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The picture above is taken from here.Mathematical rigour. Mathematical links. Presentation. etc.Now, it is not about how complicated the math you are getting involved into, or how fancy or advanced the topic you choose for your exploration, it’s a matter of how well presented is your paper.Before I go on forth, I will have to describe a bit of my paper because it will be referenced from time to time in my argument below. I received a 17/20 when marked by my teacher (I know this after getting my diploma) but as I was chosen for moderation by the IBO, they marked me up by 3 points and deemed my IA to be 20/20 (thank you, IBO). So the marks that I have obtained has shown that my IA is certified by the IBO with reduced bias - that is, it is marked and moderated by IBO certified examiners.My IA is about something very simple; rotation of a spoon, to cool down coffee. But instead of a person doing it, the sets of equations that are developed are so that a robot can be programmed to do it for you. To reach such equations, I have used, complex numbers and differential equations (even though the DE part is not even transparently shown in the paper due to the page constraint). That’s it.Now, I will go through each criterion to highlight which part is crucial and is left out by most students.N.B. I will not go through every single detail within a criterion. I will only highlight crucial parts per criterion that I found many people are missing in their IAs. For general suggested details required by the IBO, you can find so in one of the previous answers to this question.Criterion A: Communication.Unless your paper is a pure math paper, doing intense proofs (which I doubt as it is hard to find something original and new at the IB level), do you use software to aid you?In my IA, I used Tables,Graphs using GeoGebra and Adobe Photoshop,computed logarithmic regressions using TI-Nspire CXand computed errors by generating hundreds of data using Excel.And I used all of this software not solely to fulfil this criterion. Instead, I was forced to use them because each and every single one of them is crucial to arrive at my conclusion. This is what helped me secure the criteria in this one. Question yourself when tackling a problem, is technology necessary? Or a better question would be, would it help me to reach a better solution by using technology?Criterion B: Mathematical presentation.Do you use a proper mathematical editor when writing your equations? Are the variables italicised? Are the non-variables non-italicised? Are the parentheses aligned with your giant fractions? Do you define variables properly? Small things like this, if not done properly, would definitely hurt the eyes, and brains of the person reading your paper (if not yet obvious: your marker). Presentation is a key tool in scoring this criterion.Criterion C: Personal engagement.This criterion is quite hard to score to be honest. One of the many things that pushed my IA to a full score in this criterion is because I have managed to unify the Euler’s number, [math]e[/math] and [math]\pi[/math] in one single equation and realising that fact took me months.This is part of the personal engagement that they want. A pure demonstration of you appreciating the beauty of maths. That simplifying something into these two important mathematical constants are considered needed to do. I mean, look at the following example.Let [math]r[/math] be the radius, and [math]C[/math] be the circumference, both of the same circle. Then take a fraction of the two, [math]r/C[/math]. On first sight, you might think, well that's pretty nice already. But on a closer inspection, we realise something magnificent (which seemed almost trivial at first):[math]C = 2 \pi r[/math]Which implies,[math]\dfrac{r}{C} = \dfrac{r}{2 \pi r} = \dfrac{1}{2 \pi}[/math]See? You can simplify something that might look pretty simplified already at first to a better version of it.Such intuition is what IB wants from you. Thus, you need to demonstrate this level of intuition to ensure you score a full mark in this criterion.Criterion D: Reflection.This criterion is easy for you to score a 2/3, but not a 3/3. To score a full mark, the keywords that you must be aware of are critical analysis and further research. You must evaluate your findings properly. If you want to find a newer method or a better equation than the current one you have, Why? If you want to modify something, or assume something in your model, ask yourself, Why? These are important questions that will aid you to assess your own judgements critically.Furthermore, recognize whether your research can have some continuation in it (which it must if it is a good one). Identify what is lacking in your research such as the limitations of your model. For example, the model you currently build is perfect on sunny days, but