gauged in terms the particle in question, or (the {only} way to determine the mass-percentage of neutralinos) as
ratios to a single gluino (since once they begin to decay, quantum principle
limits what anyone can say). In any case, the remainder of 'critical mass'
represents 'quintessence ' or 'dark energy' (whose discrete mass-energy
is specifically co-defined by the Monolith under an inverted duality). In the next subsection, the
minimum mass and horizon radius of a stellar blackhole are explored -
essentially determining the Minimal Blackhole Horizon Radius. Which is not just
framed in usual terms of a Schwarzschild horizon relative to our sun's solar
mass, but more particularly with respect to
approximations tied to squaring or 'doubling' of our fundamental dimensionless material
(or p+e) scale, as well as some other
special mumbers. Moving further up 'mumber scale,' the next subsection analyzes the fine-structure number taken as a two-based exponent.
Which serves to define a "Truly 'Anthropic' Physical Principle" that proves to be the bio-physical frequency of human awareness and thought! This scale is also tied to electromagnetic parameters associated with the physical dimensions of
"Gaia," taken as the literal surface and atmosphere of old 'Mother Earth.' Or
equally, but more figuratively, 'she' can be seen as the, or as an, `earth
mother' {she's old, fat and pretty near burned out: i.e. the perfect
goddess-mirror for hippy feminists, or me!} As a 'public service,' we show how
the calculation further supports a relevant example of confirmed
and applied
accumulated knowledge that runs counterintuitive to what some well-meaning
scientists or other guru wannabe's hawk as popular wisdom when referring to
benefits that follow from a general technique of 'passive meditation.'5
The subsequent section, takes the
fine-structure number for the exponent in a natural logarithmic base,
as utilized in A. J. Meyer's original tautology: which serves as a
basis or 'gauge' for a 'fixed cosmic
age' (~550 million light years). Which provides a link to, or interlink
between, various parameters via a common scale identifiable with time6 -
here essentially describing the Post Big Bang Eras
of Radiation Decoupling and Anisotropic Re-ionization, or Early Stellar &
Proto-Galactic Formation, relative to a Basis of a Fixed Cosmic Age. After
a brief review of the post big-bang `radiation era,' the 'age-gauge' facilitates mapping its `decoupling' from emergent neutral hydrogen matter at around a third of a million years, which today has been dispersed and red-shifted to the chilling temperature of the cosmic microwave
background (CMB) field.
This schematic hence invites comparison with parameters provided by the 2003 results of the first year of data for the WMAP probe (its website http://map.gsfc.nasa.gov/m_mm.html serving as
info-central for most related astrophysical projects) mapping
anisotropies in the CMB at decoupling; which provides inferences about the
distribution and evolution of energy, matter and space-time operations at various stages of cosmic development. Further
calculations are shown to coincide with the peaks and troughs of the
WMAP's 'thermal angular power spectra'; but adds little beyond
supporting a broad view of an `era of re-ionization' across a swath of stages from the earliest stars unto their initial
or proto-galactic evolution. But firmer or at least more intriguing are the
underlying acoustic parameters at decoupling, which originally were released
as a mechanical energy
by gravitationally induced perturbations that produced literal Big-Banging
'waves of sound'. Which
seems to
in some sense offer a peak into the future of the universe7 that
serves as the perfect lead into the final
subsection of this chapter and book; as summarized below, and consolidated into
one diagram, that erases certain `apparent paradoxes of present measure' by
proposing a Multi/Meta-Dual Cosmic Constant for a
Closed Space-Time.' For all diagrams follow from our first;
all fluctuations constrained within a 'primaton horizon' until the quantum gravitational jump from a minimal entropy to a
lighter, larger, Planck state at Creation. Which set supersymmetric
transformations and replications of the internal 6D super-string manifold into
motion as its hypersphere bursts through the 'Planck Event Horizon' unto a
classical de Sitter era of vacuum mass creation and space-time signature
SO(4,1). Likewise, the entire 'Inflation Era' represents
'a
de Sitter Period'
an exponentially accelerated spatial expansion'. Yet the notion of a `modern
cosmic constant' lacks such creative and inflative de Sitteresque qualities;
so comparatively appears better adapted to another 'explanatory idea' of a
'repulsive quintessence' fueling the present accelerative phase, which effectively kicked in
'after decelerating in eternal expansion.'8 Half of our final diagram
includes mappings of such infinite space-time metrics with respect to what synthetic
geometry calls the `Absolute' - which the whole diagram takes special care to conformally map
in a like manner as the actual geometry, topology, and numeric tautology of the term called Lambda
as if bounded by the interior surface of a blackhole .
