Anomaly Resolution in Physics

Established The prize is a calibrated base rate: for a fresh discrepancy between an experiment and the theory it is supposed to match, knowing the odds that it is a statistical fluctuation, a hardware fault, a wrong theoretical input, or genuine new physics — and which single test decides. No such number exists today. What exists is a folk memory of famous cases, and folk memory is selected for drama.

Established The magnitude is best given as the effort a miscalibrated field spends on discrepancies that do not survive. The 750 GeV diphoton bump of December 2015 — a local excess of 3.9 standard deviations at ATLAS and 3.4 at CMS, and never once above the field’s own five-sigma discovery line — drew roughly 500 theory papers in eight months before it was declared a statistical fluctuation in August 2016. The muon anomalous magnetic moment carried a headline “4 to 5 sigma” hint of new physics for a quarter of a century; in 2025 it dissolved, not because anyone found the particle but because the theory number moved. A register that had priced those two episodes at announcement would have redirected a measurable fraction of a field’s time.

Frontier Stated in the units that matter, the upside is a decision rule about when a discrepancy earns a decisive experiment and when it earns patience. Six well-documented cases in section 3 give the first data points, and the pattern in them is blunt: of six high-profile discrepancies at three sigma or more since 2010, four resolved to no new physics, one is unresolved, and the count of new particles or forces confirmed is zero. That is not yet a base rate — six famous cases are a sample chosen for fame, not a measurement — and turning it into one is the whole of what this brief is offering.

Speculative The condition goes first: the base rate becomes real only if someone builds the prospective registry of section 7 — every discrepancy logged at announcement, with the field’s contemporaneous odds, scored a decade later by an outcome nobody can edit after the fact. The gain accrues to funders, referees and the field’s own time budget, not to any one laboratory, which is exactly why no laboratory has built it.

Established An anomaly, in the sense this brief uses, is a statistically significant divergence between a measurement and the theoretical prediction it is meant to match. The APS review that named the mid-2010s the “era of anomalies” put the working definition plainly and added the working expectation with it: most anomalies go away, in the words of one physicist it quoted, “because it’s a statistical fluctuation, or it’s an experimental error.”

Established There are exactly four ways a discrepancy can end, and the meta-science question is which one, and how you tell in advance. It can be a statistical fluctuation that regresses as data accumulate; a systematic or hardware error on the experimental side; a wrong input or approximation on the theoretical side; or a genuine signal of physics beyond the accepted model. The four are not equally likely, they are not equally easy to detect, and — the point of this brief — they are not symmetric in which side of the theory-experiment pair has to move.

Established The five-sigma discovery convention exists because three sigma is not rare enough. A three-sigma result corresponds to about a one-in-740 chance of arising from a fluctuation, and, as the same review notes, results below three sigma are frequently overturned. Five sigma — about one in 3.5 million — is the particle-physics gold standard for a discovery claim. The gap between the two thresholds is not pedantry: it is the field’s insurance against the look-elsewhere effect, the fact that scanning many mass bins or many channels multiplies the chance that one of them fluctuates high.

Frontier Significance quoted locally and significance quoted globally are different numbers, and the difference is where most bumps live. The 750 GeV excess was 3.9 sigma locally at ATLAS and roughly 2 sigma once the look-elsewhere correction across the searched mass range was applied. A field that reports the local number in its abstract and the global number in a footnote is optimised to generate excitement it will later have to retract.

Frontier The frequentist sigma is a statement about the data given the theory, not about the theory given the data, and the second is what a reader actually wants. With a low prior probability that a given hypothesis is true, a three-sigma result can leave the hypothesis more likely false than true; the replication literature outside physics found published, statistically significant findings whose median prior of being true was about nine percent. The sigma on the plot and the odds the effect is real are related only through a prior nobody writes down.

Established Sigma also assumes the errors are Gaussian and correctly estimated, and the most instructive failures are the ones where they were not. A loose cable or an under-modelled dust foreground produces a high-sigma result that is simply wrong, and no amount of statistical significance protects against it — which is why the cases in section 3 turn on hardware and inputs far more often than on statistics. The old norm that extraordinary claims require extraordinary evidence is, read this way, a demand that the systematic error budget be extraordinary too.

Established The discovery threshold is a social convention as much as a statistical one. Five sigma became the particle-physics standard partly because the field has a long history of three- and four-sigma effects that evaporated, and the look-elsewhere effect and imperfectly known systematics mean the nominal probability behind a sigma is an upper bound on how safe the result is. The convention is a scar left by the base rate this brief wants to measure.