not applicable during rainy ones. Or perhaps, your equation can be used only for something of a fixed radius, a better one would be of varying radius, hence this can be continued in a new research paper, etc.Criterion E: Use of Mathematics.This is considered to be the hardest criterion to score of them all. Before submitting your paper, please make sure that all mathematics involved is correct. Check it for the nth time. If not, you will only get a maximum of 2/6 for this criterion.Some relevant mathematics is used. The mathematics explored is partially correct. Some knowledge and understanding are demonstrated. - for achievement level of 2The above is quoted from the IBO website[1] itself.Now to score a full mark you must fully understand every single point of what the IB wants.Relevant mathematics commensurate with the level of the course is used. The mathematics explored is precise and reflects the sophistication and rigour expected. Thorough knowledge and understanding are demonstrated. - for achievement level of 6Again, another quote from IBO.The keywords are bold. The first key point, your work must commensurate with HL maths. In layman terms, this just means do not use middle school algebra as your core tool in your research. Use HL maths.Rigour. This is the most important of all.Every single math IA I have read in my entire life lack this. You can simply google for the meaning of mathematical rigour and get a very formal definition of it. But the simplest way of me explaining this in terms of an IB math IA is that you must tackle your equations with care. That is, you must present the math (or your equations) in such a way that it is strongly and logically valid. A very simple (but not very strong example) I can think and give of is:Suppose we have an equation defined by [math]z(t) = t + \ln(t)[/math] with [math]t[/math] being a variable. While it seems obvious that [math]t > 0[/math] as [math]\ln(t)[/math] is undefined in the reals when [math]t \leq 0[/math], you must state and show this fact. This is because, say you do some 'intricate' substitution with the equation, let [math]t = 1/ \cos(x) = \sec(x)[/math] with the domain [math]\{x \in \R: x \neq \pi/2 + \pi n[/math] where [math]n \in \Z \}[/math] (pronounced ‘the set x in the real domain, such that, [math]x \neq \pi/2 + \pi n[/math] where n is an integer’) . You may or may not have realised that while [math]\cos(x) \neq 0,[/math][math]t = \sec(x) > 0[/math] as [math]t > 0[/math]whereas generally this wouldn’t be true as the range/codomain/image of [math]y = \sec(x)[/math] is the set:[math]\{y \in \R\ : y \leq -1[/math] or [math]y \geq 1\} \quad (*)[/math](pronounced ‘the set y in the real domain, such that, [math]y \leq -1[/math] or [math]y \geq 1[/math]’)Note: [math](*)[/math] is pronounced as star.Now we have [math]t = \sec(x) > 0[/math], but notice [math]t = \sec(x)[/math] cannot take the values [math]t \in (0,1).[/math] We know this from [math](*)[/math]. And thus, we can make the following deduction,[math]t \geq 1 > 0[/math]which satisfies our first constraint (that [math]t > 0[/math]) and second constraint (which is [math](*)[/math] that is [math]t \geq 1[/math]).Hence, we know the new domain for [math]z(t)[/math] is indeed [math]t \geq 1[/math] if we make this substitution in [math]z(t) = t + \ln(t)[/math] instead of the obvious [math]t > 0[/math].This example might seem trivial as this ‘intricate’ substitution I’ve used in the example above is actually simple. But in reality, a substitution may get as messy as it can, and you might do it several times, say to solve a system using integration by parts. So please state such conditions as lucid as possible.This idea of being rigorous is expected of you from the IBO if you really want to score a 20/20 IA.And the last part, “thorough knowledge and understanding are demonstrated”.This is why I’ve mentioned earlier in this post that the fanciness of your topic does not matter at all. You do not have to pick some complicated topic like Stochastic analysis or the Chinese remainder theorem as suggested on some Math HL IA websites.With the (lack of) mathematical knowledge you possess during IB, you can’t demonstrate a strong understanding in these topics. Stochastic analysis is something you take in 2nd/3rd year of a Math degree to understand it properly; while the Chinese remainder theorem, to understand it properly (despite the idea itself is fairly simple), you have to take some basic abstract algebra classes to learn some ring theory (as the ones you’ve learn in the IB Discrete Mathematics Option topic is insufficient).Don’t get me wrong, I’m not against you wanting to use it. I’m against you wanting to use it but unable to show a pure grasp of the topic on paper, let alone, verbally. Even if you choose to study these topics, it will cost you too much time as remember that you have tons of other work to do like