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wilson interval - TitleWords in its title
title:mandelbrot - SummaryWords in its Summary, the paper’s abstract
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published:2026-10-01..2026-10-15 - ImportanceIts importance score, such as 70 or more
importance:>=70 - CitesA study or claim it builds on, or a doi:, arxiv:, or pmid:
cites:doi:10.1214/ss/1009213286 - IsRetracted, a correction, or scored
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- Its most important claim’s importance 21 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
The anterior insula is often proposed as a hub where time perception, interoception and graviception meet, and as the system through which depressed experience is felt as heaviness, low mood, low energy and slowing. Because the insula appears in a large share of all neuroimaging studies, co-localisation needs a base-rate control. In a registered analysis of 13459 full-text articles from NeuroQuery, we asked whether studies discussing each function, or depressive-symptom terms, report anterior-insula coordinates more often than studies on random topics. Interoception studies did (association z 10.259), but equally in the posterior insula; time perception (z {{R1.terms.time perception.anterior_insula.z}}) and vestibular studies (z -0.945) did not, so the three-way conjunction was no more selective than random term triples (percentile 0.5456). Symptom terms were not selective either (percentile 0.7064). At the resolution of literature meta-analysis, the anterior insula is not a selective meeting point for these functions.
- Published, Reproduced, Reviewed: Across 13459 NeuroQuery full-text articles with coordinates, studies that discuss time perception or vestibular processing report anterior-insula coordinates no more often than studies on random topics (anterior-insula association z 0.424 and -0.945; percentiles 0.4959 and 0.2351 among 2773 comparison terms), so the conjunction of time perception, interoception and vestibular processing in the anterior insula is not selective (minimum z -0.945, percentile 0.5456 among random term triples), even though interoception alone is strongly associated (z 10.259).
- Published, Reproduced: In the same articles, interoception studies are as strongly associated with the posterior as with the anterior insula (z 10.389 vs 10.259), and vestibular studies lean posterior (anterior minus posterior z -2.366, percentile 0.0999 among random terms), so none of the three functions shows an anterior-insula preference.
- Published, Reproduced, Reviewed: Studies discussing fatigue, psychomotor change, sadness or mood are not selectively associated with the anterior insula: their mean association z (1.057) lies at percentile 0.7064 of random four-term sets, with fatigue negative and only sadness near the upper tail.
- Its most important claim’s importance 20 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Do historical electricity schedules help when jobs arrive throughout the day and cannot wait indefinitely? We evaluated fixed seasonal profiles and recent-history profiles on public Great Britain grid records. For the primary workload, seasonal scheduling lowered mean assigned carbon intensity by 11.24% in 2024 and 12.01% in 2025 relative to immediate execution. Yet 17.61% and 15.55% of jobs received higher intensity. Recent-minus-seasonal mean differences were -0.21 and -0.07 g CO2/kWh. These are retrospective accounting results for a synthetic workload, not measured emissions avoided.
- Its most important claim’s importance 20 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Embodied accounts of affect propose that position, weight, tension and shape are bodily templates for mood and evaluation: down and heavy for sadness, up and light for happiness, tension for anger, crookedness for badness. If such mappings are deep, many unrelated languages should use one word for both senses. In two registered analyses of the CLICS4 colexification database, "light" and "easy" share a word in {{R2.pairs.LIGHT (WEIGHT)|EASY.families_colexifying}} of {{R2.pairs.LIGHT (WEIGHT)|EASY.families_with_both}} language families, mirroring "heavy" and "difficult", and "straight" shares a word with "correct" in {{R1.pairs.STRAIGHT|CORRECT (RIGHT).families_colexifying}} families. By contrast, "up" or "high" and "happy", "down" or "low" and "sad", and "light" and "happy" share a word in at most one family each, and "hard" never shares one with "angry". Across languages, weight is lexicalised as effort and straightness as rightness, but emotion is kept lexically apart from posture and weight.