Established The most careful anomaly-watchers now demand corroboration across channels or experiments before they will even list a discrepancy. A 2024 review would enter an anomaly only if its combined global significance reached at least three sigma including the look-elsewhere effect and its signature appeared in more than one observable or independent experiment. That is the field encoding, as an admission rule, the lesson that a single high-sigma channel is not enough.

Frontier The organising question of this brief has no settled answer in the philosophy of science either. Whether a discrepancy indicts the theory or the measurement is, in the abstract, underdetermined — the Duhem-Quine point that any prediction rests on a bundle of auxiliary assumptions — and in practice the bundle that gets revised is the one someone finds a concrete fault in. The cases here are that abstract point made concrete and countable.

Established The muon anomalous magnetic moment is the case this brief is tethered to, and it is the one where the theory moved. In 2025 the Fermilab Muon g-2 experiment published its final result, combining six runs into a measurement of the muon’s anomaly at 127 parts per billion — a factor of four more sensitive than the 2001 Brookhaven result it inherited, and fully consistent with it. The experimental world average of the Brookhaven and Fermilab measurements stands at 116,592,071.5 with an uncertainty of 14.5, in units of 10⁻¹¹. The experiment, in other words, quadrupled its precision and did not move.

Established What moved was the Standard Model prediction. The 2020 Theory Initiative white paper, using the data-driven “R-ratio” method that turns measured electron-positron collision rates into the hadronic vacuum polarization term, predicted 116,591,810 with an uncertainty of 43 — some 4 to 5 standard deviations below the measurement, the gap that launched a thousand new-physics papers. The 2025 white paper, adopting lattice-QCD computations of that same hadronic term, predicted 116,592,033 with an uncertainty of 62. The difference between measurement and theory fell to 38 with an uncertainty of 63: about six-tenths of a standard deviation, which is agreement.

Established The two theory numbers are incompatible with each other at about three sigma, and that is the real event. The lattice value of the leading-order hadronic vacuum polarization, 7132 with an uncertainty of 61, sits above the data-driven value of 7045; the discrepancy that used to be experiment-versus-theory is now theory-input-versus-theory-input. As one account of the resolution put it, without the precision measurement to arbitrate, theorists using different methods would have remained 5-sigma apart with no arbiter. The experiment did not confirm new physics; it adjudicated a disagreement inside the calculation.

Frontier The anomaly did not vanish so much as migrate. A 2023 measurement from the CMD-3 experiment in Novosibirsk found a larger hadronic contribution than the entire catalogue of earlier electron-positron data, and the lattice results and CMD-3 pull one way while decades of prior collider data pull the other. The 2025 white paper judged the data-driven approach currently unable to produce a reliable estimate, and physicists now say the puzzle has shifted rather than closed: the tension between CMD-3, lattice QCD and the older data must still be explained. The headline — a four-sigma hint of new physics — is gone; a quieter data-versus-data problem has taken its place.

Established The OPERA superluminal-neutrino episode is the pure case: the theory never moved because the experiment was simply wrong. In September 2011 the OPERA collaboration reported neutrinos arriving at Gran Sasso about 60.7 nanoseconds earlier than light would, a result quoted at six sigma and refined to 6.2 sigma that November. Special relativity was not revised for a moment; the collaboration asked the world to find the error, which is the correct response to a six-sigma violation of a theory with a century of support.

Established The error was hardware, and there were two of them pushing opposite ways. A fiber-optic cable carrying the GPS timing signal to the master clock was not fully screwed in, which shortened the reported flight time by about 73 nanoseconds and made the neutrinos look fast; a clock oscillator running slightly off its 10 MHz frequency pushed the other way. OPERA announced the two faults in February 2012, confirmed the loose connector in March, and in July 2012 published a corrected difference of 6.5 plus or minus 15 nanoseconds — consistent with no effect at all. The independent ICARUS detector, sharing the same beam, had already timed seven neutrinos at the speed of light.

Established BICEP2 is the case where a real, high-sigma signal turned out to be foreground. In March 2014 the BICEP2 collaboration announced the first detection of primordial B-mode polarization in the cosmic microwave background — a signature of gravitational waves from inflation — with a statistical certainty quoted around seven sigma, above the discovery threshold. The claimed tensor-to-scalar ratio was near 0.2, and the result was reported worldwide as direct evidence for cosmic inflation.

Established The signal was Galactic dust. Planck’s maps showed the patch of sky BICEP2 had observed carried far more polarized dust than the team had assumed, and the dust emission was nearly as large as the entire BICEP2 signal. A January 2015 joint analysis by BICEP2, Keck and Planck concluded the earlier interpretation was no longer secure and that gravitational waves could account for no more than about half the observed B-mode signal. The theory of inflation was neither confirmed nor refuted; the measurement had detected the Milky Way.