your other 5 IAs, your EE, your TOK essay, the TOK presentation and even your CAS reports.You can pick a simple topic say, vectors, and do some clever manipulations in it as long as you can demonstrate that you have a thorough understanding of it. What is this example of manipulations that can demonstrate your understanding in a topic you asked?Well, an example would be:Given two vectors [math]\mathbf{a}[/math] and [math]\mathbf{b}[/math]. Then what is the component of [math]\mathbf{a}[/math] in the direction of [math]\mathbf{b}[/math]? Well, we know that:[math]\mathbf{a} \cdot \mathbf{b} = | \mathbf{a} | | \mathbf{b} | \cos(\theta)[/math]through our understanding (of the definition) of the dot product.where [math]\theta[/math] is the angle between the two vectors and [math]| \mathbf{a} |[/math] is the norm/magnitude of the vector [math]\mathbf{a}[/math] and similarly [math]| \mathbf{b} |[/math] for the vector [math]\mathbf{b}[/math].Then we can rearrange to have in terms of [math]\mathbf{b}[/math]. That is we have,[math]| \mathbf{a} | \cos(\theta) = \dfrac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{b} |}[/math].And thus this is the component of [math]\mathbf{a}[/math] in the direction of [math]\mathbf{b}[/math]. The clever manipulation part is just when you realised that you can just divide both sides by [math]| \mathbf{b} |[/math] to get the desired result.Well now you’re asking me, ‘What is the application of what I have just shown in the example above. Some manipulations, yeah, but why would we do that?Well it turns out. If we let Force [math]= \mathbf{F}[/math] and Displacement [math]= \mathbf{s}[/math]. And substitute [math]\mathbf{a} \rightarrow \mathbf{F}[/math] and [math]\mathbf{b} \rightarrow \mathbf{s}[/math]. We have that,[math]| \mathbf{F} | \cos(\theta) = \dfrac{\mathbf{F} \cdot \mathbf{s}}{| \mathbf{s} |}[/math].We have not just found an equation to represent Force in terms of Displacement, but better, we found a representation of the component of Force in the direction of the Displacement of which the force is applied! Now is that not useful?!If you can do this multiple times in your paper, you have clearly demonstrated that you indeed understand the tool/topic you are using and you are capable of manipulating it in such a way that it becomes useful for you that you can draw a meaningful conclusion (if not many conclusions) from it.On top of all that, remember THE MOST IMPORTANT aspect of the Math IA!The exploration should be accessible to fellow students.I did not say this. The IBO said this in their FAQ[2]. It is a very important aspect that your IA must satisfy. What you can do is give your completed IA to your peers who are equally mathematically driven as you are to read and evaluate it. Ask them if they can understand every step of it. Ask them where are the holes that got them lost.Congratulations for reading up to this point, it shows that you are determined and have the drive and motivation to write a good IA. Or maybe you are just desperate? At this point, it doesn’t matter. Just go and try to write the best IA you can with this guide in hand. Even if you are not able to demonstrate with the precision as described in this guide, you would still be getting a mark within the 15+ range if you follow it as close as possible.If some of you feel that this is too much and want to just score a 14/20. My two cents would be to just read the IBO website[3] and the Internal Assessment section under the Mathematics HL guide (this is SO important to read!).I really hope this helps all of you readers. Do give an upvote if you feel this is helpful and please share it with your friends. Best of luck everyone!Some topics that I see as very useful and feasible for the average IB Math HL student:Pure MathematicsAnything that falls under this is quite hard. Do a pure mathematics IA only if you are crazily confident in your mathematical knowledge and skill.Proofs (by contradiction & induction) - weak induction is sufficient. Note that a lot of mathematical proofs are by contradiction. You must learn it and see many examples of the proofs.Prime numbers (Option 10)Linear diophantine equations (Option 10)Modular arithmetic and hence, Fermat’s Little Theorem (Option 10)Group theory (from Option 8)Lagrange’s theorem (from Option 8)Homomorphisms and isomorphism (from Option 8)Harder but more rewarding Pure MathematicsAnything that falls under here is super hard. But the journey of understanding things is very rewarding. Do this if and only if you have a suitable and sufficient math background beforehand. It is DEFINITELY not for everyone.Bounds on trigonometric functions or logarithms (this is super useful for mathematicians in general e.g. [math]|\sin x| \leq x[/math] for all [math]x[/math] real.)First Isomorphism TheoremThe First and Second Supplementary Laws to Quadratic Reciprocity (or even the Quadratic Reciprocity