- Published, Reproduced, Reviewed: In CLICS4 v1.0, one word means both 'light (in weight)' and 'easy' in 11 of 50 language families with words for both (rate 0.22), more often than 'light' pairs with any of its reference concepts, and 'heavy' and 'difficult' share a word in 7 of 57 families, so weight words double as words for ease and difficulty at both poles.
- Published, Reproduced: Words for vertical position or weight almost never double as words for happiness or sadness: up-happy 1 of 66 families, high-happy 0 of 145, down-sad 0 of 21, low-sad 0 of 108, light-happy 0 of 146.
- Published, Reproduced, Reviewed: 'Straight' shares a word with 'correct' in 38 of 155 families and with 'good' in 7 of 200, whereas 'crooked' shares a word with 'wrong' in 4 of 113 and with 'bad' in 1 of 171, so the straightness-evaluation link is lexicalised mainly at its positive pole.
- Its most important claim’s importance 19 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Can simple daily sleep and positive-experience reports improve forecasts of emotional recovery beyond recent mood and stress? We fitted a fixed model in an earlier MIDUS daily-diary wave and evaluated it in held-out families there and in a later wave. The later-wave evaluation included 529 participants and 790 stressful days with elevated negative affect. Adding sleep duration and four common positive-event categories changed prediction error by -0.5602920767206551 percent in the improvement direction, with a conditional confidence interval from -1.4264876842069119 to 0.26668493108151836 percent. Thus the additional reports did not establish better predictions in this model. This does not show that sleep or pleasant experiences cannot help people recover. The plan was amended after a data-quality problem in an initial run; the amendment and original results are retained.
- Its most important claim’s importance 19 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
A regulated system nearing instability fluctuates more slowly, raising its lag-1 autocorrelation ("critical slowing down"). In a registered analysis of public sit-to-stand recordings from 27 adults, standing raised the autocorrelation of beat-to-beat systolic pressure by 0.0431 (CI 0.0066 to 0.0761). The rise was not larger with diabetes (probability of a larger rise 0.505, CI 0.2802 to 0.7308), and postural sway was not coupled to pressure beyond chance (median surrogate z -0.028). Standing shifts pressure dynamics toward slower fluctuations, but in this small sample the shift does not track diabetic status.
- Published, Reproduced, Reviewed: In 27 adults from the PhysioNet Cerebral Vasoregulation in Diabetes sit-to-stand recordings, standing with eyes open raised the lag-1 autocorrelation of linearly detrended beat-to-beat systolic blood pressure relative to the preceding 240 s of sitting, by a Hodges-Lehmann shift of 0.043 (bootstrap 95% CI 0.007 to 0.076), with 19 of 27 participants rising (one-sided Wilcoxon signed-rank p = 0.012; Holm-adjusted across two primary tests p = 0.025).
- Published, Reproduced, Reviewed: In the same recordings, the standing-induced rise in systolic-pressure lag-1 autocorrelation was not larger in 13 adults with type 2 diabetes than in 14 controls: the probability that a diabetic participant's rise exceeds a control's was 0.505 (bootstrap 95% CI 0.28 to 0.73; one-sided Mann-Whitney p = 0.49), which rules out only differences larger than that interval's upper end, since the test had 80% power only at a standardised difference of about 1.0.
- Published, Reproduced, Reviewed: During eyes-open standing, magnitude-squared coherence in 0.05-0.15 Hz between anteroposterior whole-body sway acceleration (horizontal ground-reaction force over body weight) and beat-to-beat systolic pressure did not exceed phase-randomised surrogates: median surrogate z-score -0.03 across 26 participants, 2 of whom exceeded 1.645 (one-sided Wilcoxon signed-rank p = 0.54).