Frontier The repair was methodological, and it worked. Later BICEP/Keck analyses added observing frequencies at 95, 150 and 220 GHz specifically to separate dust from any cosmological signal, and by 2021 had pushed the upper limit on the tensor-to-scalar ratio low enough to disfavour several standard inflationary models. The episode is now cited less as a scandal than as a demonstration that a single-frequency instrument cannot tell a cosmological signal from a local one — a systematic that no sigma could have flagged.

Established The 750 GeV diphoton bump is the textbook statistical fluctuation, and the textbook overreaction. In December 2015 ATLAS and CMS both reported a small excess of photon pairs near 750 GeV, at 3.9 and 3.4 sigma locally. Neither number survived the look-elsewhere correction as a discovery-grade signal, and neither experiment ever reached five sigma. By the ICHEP conference in August 2016, with more data, the excess was gone, and a Bayesian reading of the combined 2015-and-2016 data went from substantial evidence for a new particle to evidence against it.

Frontier What the episode measured was the field’s appetite, not a particle. Roughly 500 theoretical papers were written about the 750 GeV excess between its announcement and its disappearance — a body of work explaining, in careful detail, a fluctuation. The bump broke no rule of statistics; it was under the discovery line the whole time. It broke a rule of attention, and it is the single clearest argument in this brief for pricing a discrepancy at announcement rather than after the stampede.

Established The proton radius puzzle is the case where the more precise measurement was right and the less precise one moved. In 2010 Randolf Pohl’s team measured the proton’s charge radius using muonic hydrogen and found 0.84184 femtometres — nearly four percent below, and between 4.4 and 7 standard deviations short of (depending on which older data are averaged) the accepted value near 0.88 fm that decades of electron-scattering and ordinary-hydrogen spectroscopy had established. For most of a decade this looked like it might be new physics in the muon sector.

Established It resolved by convergence, not by discovery. A 2019 electronic-hydrogen Lamb-shift measurement by Eric Hessels’s group returned about 0.83 fm, and the PRad electron-scattering experiment at Jefferson Lab returned about 0.83 fm as well, both consistent with the muonic value. The conclusion, in the words of the reporting, requires no new physics: the older electron-based determinations had been in error, and the muonic measurement had been right all along. CODATA folded the muonic value in and revised its recommended proton charge radius to 0.8414 femtometres in 2018.

Frontier The residual scatter is a caution against declaring victory. Not every modern measurement agrees: a 2020 Max Planck 1S-3S determination gave 0.8482 fm and a Paris-group result had earlier landed near the old larger value, and PRad’s leaders themselves called for more accurate experiments before treating the puzzle as definitively closed. The gross discrepancy — a four-percent gap — is gone; a finer disagreement at the level of the error bars persists, which is what resolution usually looks like up close.

Established The Hubble tension is the control case: a discrepancy at least as significant as the others, in which neither side has moved. Local distance-ladder measurements led by the SH0ES team give an expansion rate near 73.0 kilometres per second per megaparsec; the value inferred from the Planck cosmic-microwave-background data under the standard cosmological model is 67.4. The gap sits around five sigma — the same one-in-3.5-million threshold that defines a discovery — and it has widened rather than narrowed as both measurements improved.

Frontier The usual escape routes have been closed off one by one. JWST observations in 2024 and 2025 confirmed the Cepheid distances underpinning the local measurement, ruling out stellar crowding and dust as the culprit; DESI’s baryon-acoustic-oscillation results largely track the Planck value near 68.5 while hinting that dark energy may evolve with time. As of late 2025 the tension remains the outstanding puzzle in cosmology, with neither the early-universe nor the late-universe determination yielding.

Speculative Which is why it is the interesting case: the meta-science question is what distinguishes a tension that will resolve like the muon from one that signals new physics. If the Hubble tension ends the way BICEP2 or the proton radius did, it will be a systematic hiding in one of the measurements; if it ends the way its defenders expect, it will be the first genuine new-physics anomaly in this set. There is at present no principled way to tell those futures apart in advance, and building one is the point of section 7.

Frontier A seventh case sits deliberately outside the tally because it shows how a cluster can look stronger than any single bump. As of the 2020 APS review the B-meson lepton-universality anomalies were characterised as a collective 5-to-7-sigma deviation, more compelling than isolated discrepancies precisely because several measurements pointed the same way. Correlated anomalies are harder to dismiss as independent fluctuations, which is a strength when they are real and a trap when a common systematic drives them all; this brief leaves it uncounted rather than assert a resolution it did not verify.