Law itself)Rational Root TheoremAlgebraic and transcendental numbersApplied MathematicsRudimentary topics are as below:Precalculus (Differentiation & integration) - obviously?Vectors (Dot product, cross product, triple scalar product)Trigonometry (clear applications, sine and cosines are everywhere)Probability & statistics (also everywhere)These are considered rudimentary because they form most of the tools used in more ‘advanced’ mathematics. Here are some of the more advanced (but still in syllabus) ones:Power series (very, very, very helpful but you have to understand it first! - from Option 9, anyone can do it)Matrices! (everyone can learn it, so many applications such as Linear maps)Linear ordinary differential equations (Linear ODEs - if you do Option 9)Inverse trigonometryGraph theory (if you do Option 10)Mean Value Theorem (MVT - Option 9 anyone can do it)Hypothesis testing & confidence intervals (if you do Option 7)Type I, type II error (if you do Option 7)etc.N.B. I put an anyone can do it wherever I feel that someone can just understand it by directly reading that particular topic and an if you do wherever I think you have to learn it step by step before diving into that particular topic. Say Hypothesis testing, you have to learn some new definitions first like the null and alternative hypotheses, significance level, critical region, which takes time to understand. However, such process sometimes can be quick depending on a person.Power series is put first and bolded because it gives so much new insight to the user when tackling a problem. The fact that I didn’t know how to understand it during my IB years (because I didn’t take the Calculus option) upsets me as it could have helped me to further my research a lot. An example of a power series is:[math]e^x = 1 + x + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + ... \,= \displaystyle \sum_{n=0}^{\infty} \dfrac{x^n}{n!}[/math]Very advanced:Multivariable calculus (Partial differentiation without integration as integration is harder). Use only when you truly need more than one variable to solve your problem.This falls under very advanced not because it is hard, but because it is out of the IB syllabus, which I am strongly against. However, there are certain conditions where you truly need to address your system in terms of two variables (or more), and such attempt would require the usage of multivariable calculus (also known as vector calculus).I hope this additional section would give some new insights on what topics you should focus on. However, note that I am in no position to discourage you from doing any other topics. This is just a suggestion by me in which, I think, is sufficient and feasible for any IB math HL IA student to take their time to learn, adapt despite their other IAs, EEs, TOKs and everything and apply in solving their problem in their respective IAs.Good luck again!EDIT:I’ve updated the example under Rigour to make it look more rigorous to give a better idea on what it really means for an IB level research paper.Added pictures of tools used to support Criterion A.Updated on how to read the set notation of the domain and codomain under the Rigour example.Added a (nice) application to the example under demonstrating thorough understanding.Added suggestions of topics that are feasible for a math IA for the average IB student.Remove a sentence regarding the norm as it is convention in the IB to write the norm as it is written up there.Added the MOST IMPORTANT ASPECT sectionMade small fixes, added more suggestions to feasible topics (25/5/2020). Thank you for 125 votes!Footnotes[1] Mathematics SL and HL teacher support material[2] Mathematics SL and HL teacher support material[3] Mathematics SL and HL teacher support material

LIGO is certainly not a scam. GR and GW are valid and can be tested. However, LIGO is possibly a blunder with far-reaching epistemological consequences. We must anticipate disruptive political and social implications of a retraction of a magnitude appropriate for the cultural preponderance that LIGO seeks, built upon retroductive verificationism and communicated through its discursive cliche. See orphans of abductivism.There is a common source for lagged phase-locked noise with identical scaled spectral components to the GW transients during each of the seven detected events, including GW170817. GRB/hard X-ray signals for GW150914 and a few other GRB and hard X-ray triggers associated directly with GW triggers are no longer being categorically dismissed, as LIGO had almost polemically campaigned, as theoretical complications relative to phenomenology of data can weaken Bayesian proxies for empirical confidence. Here is a condensed and direct introduction into evidence for coincident sources of LIGO noise I have gathered through my own analytical work:Magnetospheric sawtooth event from GOES magnetometer data for