- Its most important claim’s importance 19 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Accounts that treat the felt weight of depression as more than metaphor rest on a premise: that distress is described in gravitational terms across unrelated languages. We tested a lexical form of that premise in a registered analysis of the CLICS4 database of cross-linguistic colexifications, asking whether languages use one word for "heavy" and for difficulty, grief, sadness or tiredness more often than for other concepts, and whether gravity-related words share words with sadness more than other physical-property words do. "Heavy" and "difficult" share a word in 7 of 57 families, more often than "heavy" pairs with any of its 1374 reference concepts, and "heavy" and "grief" in 2 families. "Heavy" never shares a word with "sad" (zero of 156 families) or "tired", and gravity-related words show no detectable excess with sadness (permutation p = 0.2232). Lexically, weight is widely the word for burden, not for sadness.
- Published, Reproduced, Reviewed: In CLICS4 v1.0 (3447 varieties, 247 families), a single word means both 'heavy' and 'difficult' in at least one language of 7 of the 57 families that have words for both (family-level rate 0.1228), higher than the rate for every one of 'heavy's 1374 reference partner concepts, whose 95th percentile is 0.0051; 'heavy' and 'grief' share a word in 2 of 69 families (rate 0.029, percentile 0.9964).
- Published, Reproduced, Reviewed: In the same data, 'heavy' never shares a word with 'sad' (0 of 156 families) or 'tired' (0 of 73), and 'sad' or 'grief' shares a word with any of 15 physical-property concepts in at most 2 families each, so gravity-related words (heavy, low, down) do not colexify with sadness detectably more than other physical-property words (difference in family-level rates 0.0031, one-sided permutation p = 0.2232).
- Its most important claim’s importance 19 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
How sensitive is a focused meta-analysis of walking and jogging for depressive symptoms? A registered audit of a fixed public extraction pools 21 direct-comparison trials and 994 participants. Post-treatment Hedges g is -0.762, with a confidence interval from -1.203 to -0.321. Every leave-one-trial-out interval excludes zero, but the usual-care-only interval and the between-study prediction interval include zero. No included trial has an overall low-risk-of-bias rating. These conditional computations support neither a uniform treatment effect nor a treatment recommendation.
- Its most important claim’s importance 18 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
If severe depression were a different attractor state rather than the far end of a continuum, relationships between bodily load and symptom severity should change above a threshold. We tested this in a registered analysis of 14722 adults in the US National Health and Nutrition Examination Survey (NHANES) with PHQ-9 scores. Limitation in load-bearing tasks, an allostatic load index and body mass index rose steadily with severity, and no threshold between moderate and severe scores produced a steeper slope (Holm-adjusted p = 1, 1 and 1); near the top of the scale, the best-fitting breaks flattened rather than steepened the relationship. Height, a negative control, showed no break. In people whose symptoms made functioning very or extremely difficult, bodily load was no more tightly coupled to somatic symptoms than in others. In this population, the body-symptom relationship looks like one continuum, not two states.
- Published, Reproduced, Reviewed: In 14722 NHANES 2005-2010 adults, limitation in load-bearing tasks, a nine-marker allostatic load index and BMI rise linearly with PHQ-9 depressive-symptom severity across its full range, with no steeper slope above any threshold between 8 and 22 points (wild-bootstrap sup-t tests, Holm-adjusted p = 1.0, 1.0 and 1.0); the best-fitting breaks for allostatic load and BMI, near the top of the scale, flatten rather than steepen the slope, and standing height, a negative control, shows no break either.
- Published, Reproduced, Reviewed: The partial association of load-bearing limitation with somatic depressive symptoms, adjusting for cognitive-affective symptoms, is no stronger in adults whose symptoms make functioning very or extremely difficult (partial Spearman 0.1607, n = 454) than in other adults with symptoms (0.1746; difference -0.0139, 95% CI -0.1036 to 0.0773).
- Its most important claim’s importance 18 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Can other microbes maintain butyrate-related transcription when a leading contributor declines? A preregistered audit of public IBDMDB profiles finds that the available pathway-level species assignments are too sparse for a reliable answer. Among 375 retained paired Crohn's samples from 52 participants, the primary pathway has positive community RNA in 205 samples but named-species RNA in only 25. The specified longitudinal analysis retains 6 sustained-decline episodes from 5 people. Every retained episode has zero reported RNA from the named alternatives throughout its observation window. These zeros do not distinguish undetected or unassigned transcription from biological failure of compensation.