Established The muon case is now settled enough that anomaly-watchers have struck it off their lists. A 2024 survey of live particle-physics anomalies removed the muon anomalous magnetic moment from its catalogue entirely, citing the lattice-QCD hadronic light-by-light and vacuum-polarization work that brought the Standard Model prediction into agreement with the direct measurement. An anomaly can go from the field’s headline discrepancy to formally delisted in five years without a single new particle being found.

Frontier The W-boson mass anomaly is the case that turns on which measurements you agree to combine. In 2022 the CDF II experiment reported a W mass some 7 sigma above the Standard Model, but LHC and LEP determinations sat only about 1.8 sigma high, and a conservative combination that accounts for the tension between measurements pulled the global significance down to about 3.7 sigma. A discrepancy whose size depends on the averaging convention is a warning that the number on the plot is a choice as much as a fact.

Established Tallied, the six counted cases say something uncomfortable and something useful. Two ended in experimental error (OPERA, BICEP2), one in a statistical fluctuation (750 GeV), one in a corrected theoretical input with the measurement vindicated (proton radius), one in the theory prediction moving to meet an unchanged measurement (muon g-2), and one is unresolved (Hubble). The count of confirmed new particles or forces is zero. But six cases chosen because they were famous are a sample selected on the outcome, and the honest reading is that this is a vivid illustration in search of the base rate that section 7 would actually measure.

Frontier The contemporaneous odds on the muon anomaly were never logged, which is exactly the gap this brief is about. The 2020 APS review recorded the gap at the 3-to-4-sigma level and treated new physics as a live possibility; five years later the mainstream reading is that the Standard Model holds and the interesting fight is between calculation methods. Nobody wrote down, in 2020, the probability the community actually assigned to new physics, so the swing cannot now be scored.

Established The scoreboard for which side moved is itself the finding. In two cases the experiment was wrong and the theory never budged; in one the data fluctuated and neither side was ever really challenged; in one the less-precise measurement moved to the more-precise; in one the calculation moved to the measurement; and in one nothing has moved at all. The naive rule that theory yields to experiment fits only a minority of the record.

Frontier The first open question is whether a field-wide base rate even exists, or whether it is so domain-dependent as to be meaningless. A three-sigma bump in a collider search, a three-sigma tension in a precision spectroscopy measurement, and a three-sigma cosmological discrepancy have different priors, different systematic-error cultures and different look-elsewhere factors. A base rate pooled across all of physics might be a number with no referent; base rates computed per subfield might have too few high-sigma events per decade to estimate.

Frontier The second is the asymmetry this brief is named for: when experiment and theory disagree, is there a rule for which moves? The folk rule — experiments are facts, theories are provisional, so the theory yields — is contradicted by the muon case, where the theoretical input was the fragile side, and by OPERA, where the experiment was. What the cases suggest instead is that the least-scrutinised link moves: a hardware timing chain nobody had re-checked, a dust foreground nobody had mapped at the right frequency, a lattice-versus-data-driven choice nobody had forced. The asymmetry may be about scrutiny, not about the experiment-theory distinction at all.

Frontier The third is whether the field’s own contemporaneous judgement carries usable information. Outside physics, prediction markets and structured surveys have been tested against replication outcomes and shown to forecast them: across 103 findings and more than 15,000 forecasts, markets classified replications correctly about 73 percent of the time. Whether physicists’ contemporaneous odds on an anomaly would be as informative is untested, and section 7 is the test.

Speculative The fourth is whether AI-accelerated theory and measurement will raise the anomaly rate faster than the field can adjudicate it. More automated analyses scanning more channels means more look-elsewhere exposure and more three-sigma excursions; if the adjudication machinery does not scale with the anomaly rate, the 750 GeV stampede becomes the normal case rather than the cautionary tale.

Speculative A fifth question is whether unresolved tensions can be taxonomised in advance by how their two sides were built. The Hubble tension pits two mature measurement programmes with independent systematics; the muon gap pitted one measurement against one calculation with a shared, recomputable input. If the shape of a discrepancy — measurement-versus-measurement, measurement-versus-calculation, calculation-versus-calculation — predicts how it resolves, that is a structural prior the registry could extract without waiting for outcomes.

Established There is no standard, enforced format for reporting the significance of a discrepancy, and the choices are exactly the ones that inflate it. Local significance is more impressive than global; the trials factor that converts one into the other is often relegated to a footnote or omitted; and a reader without the correction cannot tell a discovery-grade signal from a look-elsewhere artefact. The 750 GeV case ran on the difference between a local 3.9 and a global 2.