GW150914; coincident changes in lightning impulse density are dashed lines, all centered at GW150914 (grey bar); the ACF of the PSD for GW150914-L1 for 0.2 s is blue, and the ACF of GW150914-H1 0.2 s time series is green:Magnetospheric sawtooth injection event recorded in GOES-13 magnetospheric protons with shock arrival and precipitous flux spike at geostationary orbit calculated to arrive during the few minutes surrounding GW170817. The GW170817 event is the green bar. This delay between magnetometer peak and GW170817 signal arrival is 37.9 min ± 3 min. Standard feedback-modulated/stabilized lags for the Northern Hemisphere are coincidentally identical with certain multi-phase quasiperiodic particle injection arrival lags from magnetosphere bow shock ahead of magnetopause, with approx 3-5 minute delay added to 30-40 minute terrestrial polar magnetosphere-ionosphere propagation preceding transverse-coherent geomagnetic coupling response:(https://scholars.unh.edu/cgi/vie..., https://encompass.eku.edu/cgi/vi..., https://www.ann-geophys.net/36/2..., https://scholars.unh.edu/cgi/vie..., https://www.sciencedirect.com/sc..., http://www.iwf.oeaw.ac.at/filead... )Transient response functions of magnetospheric sawtooth mode is potentially associated with long or multiple (distributed) TGFs from TGEs (or a potentially unknown kind of magnetospheric hard x-ray burst, if not itself a complex-chaotic energetic response to arrival of a delayed particle flux from a CME). A superposed local <300 keV flux from weak magnetospheric transient activity (with dead time corrected from empirical bounds) actually fits spectral calibrations much better than a weak and off-axis GRB from a kilonova in NGC 4993, if one permits oneself to rescale the unknown luminosity distance of the GRB transient directly following the weak and glitch-laden signals that were subsequently heavily manipulated by LIGO.full GOES .csv data: https://satdat.ngdc.noaa.gov/sem...https://satdat.ngdc.noaa.gov/sem...information on the GOES Space Environment Monitor (SEM): https://satdat.ngdc.noaa.gov/sem...https://en.wikipedia.org/wiki/Ge...Work with GW150914 coincident IMF and solar wind data,showing identical(scalable/ quasi-renormalizable) phase and amplitude information for autocorrelations between IMF and GW data:Solar wind dynamic pressure and density are bound during detector noise phases with identical lags to GW events, and show uncanny identity at a period similar to the lunar cycle or one of the inertial solar coronal rotation periods, even sharing data gaps from excess charging preceding the sawtooth event and “between” GW impulses is the cross-correlation between these indicators that isolates a determinsitic and scale-invariant crossover from autocorrelations to GW signals as I have shown above. Lightning activity is represented by short colored bars in the triple parameter superposition between P, PDYN, and BZ with GW/LVT events indicated with tall bars:INTEGRAL GRB relocation overlay (orange nebulous zones) over North American 24 hour lightning around GW150914, and the sky localization area for GW150914 (irregular outlines) embedded within a semi-empirical critical domain model for thunderstorm eigenmodes projected from the centroid of the active Oklahoma thunderstorm (also the centroid of the entire NA ground striking lightning activity for that period). This thunderstorm produces the same time lags as are accepted for GW150914, recognized by many as a standing problem for GW signal processing orphans of abductivism.Map legend:1. Blitzortung.org lightning ground flash data for 24 period surrounding GW1509142. Yellow points are major CG lightning strikes occurring within 60 seconds of GW150914; I extend my boundaries from the cluster centroid, also a CG strike.3. INTEGRAL gamma discharge upper limit for Fermi reading - ensconcing the lightning regime which in turn scales by the boundaries projected from the OK lightning event.4. Range antipode from central OK point, extrapolated intersect for GW1409145. Double antipodal range for centroid of hemispheric gamma ray counterpart predicted by Fermi-INTERGRAL, its centroid and boundaries delimited by strongly correlated lightning cells6. Highly-ordered circular region of lightning cells with active centroid. Its predictive range boundaries, as cleft antipodal centroids, are tangent and longitudinally aligned with GW150914, as well as non-trivial harmonic fits for all aforementioned systems7. Fermi probability range for hard x-ray/gamma ray burst associated with GW150914, version 1 from 2016 publication8. Fermi probability range for hard x-ray/gamma ray burst associated with GW150914, version 2 from revised 2016 publication9. Sky source constrained probability space for LIGO GW15091410. Antipodal scaling range for OK lightning centroid, edge intersecting with INTEGRAL model gamma hemispheric counterpart11. antipodal centroid