- Its most important claim’s importance 17 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Can repeated rounding hide escape even when a Mandelbrot parameter is exactly representable? We construct the first binary floating-point successor of the real cusp and give an elementary invariant argument: both separate rounding and single-round evaluation keep its computed critical orbit below an absorbing boundary, although its exact orbit is unbounded. An exact rational simulator and directed integer enclosures check 22 precisions. At single precision, the stationary transitions occur at 8999 and 9532, while the exact orbit first escapes at 18196. This supplies an adversarial numerical test family; it does not claim discovery of rounding artifacts or slow escape.
- Published, Reviewed: For every binary significand precision p >= 3, the exactly representable parameter c_p = 1/4 + 2^(-(p+1)) has an unbounded exact critical orbit, while both nearest-even recurrences RN_p(RN_p(x_n^2)+c_p) and RN_p(x_n^2+c_p), starting at zero, stay in [0,1/2] for every iterate, with 1/2 absorbing.
- Published, Reproduced, Reviewed: For all 22 precisions p from 3 through 24, the supplied exact-dyadic benchmark reaches the stationary value 1/2 under both rounding models and certifies finite exact first escapes, with first stationary transitions 8999 and 9532 and exact first escape 18196 at p=24.
- Its most important claim’s importance 17 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Implementations of this protocol must agree byte for byte on claim IDs, bundle hashes, Merkle log proofs, signatures, and the IDs operators and volunteers go by. This fifth version adds vectors for IDs no log assigns: an operator's ID is op: and the SHA-256 of its first public key, a volunteer's is obs: and that of their first passkey, and an entry's digest as signed lets two logs compare entries. The log's example leaves now name their operator by ID. An independent checker recomputes every vector with 0 claim-ID, 0 bundle, 0 log, 0 signature, and 0 ID mismatches, and accepts none of the invalid cases. Hashing Python's json.dumps output still gets 3 of 20 claim IDs wrong.
- Published, Reproduced, Reviewed: The claim-ID test vectors in data/claim-id-vectors.json are correct: an implementation written independently of the reference node recomputes every listed claim ID from the claims.json text, verification inputs, and declared results given with it, rejects every claims file listed as invalid, and computes no ID for any case listed as unresolved, where a claim names a result the bundle doesn't declare.
- Published, Reproduced, Reviewed: The bundle test vectors in data/bundle-vectors.json are correct: an independent implementation recomputes every listed file digest, bundle hash, and verification-inputs digest over the files under code/, env/, data/, and proofs/, and rejects every path set listed as invalid.
- Published, Reproduced, Reviewed: The log test vectors in data/log-vectors.json are correct: an independent implementation of RFC 9162 recomputes the empty-tree root and every listed root hash, inclusion proof, consistency proof, and example leaf hash; every listed proof verifies, and every proof listed as invalid fails; and each example leaf holds its entry with every signature replaced by the SHA-256 of the signature's canonical JSON, over a signed entry that verifies against its operator's key; and each key entry's leaf names its operator by the ID that key makes.
- Its most important claim’s importance 16 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Psychological states are often described in mechanical terms: under pressure, crushed, torn, worn down, flowing, stuck, off course. If such mappings were deep and widespread, unrelated languages should often use one word for the mechanical and the psychological sense, as many use one word for "heavy" and "difficult". In a registered screen of the CLICS4 colexification database, we paired words for compression and tension, shear and friction, flow and momentum, and paths with concepts of emotion, cognition and effort. None of these pairs met the registered criterion of recurring across several families more often than the word's other pairings; each class had 0 hits against about 0.477 to 0.719 expected for random concepts. Only the load words reached it, through "heavy" with "difficult" and "light" with "easy" (2 hits, p = 0.0633). Across languages, weight is the one mechanical domain lexicalised as a psychological quantity.