Frontier The theoretical side of a discrepancy carries an uncertainty that is frequently invisible until someone recomputes it. The muon case is the warning: for two decades the “4 to 5 sigma” gap was quoted as if the theory number were fixed, when in fact the hadronic-vacuum-polarization input carried a model-dependence large enough to erase the anomaly. A discrepancy is a difference of two numbers with two error bars, and the theory error bar is the one most often quoted without its full systematic.

Established The incentive structure rewards the bump and not the correction. Five hundred papers followed the 750 GeV excess up; the analysis that showed it was a fluctuation drew a fraction of that attention, and the careful global-significance caveats drew less. Citation and career incentives are aligned with announcing anomalies and misaligned with retiring them, which is precisely the distortion a scoring registry would have to counteract.

Frontier Nobody logs the field’s odds at announcement, so the base rate cannot be reconstructed after the fact. By the time an anomaly resolves, the contemporaneous sense of how likely it was to be real has evaporated into selective memory. Without a timestamped record made before the outcome is known, any base rate computed later is contaminated by hindsight and by the selection of famous cases — the exact defect in this brief’s own six-case tally.

Frontier Blinding is applied unevenly, and its effect on the anomaly rate is unmeasured. Some collaborations freeze their analysis before looking at the signal region and some do not, but there is no systematic record linking blinding practice to whether an announced anomaly survived. The one intervention most likely to reduce false anomalies is deployed without anyone measuring its return.

Established Retractions and null resolutions are poorly indexed, so even the outcomes are hard to harvest. There is no systematic, searchable record that ties an anomaly announcement to its eventual fate; the outcome lives in a later paper, a conference talk, or the collective memory of a subfield, and assembling it after the fact is archival work. The registry would have to capture the outcome as deliberately as the announcement.

Established This topic depends first on metrology: a discrepancy is only as trustworthy as the calibration of the measurement that produced it. The OPERA timing chain and the BICEP2 foreground were both, at root, metrology failures, and a registry of discrepancies inherits the reliability of the underlying measurement standards. That dependency is developed in the companion brief on metrology infrastructure.

Established It depends on the instruments of the science-of-science, which supply the citation, authorship and timing data any registry would draw on. The tools that count papers, detect emerging research fronts and study how findings propagate are the substrate a discrepancy registry would sit on top of, and their known weaknesses — citation signals that cannot honestly fire for about three years, detectors validated only backwards — are inherited here too.

Frontier It depends on a consistent, enforced convention for reporting global significance and the trials factor. Without it, the registry’s central field — how significant was this at announcement — is not comparable across entries, and the base rate it computes is an average over incommensurable numbers. This is a standards dependency, not a research one, and standards are slow.

Frontier It depends on the theory side quantifying its own uncertainty honestly, which for the hardest cases means large-scale computation. The muon resolution required lattice-QCD calculations of the hadronic term to sub-percent precision; without that compute, the theory error bar stays a guess, and a discrepancy against a guessed error bar is not scorable.

Established It depends on the natural history of claims that never resolved cleanly, which a sister brief already assembles. Episodes that festered rather than dissolving — the ones where blinding never happened and no decisive test was run — are the negative space around this brief’s clean cases, and pathological-science case histories supply them.

Speculative The decisive instrument is a prospective registry that logs every discrepancy at or above three sigma at the moment it is announced, records the odds the field then assigns to its outcome, and is scored a decade later by a custodian with nothing to sell. It is a meta-science instrument, not an experiment in physics: it measures the field’s calibration rather than any quantity of nature. Its output is the number this whole brief is missing — the base rate at which high-sigma discrepancies resolve into fluctuation, experimental error, theoretical-input error, new physics, or lasting tension.

Speculative Each entry is fixed at announcement and cannot be edited afterward: the claim, the local and global significance, the proposed resolving test, and the field’s odds elicited through a structured survey or a small prediction market. The resolution categories are set in advance, and scoring happens at five and ten years against them, so that the record of what the field believed cannot be rewritten once the answer is known. Pre-registration is the entire point; a registry assembled retrospectively reproduces the selection bias it exists to remove.

Established The evidence that a field’s contemporaneous odds carry real information comes from outside physics, and it is encouraging. A 2015 study using prediction markets on 44 psychology replications forecast the outcomes correctly 71 percent of the time, beating expert surveys; a later meta-analysis across 103 findings and more than 15,000 forecasts found markets right about 73 percent of the time, with market prices correlating around 0.6 with actual replication. The community demonstrably knows something at announcement that it does not write down.