in hemispheric gamma ray counterpart predicted by Fermi-INTERGRAL12. Secondary antipodal centroid (a known stationary point in the domain of the oscillation of the SW boundary of the SAA http://meetingorganizer.copernic...)Time lags for storm boundary-detector time-limited path lengths at [spin] rates specified in LIGO publications, given dispersion relations through dense, highly-charged cloud cover :3,001-((((0.67* c))*(0.01095-0.0069))=2187.51316522 km(0.67* c))*(0.01095-0.0069)=813.486834783 km2187.51316522+813.486834783=3001km2187.51316522-813.486834783=1374.02633044 kmadjusted for line-of-sight atmospheric source bound by ionosphere and troposphere emission altitude: 0.88 c is value for global ELF propagation velocity quoted in Schumann resonance transients and the search for gravitational waves:3,030-((0.88* c)*(0.01-0.0069))=2212.16617458(0.88* c))*(0.01-0.0069)=817.833825424(3030-(2*((0.88* c)*(0.01-0.0069))))=1394.33234915((((0.679+0.67)/2)* c)*(0.0069))=1395.24908915time lag after arrival of L1 signal, assuming group velocity dispersion:1394.33234915 km/(c*(0.679+0.67)/2))=0.00689546639 s.LIGO GW150914 H1|L1 lag shift: 0.0069 s.https://losc.ligo.org/events/GW1...The circular wave-guided TE mode 0 and TM mode 1 lower cutoff [ pm1] for combined inter-detector domain lengths as an input hovers around 60–61 Hz for the range of values for total path length between detectors, which indicates possible feedback that may have little to do with total detector noise undifferentiated from GW signal, although it is compelling to recognize that there was potentially lower attenuation of both TE and TM modes through the complex framework modeled by waveguide networks.The correlation of phase-locked lightning triggering and the time period for inter-detector phase-locked quasiperiodic noise occurs during each of the seven detections, with an active storm centered in the sky localization area for GW170817 also involved with this globally-coherent discharge triggering (two to three-minute phases of little to no detected ground strikes followed by a global burst and a downward trend for another two minutes, with total triplet-periodic phase length of five minutes): Solar elevation difference from 90° during the GW170817 event with respect to dual messenger co-localization centroid between Tanzania and Madagascar is identical to the upper limit (28°- the calculated angle of the so-called off-axis short GRB associated with GW170817 a short GRB seen off-axis,[1710.06421] Off-Axis Emission of Short GRB Jets from Double Neutron Star Mergers and GRB 170817A), and this radius is significant, given the near-solar sky localization for NGC 4993.The lower solar elevation deviation bound from linked publications (16°) is the solar elevation deviation from the Northern bound (Horn of Africa) with identical longitude for the Fermi-Integral and first LIGO-VIRGO sky localization with respect to the final SL centroid longitude (see small thunderstorms in general region, showing discharge synchronzed with global magnetospheric-ionospheric modes). The mean differential angle I calculated from the five relevant coordinates (E boundary of joint GW/GRB sky localization area, W boundary, VIRGO, LIGO Livingston, and LIGO Hanford is 24.2° (differentials from right orthogonality not treated like circular quantitites, although they imply a circular horizon):var (decimal values): 62.67sd (decimal values): 7.92arith. mean: 24.2°geomean 23.2°harmean 22.22°HLV (Hanford-Livingston-Virgo) sky area: 28 deg^2viewing angle: (without host galaxy identification) ≤ 56°, (with host galaxy identification) ≤ 28°θ_obs ∼ 20° — 28° a short GRB seen off-axisθ_obs≈16°—26° [1710.06421] Off-Axis Emission of Short GRB Jets from Double Neutron Star Mergers and GRB 170817Ahttps://www.suncalc.org/NGC 4993 was not instrumentally visible for three months due to the sun’s obstruction, and was not (adaptively Look-elsewhere effect - Wikipedia) localized given LIGO parameter estimation for nine hours following GRB170817A trigger.Brightening neutron-star collision stumps astrophysicists - FuturityTGF triggers are correlated to GW events - namely, crossovers between vacuum-like phases and sudden increases in TGF count. Minute correlations show this same pattern, which is not, contrary to implication in LIGO papers, evidence of low-noise phases optimizing GW detection. GW power spectra and time evolution are no different that the coincident evolution of IMF-solar wind coupling modes. A link to the rest of the graphs from my superposed epoch analysis of amplitude-scaled LIGO trigger times: orphans of abductivism.