Which rather easily shows why the cosmos is presently measured to be in
an accelerative phase interpretable as an repulsive cosmic constant (equivalent
to a `negative ('quintessential')
pressure'). The brunt of issue being while 1: there are no reasons not to accept this `now standard' (for the last 7-8
years) interpretation of the data as a repulsive dark energy; 2: I anticipated a problem for 25 years with (`fashion queens' and their) spokesmen at the 'Court of Science' who measure present parameters,
but perhaps again "Measure Not" the proper latter-day cosmic constant.9 Which sums up an educated opinion based upon
a theoretical revamp of Einstein-Bergmann generalization of Kaluza-Klein 5D
theory the serves as a unified and non-locally quantified system of dimensional
(metric) analysis describing the five-dimensional world tensor across the whole
space-time continuum (all conclusions being backed by a massive statistical/experimental analysis
[saving all details for the advanced casino course]). Such
deductions are presently extended to accord a discrete cosmology of
Creation and dimensionless
analysis provided by the Meyer-Sheeter Monolith, augmented by a categorically
complete geometric isomorphism with the full 11D Membrane, and garnishes some support by the
small angle acoustic parameters at decoupling, as well as other interpretations of large angular scales that suggest a finite spatial horizon or radius.7 Which
is to say that despite the data supporting a present repulsive cosmic constant, what we're talking about is
again a dualistic cosmic constant: its true universal geometry and topology revealing a Conformal
Anti-de Sitter
(Clifford/Klein) Mapping covering the entire two time dimensions of the Whole 5D World Membrane of space-time signature SO(3,2). Likewise, that world, our
World, in a some physical sense possesses all subgeometries at the
Interior of a Riemann/Meyer Cosmic Blackhole (AdS x R5), whose Event Horizon or
'Absolute' Closure Radius, and
AdS Geometry, Governs the State Function of the Universe
(as a few
quantum theorists like Brad Holland have conjectured). A final discussion of the various cosmic eras and membrane dualities
suggests a presently accelerating era having a14 billion light years radius, which times two pi marks the end of time when the universe collapses back to a final/initial state Planck primaton in a fixed 88 billion light year cycle - a
maximized cyclical entropistic constant.
Yeah, that's the punch-line folks - but as ever, the proof's in the pudding -
yet who wants to wait another 14-30 billion years, especially when a small
additional casino fee can
save you all that time!
The Infinity Problem, Projective Geometry and its Regional Subgeometries
Sheeter’s supporting 290 page text, provides the categorically consistent and complete geometric basis for this 11-dimensional tautology. A distillation of Felix Klein, Veblen and Coxeter’s works in one volume, it unites all subgeometries, so
too every substage of (physical) existence, with a synthetic ‘formal simplicity’ emphasizing common projective tenets that fueled Klein’s old
'Erlangen program.' Given the series title of this 1987 printing (process press, Berkeley) is Volume One of Projective/Elliptic Geometry and Unified Space-Time, it should be evident the 241 Mumbers far exceeds the original expectations for the second volume of this series, justifying why the geometry book was withheld, remaining
unpromoted until this more opportune moment. (So, now a national mailing failed to get one order from a math library; which figures, believe it!)1,10
And 241 Mumbers also offers both books as part of the e-interactive
program of advanced courses and an up-dated subscription service - check the order page for a few further details.
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