Frontier The transfer of that result to physics is exactly what is untested, and the differences cut both ways. Physics has far fewer high-sigma events per year than psychology has publications, so the registry accrues statistics slowly; but physics anomalies resolve more cleanly, into hardware faults and recomputations rather than contested effect sizes, so each entry is easier to score. Whether markets calibrated on collider bumps would transfer to cosmological tensions is itself one of the questions the registry would answer.

Speculative A secondary experiment is cheaper and could run first: mandatory reporting of global significance and the trials factor alongside every local significance. It requires no new instrument, only an editorial rule, and it would make the registry’s central field comparable across entries. It is the kind of intervention whose effect could itself be measured — the anomaly-retraction rate before and after the rule.

Frontier A third is blinded re-analysis as a routine step before announcement rather than after retraction. Blind analysis, in which the answer is hidden from the analysts until the procedure is frozen, already exists in parts of particle physics; measuring whether anomalies announced from blinded analyses survive at a higher rate than those from unblinded ones is a natural experiment the registry would capture for free.

Speculative The registry’s hardest design problem is the denominator. A base rate needs a defined population of discrepancies, and “every claim at or above three sigma” is a fuzzy set that grows with how many channels a field chooses to scan. Fixing the denominator — by subfield, by significance band, by a pre-agreed inclusion rule — is what separates a genuine base rate from another anecdote pile, and it is the part no existing effort has solved.

Handwave The clean version of the payoff — a single calibrated probability, quoted at announcement, that a given anomaly is real — is an aspiration the instrument would only approach. The honest deliverable is a set of subfield-specific, significance-banded resolution frequencies with wide error bars, improving slowly over decades. Anyone promising the tidy single number is describing the marketing, not the measurement.

Established The instrument needs almost no new hardware, which is the strongest argument for building it. The measurements, the significance figures and the eventual outcomes are already public; what is missing is the discipline of logging them prospectively with the field’s odds attached. The cost is custodial and cultural, not experimental, and section 10 is where the real difficulty lives.

Frontier A useful early output arrives before any base rate: calibration curves. Even a handful of scored entries lets the registry ask whether the field’s twenty-percent-likely anomalies come true about a fifth of the time, which is a calibration statement that needs far fewer events than a full base rate and would already discipline the announcement culture.

Frontier Engineered as a system, the registry is a versioned, timestamped public database with pre-registered resolution criteria and an append-only history. Its non-negotiable property is that entries cannot be altered after the outcome is known; the value of the instrument is destroyed the moment its records can be edited with hindsight. That is a solved problem in software — content-addressed, cryptographically timestamped records — but an unsolved one in scientific culture.

Frontier It needs an odds-elicitation layer: either a structured survey of qualified researchers or a small-stakes prediction market. Both have been built and validated for replication forecasting elsewhere; the engineering task is integrating them with the existing infrastructure of preprint servers and citation databases so that logging an anomaly and its odds is a low-friction step at announcement, not a separate chore. The dependency on that infrastructure is developed in the brief on metrology infrastructure and the brief on research front detection.

Established The theory side needs sustained large-scale computation, because the hardest discrepancies turn on inputs only lattice-scale calculation can pin down. The muon resolution rested on lattice-QCD hadronic-vacuum-polarization results at sub-percent precision, which required leadership-class supercomputing; a registry that wants scorable theory error bars for the hard cases depends on that compute continuing to be available. The forecasting horizons for all of this are set out in section 13.

Frontier Scoring requires an outcome-adjudication protocol that is itself pre-registered. Deciding, ten years on, whether a discrepancy resolved as fluctuation, error, input-correction, new physics, or still-open is a judgement, and unless the criteria for each verdict are fixed in advance the scoring reintroduces the hindsight bias the registry exists to remove. The adjudication rule is a piece of engineering, not an afterthought.

Established The nearest working technology is the replication-forecasting machinery from the social and life sciences: prediction markets and structured surveys run against actual replication outcomes. These are the direct proof-of-concept for the registry’s odds layer, and their measured accuracy — around 73 percent — is the best available estimate of how well a field can price its own claims.

Established The CODATA adjustment process is an existing, respected mechanism for arbitrating which of several discordant measurements to believe. The proton radius puzzle was ultimately absorbed into a revised recommended value once the modern measurements converged; CODATA is a standing example of a neutral custodian resolving a discrepancy, and a discrepancy registry is in part a proposal to make that function continuous and prospective.

Frontier Registered reports and blind analysis are adjacent methodological technologies that attack the same problem earlier in the pipeline. Where the registry scores anomalies after announcement, registered reports fix the analysis before the data are seen and blind analysis hides the answer until the method is frozen; both reduce the flow of look-elsewhere artefacts into the literature that the registry would otherwise have to catalogue.