https://fulguritics.blogspot.comThere is a common source for lagged phase-locked noise with identical scaled spectral components to the GW transients during each of the seven detected events, including GW170817. GRB/hard X-ray signals for GW150914 and a few other GRB and hard X-ray triggers associated directly with GW triggers are no longer being categorically dismissed, as LIGO had almost polemically campaigned, as theoretical complications relative to phenomenology of data can weaken Bayesian proxies for empirical confidence. Here is a condensed and direct introduction into evidence for coincident sources of LIGO noise I have gathered through a bit of my own analytical work:Magnetospheric sawtooth event from GOES magnetometer data for GW150914; coincident changes in lightning impulse density are dashed lines, all centered at GW150914 (grey bar); the ACF of the PSD for GW150914-L1 for 0.2 s is blue, and the ACF of GW150914-H1 0.2 s time series is greenMagnetospheric sawtooth injection event recorded in GOES-13 magnetospheric protons with shock arrival and precipitous flux spike at geostationary orbit calculated to arrive during the few minutes surrounding GW170817. The GW170817 event is the green bar. This delay between magnetometer peak and GW170817 signal arrival is 37.9 min ± 3 min. Standard feedback-modulated/stabilized lags for the Northern Hemisphere are coincidentally identical with certain multi-phase quasiperiodic particle injection arrival lags from magnetosphere bow shock ahead of magnetopause, with approx 3-5 minute delay added to 30-40 minute terrestrial polar magnetosphere-ionosphere propagation preceding transverse-coherent geomagnetic coupling response.https://scholars.unh.edu/cgi/vie..., https://encompass.eku.edu/cgi/vi..., https://www.ann-geophys.net/36/2..., https://scholars.unh.edu/cgi/vie..., https://www.sciencedirect.com/sc..., http://www.iwf.oeaw.ac.at/filead... ); its transient response function is potentially associated with long or multiple (distributed) TGFs from TGEs (or a potentially unknown kind of magnetospheric hard x-ray burst, if not itself a complex-chaotic energetic response to arrival of a delayed particle flux from a CME), which actually fits spectral calibrations much better than a weak and off-axis GRB from a kilonova in NGC 4993, if one permits oneself to rescale the unknown luminosity distsnce of the GRB transient directly following the weak and glitch-laden signals that were subsequently heavily manipulated by LIGO.full GOES .csv data: https://satdat.ngdc.noaa.gov/sem...https://satdat.ngdc.noaa.gov/sem...information on the GOES Space Environment Monitor (SEM): https://satdat.ngdc.noaa.gov/sem...https://en.wikipedia.org/wiki/Ge...Work with GW150914 coincident IMF and solar wind data,showing identical phase and amplitude dependency for autocorrelations between IMF and GW data:Solar wind dynamic pressure and density are bound during detector noise phases with identical lags to GW events, and show uncanny identity at a period similar to the lunar cycle or one of the inertial solar coronal rotation periods, even sharing data gaps from excess charging preceding the sawtooth event and “between” GW impulses is the cross-correlation between these indicators that isolates a determinsitic and scale-invariant crossover from autocorrelations to GW signals as I have shown above. Lightning activity is represented by short colored bars in the triple parameter superposition between P, PDYN, and BZ with GW/LVT events indicated with tall bars:INTEGRAL GRB relocation overlay (orange nebulous zones) over North American 24 hour lightning around GW150914, and the sky localization area for GW150914 (irregular outlines) embedded within a semi-empirical critical domain model for thunderstorm eigenmodes projected from the centroid of the active Oklahoma thunderstorm (also the centroid of the entire NA ground striking lightning activity for that period). This thunderstorm produces the same time lags as are accepted for GW150914, recognized by many as a standing problem for GW signal processing orphans of abductivism.Map legend:1. Blitzortung.org lightning ground flash data for 24 period surrounding GW1509142. Yellow points are major strikes occurring within 60 seconds of GW150914 in a double ringed giant "coalesced" thunderstorm; I extend my boundaries from the central strike3. INTEGRAL gamma discharge upper limit for Fermi reading - ensconcing the lightning regime and in turn scales by the boundaries projected from the OK lightning event.4. Range antipode from central OK point, extrapolated intersect for GW1409145. Double antipodal range for centroid of hemispheric gamma ray counterpart predicted by Fermi-INTERGRAL, its centroid and boundaries delimited by strongly correlated lightning cells6. Highly-ordered circular region of lightning cells with active centroid. Its predictive range boundaries, like the double antipodal centroid, are tangent and longitudinally aligned with GW150914, as well as obvious harmonic fits for all aforementioned systems7. Fermi probability range for hard x-ray/gamma ray burst associated with GW150914, version 1 from 2016 publication8. Fermi probability range