Established Systematic-review and meta-analysis infrastructure is the closest cousin in method. The discipline of pooling studies, weighting by quality and reporting heterogeneity is exactly what scoring a registry at ten years amounts to, and the registry would borrow its statistical apparatus wholesale.

Frontier Public forecasting tournaments and long-running question platforms are a live testbed for eliciting calibrated odds on scientific questions. They already run questions on whether specific results will replicate or specific tensions will resolve, and their scoring rules and calibration records are directly transferable to a physics anomaly registry; the missing piece is a disciplined, physics-specific question set logged at announcement.

Established The registry needs a neutral custodian, and the natural candidates are the bodies that already arbitrate measurement. A metrology institute, an international physics union or a learned society has the standing and the disinterest the task requires; a custodian with a stake in any particular anomaly cannot credibly score it. Neutrality is the institutional precondition, and it is scarce.

Frontier It needs funding for an instrument that produces nothing for ten years. The first scorable base rate is a decade out by construction, and no ordinary grant cycle rewards a project whose deliverable is a spreadsheet of resolved bets ten years hence. This is the same funding pathology that afflicts long-baseline cohort studies, and it is why the instrument is more likely to be built by a foundation or a standards body than by a competitive research programme.

Frontier It needs an incentive to log the un-glamorous outcome. A field that gets credit for announcing anomalies and none for retiring them will under-populate the registry’s resolution column; making a clean retraction or a null resolution a citable, creditable act is an institutional design problem as much as a technical one. The companion brief on the science of science takes up these incentive questions directly, and the brief on pathological science supplies the natural history of claims that were never retired at all.

Established The CODATA task group is a proof that a neutral custodian for measurement disputes can exist and persist. It has arbitrated discordant fundamental-constant values for decades, absorbing the proton-radius revision when the evidence turned; a discrepancy registry asks for the same institutional form, extended from constants to claims and made prospective rather than periodic.

Frontier Logging odds against a colleague’s claim is a social act with reputational stakes, and the registry has to be designed so that it reads as calibration rather than as a bet against a person. A public record that a discrepancy was given, say, one-in-ten odds of being real at announcement is useful meta-science and also a potential embarrassment to the team that announced it; anonymised, aggregated odds mitigate this, but the tension is real and it is why individual forecasters may prefer markets to signed surveys.

Speculative A registry could chill bold claims, and that would be a cost, not only a benefit. Some anomalies worth chasing look unlikely at announcement; a culture that scores everyone’s calibration could push the field toward safe, high-prior claims and away from the long-shot measurements that occasionally pay off. The instrument measures calibration, and calibration is not the only virtue a research culture needs.

Established The honest handling of anomalies that vanish is itself a public-trust question. Each cycle of “new physics” headlines followed by quiet retraction — the muon hint, faster-than-light neutrinos, gravitational waves that were dust — spends public credibility, and a field that priced its anomalies honestly at announcement would have less to walk back. The register is partly an instrument of scientific integrity aimed at the gap between the press release and the eventual result.

Frontier There is a fairness question in who gets scored. High-profile collaborations announce most of the high-sigma anomalies and would carry most of the registry’s scored record, while smaller groups whose claims never reach three sigma stay off it entirely; a calibration instrument that only measures the loudest voices is not measuring the field.

Established A civilization that spends billions on frontier measurement has a stake in knowing how often its most exciting results survive. The direct cost of miscalibration is measurable in the units this brief has used: 500 papers and the attention behind them spent on one fluctuation, a quarter-century of new-physics theorising built on a theory number that would move. Multiplied across the anomaly stream, the misallocated effort is a real line item in the cost of science.

Frontier The value rises as science accelerates. If AI-assisted analysis multiplies the number of channels scanned and the number of three-sigma excursions reported, the ratio of genuine signals to look-elsewhere artefacts falls, and the ability to price a discrepancy at announcement becomes the difference between a field that chases every bump and one that spends its finite attention well. The instrument is cheap relative to the effort it would redirect.

Speculative The downside is a subtler form of miscalibration: a field that trusts the registry’s base rate too much and dismisses the one real anomaly because it looked like the last ten false ones. Every genuine discovery was, at announcement, a low-prior claim; a base rate is a prior, and a prior wrongly applied suppresses exactly the outliers that matter. The registry is a decision aid, and a civilization that mistakes a decision aid for a verdict has swapped one calibration error for another.

Established The record already shows the method self-correcting, which is the reassuring half of the story. Every one of the resolved cases here was overturned by the field’s own instruments — a rival detector, a better foreground map, a recomputed input, more data — usually within a decade. A base rate would not replace that self-correction; it would let the field spend its correction effort where the odds say it will pay.

These horizons track the building of the registry and the arrival of a calibrated base rate, not the resolution of any single anomaly.

• 10 yr: Frontier a prototype registry running in one or two subfields with pre-registered resolution criteria and an odds layer, plus mandatory global-significance reporting adopted by major journals; the first five-year scores landing but the sample still too small for a firm base rate. Cross-referenced with research front detection.
• 25 yr: Speculative enough scored entries across several subfields to quote significance-banded resolution frequencies with wide error bars, and a first test of whether physicists’ contemporaneous odds forecast outcomes as well as replication markets do elsewhere.
• 50 yr: Speculative a base rate stable enough to function as a genuine prior in funding and refereeing decisions, if the custodial and funding problems of section 10 were solved early; contingent on the instrument having survived two funding generations.
• 100 / 250+ yr: Handwave anomaly adjudication as a routine, calibrated part of the scientific method, with the base rate updated continuously and the 750 GeV stampede a historical curiosity; entirely dependent on institutions that do not yet exist choosing to maintain the record for a century.

• Depends on the instruments and standards developed in Science of Science, Research Front Detection, Metrology Infrastructure and the natural history assembled in Pathological Science; nothing on the map physically blocks a registry, but it inherits every one of their weaknesses.
• Requires (not on this map) a disinterested body willing to hold the record; an enforced editorial rule that every local significance is reported with its global counterpart and trials factor; patient capital for a project whose first scorable output is a decade away; and a prospective, timestamped log of the field’s odds made before any outcome is known.
• Enables a calibrated base rate that funders and referees could use as a prior, and an evidence-based answer to the question of which side moves when experiment and theory disagree.
• Adjacent to Hidden-Sector Searches, whose atlas of excluded parameter space is the same lesson from the other direction — that a null or a dissolved anomaly is a real scientific asset — and to Technology Forecasting, which shares the problem of scoring predictions honestly.

Established “A five-sigma result is a discovery.” Five sigma is the convention for a discovery claim, but it is necessary, not sufficient: it assumes Gaussian, correctly-estimated errors, and a systematic fault produces a high-sigma result that is simply wrong. OPERA’s faster-than-light neutrinos reached 6.2 sigma and were a loose cable; the threshold protects against fluctuations, not against a mis-modelled apparatus.

Established “When experiment and theory disagree, it is the theory that is on trial.” The muon g-2 case is the counterexample the field just lived through: the experiment quadrupled its precision and held, and the discrepancy dissolved because the theoretical input moved when lattice QCD displaced the data-driven value. Sometimes the fragile side is the calculation, and there is no general rule that the experiment is the fact and the theory the guess.

Established “The 2025 measurement confirmed the muon anomaly.” It confirmed the measurement, not the anomaly. The Fermilab result agreed with Brookhaven; what changed was the Standard Model prediction, which rose to meet it, leaving a difference of about six-tenths of a sigma. The anomaly was not confirmed — it was retired, and a new tension between lattice QCD, CMD-3 and older collider data took its place.

Frontier “Anomalies that vanish are wasted effort or failures of the scientists involved.” Exclusion and error-finding are the product, not a byproduct: BICEP2 taught the field to separate dust with multiple frequencies, OPERA’s cable tightened timing metrology, and the proton radius puzzle drove three independent measurements to sub-percent agreement. A dissolved anomaly can leave the field measurably better calibrated, which is the same point the brief on Hidden-Sector Searches makes about nulls.

Speculative “The Hubble tension will resolve like the muon g-2 anomaly did.” Perhaps, but the cases are not analogous: muon g-2 had a single quantity that two methods computed differently and a precise experiment to arbitrate, whereas the Hubble tension pits two robust, independently-checked measurement programmes against each other with no agreed arbiter and JWST having closed the easiest escape routes. Treating one as a template for the other is the base-rate error this brief warns against.

Handwave “A registry would tell you the probability that a given new anomaly is real.” Only in the marketing version. The achievable output is a set of subfield-specific, significance-banded resolution frequencies with wide and slowly-shrinking error bars — a prior, not a verdict, and one that must never be used to dismiss the low-prior claim that turns out to be the real discovery.

Frontier “A cluster of correlated anomalies is safer than a single bump.” Correlation cuts both ways: several measurements agreeing is strong evidence when they are independent and a shared trap when one systematic or one theoretical assumption feeds them all. The B-meson lepton-universality cluster looked like a 5-to-7-sigma case in 2020 for exactly this reason, which is why this brief leaves it uncounted rather than scored.