for hard x-ray/gamma ray burst associated with GW150914, version 2 from revised 2016 publication9. Sky source constrained probability space for LIGO GW15091410. Antipodal scaling range for OK lightning centroid, edge intersecting with INTEGRAL model gamma hemispheric counterpart11. antipodal centroid in hemispheric gamma ray counterpart predicted by Fermi-INTERGRAL12. Secondary antipodal centroid (a known stationary point in the domain of the oscillation of the SW boundary of the SAA http://meetingorganizer.copernic...)Time lags for storm boundary-detector time-limited path lengths at [spin] rates specified in LIGO publications, given dispersion relations through dense, highly-charged cloud cover :3,001-((((0.67* c))*(0.01095-0.0069))=2187.51316522 km(0.67* c))*(0.01095-0.0069)=813.486834783 km2187.51316522+813.486834783=3001km2187.51316522-813.486834783=1374.02633044 kmadjusted for line-of-sight atmospheric source bound by ionosphere and troposphere emission altitude: 0.88 c is value for global ELF propagation velocity quoted in Schumann resonance transients and the search for gravitational waves:3,030-((0.88* c)*(0.01-0.0069))=2212.16617458(0.88* c))*(0.01-0.0069)=817.833825424(3030-(2*((0.88* c)*(0.01-0.0069))))=1394.33234915((((0.679+0.67)/2)* c)*(0.0069))=1395.24908915time lag after arrival of L1 signal, assuming group velocity dispersion:1394.33234915 km/(c*(0.679+0.67)/2))=0.00689546639 s.LIGO GW150914 H1|L1 lag shift: 0.0069 s.https://losc.ligo.org/events/GW1...The circularly-waveguided TE mode 0 and TM mode 1 lower cutoff [ pm1] for the total domain length as an input hovers around 60–61 Hz for the range of values for total path length between detectors, which indicates possible feedback that may have little to do with total detector noise undifferentiated from GW signal, although it is compelling to recognize that there was potentially lower attenuation of both TE and TM modes through the complex framework modeled by waveguide networks.The correlation of phase-locked lightning triggering and the time period for inter-detector phase-locked quasiperiodic noise occurs during each of the seven detections, with an active storm centered in the sky localization area for GW170817 also involved with this globally-coherent discharge triggering (two to three-minute phases of little to no detected ground strikes followed by a global burst and a downward trend for another two minutes, with total triplet-periodic phase length of five minutes): Solar elevation difference from 90° during the GW170817 event with respect to dual messenger co-localization centroid between Tanzania and Madagascar is identical to the upper limit (28°- the calculated angle of the so-called off-axis short GRB associated with GW170817 a short GRB seen off-axis,[1710.06421] Off-Axis Emission of Short GRB Jets from Double Neutron Star Mergers and GRB 170817A), and this radius is significant, given the near-solar sky localization for NGC 4993.The lower solar elevation deviation bound from linked publications (16°) is the solar elevation deviation from the Northern bound (Horn of Africa) with identical longitude for the Fermi-Integral and first LIGO-VIRGO sky localization with respect to the final SL centroid longitude (see small thunderstorms in general region, showing discharge synchronzed with global magnetospheric-ionospheric modes). The mean differential angle I calculated from the five relevant coordinates (E boundary of joint GW/GRB sky localization area, W boundary, VIRGO, LIGO Livingston, and LIGO Hanford is 24.2° (differentials from right orthogonality not treated like circular quantitites, although they imply a circular horizon):var (decimal values): 62.67sd (decimal values): 7.92arith. mean: 24.2°geomean 23.2°harmean 22.22°HLV (Hanford-Livingston-Virgo) sky area: 28 deg^2viewing angle: (without host galaxy identification) ≤ 56°, (with host galaxy identification) ≤ 28°θ_obs ∼ 20° — 28° a short GRB seen off-axisθ_obs≈16°—26° [1710.06421] Off-Axis Emission of Short GRB Jets from Double Neutron Star Mergers and GRB 170817Ahttps://www.suncalc.org/NGC 4993 was not instrumentally visible for three months due to the sun’s obstruction, and was not (adaptively Look-elsewhere effect - Wikipedia) localized given LIGO parameter estimation for nine hours following GRB170817A trigger.Brightening neutron-star collision stumps astrophysicists - FuturityTGF triggers are correlated to GW events - namely, crossovers between vacuum-like phases and sudden increases in TGF count. Minute correlations show this same pattern, which is not, contrary to implication in LIGO papers, evidence of low-noise phases optimizing GW detection. GW power spectra and time evolution are no different that the coincident evolution of IMF-solar wind coupling modes. A link to the rest of the graphs from my superposed epoch analysis of amplitude-scaled LIGO trigger times: orphans of abductivism.