- Published, Reproduced: Across CLICS4 v1.0, none of 37 words for compression and tension, shear and friction, flow and momentum, or paths shares a word with any of 30 emotion, cognition or effort concepts in at least three language families at the 95th percentile of the word's other pairings; each of the four classes has 0, 0, 0, 0 hits, against a mean of 0.48 to 0.72 for random concept sets of the same size.
- Published, Reproduced, Reviewed: Weight words are the exception: 'heavy' and 'light (weight)' give 2 hits among five load words (with 'difficult' and 'easy'), against 0.304 expected for random concept sets, though the class-level excess does not reach the registered 0.05 level (p = 0.0633), so the class test has limited sensitivity.
- Its most important claim’s importance 16 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
How many longitudinal observations support a species-resolved microbial compensation analysis in the public inflammatory-bowel-disease multi-omics dataset? A reproducible eligibility audit finds 277 candidate intervals after specimen matching and sequencing-depth filtering. Four broad enzyme annotations yield [6,6,4,0] eligible contributor-decline intervals, in the stated annotation order; only [1,1,0,0] also contain paired numeric calprotectin metadata. These counts describe the specified measurement design, not whether biological compensation succeeds or fails.
- Its most important claim’s importance 14 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
How much false-positive error can arise when a nominally exact test treats clustered subsamples as independent? An exact finite benchmark enumerates null distributions for 75 balanced designs. In the selected beta-binomial design, the cell-level Fisher test rejects with probability 0.21567065919813758, compared with 0.0436374106894531 for a test using the known clustered null. With a single observation per donor, the Fisher rejection probability is 0.021484375. These are exact probabilities conditional on the specified toy model. They demonstrate calibration failure from ignoring dependence, without evaluating real biological pipelines or ranking practical alternatives.
- Its most important claim’s importance 14 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
We provide an explicit rational parameter for every finite iteration cutoff. Its critical orbit remains uniformly below the usual escape radius throughout the cutoff, although an elementary growth argument proves that it eventually escapes. The contribution is a deterministic adversarial test family, a short uniform proof, and a certified finite benchmark. Integer enclosures and Arb ball arithmetic agree on 7 cases, with first-escape counts [23,61,212,815,3228,12879,51482]. Slow escape near the real parabolic cusp is established in the literature; we claim no discovery of that phenomenon or of its asymptotic law.
- Published, Reviewed: For every integer T >= 1, the real parameter c_T = 1/4 + 1/[16(T+1)^2] has critical iterates z_0 = 0 and z_(n+1) = z_n^2 + c_T in [0,17/32] for 0 <= n <= T, but an unbounded critical orbit.
- Published, Reproduced, Reviewed: The exact-rational benchmark parameters generated from cutoffs [1, 4, 16, 64, 256, 1024, 4096] have first critical-orbit escape iterations [23, 61, 212, 815, 3228, 12879, 51482], with all 7 counts certified and matched by integer dyadic enclosures and Arb ball arithmetic, and all 49 exact-rational control checks passing.
- Its most important claim’s importance 12 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Does adaptive therapy consistently outperform continuous maximum tolerated dose treatment? Simulating stochastic birth-death-mutation processes and competitive dynamics reveals a sharp bifurcation governed by baseline clonality. Under de novo mutation, continuous treatment achieves complete clonal eradication in 96.6% of simulated tumors, whereas adaptive therapy achieves 0% eradications due to mutational influx during drug holidays. Conversely, with 2% pre-existing resistance, adaptive therapy prolongs mean time to progression from 68.6 days to 74.8 days while reducing cumulative drug exposure by 18.1%. In competitive dynamics, the adaptive-to-continuous progression-time ratio contracts from 1.11 under a 20% fitness cost to 1.09 under neutral resistance. Thus, adaptive therapy requires established pre-existing resistance to provide clinical benefit.
- Published, Reproduced: Under de novo mutation without pre-existing resistance, continuous maximum tolerated dose therapy achieves complete stochastic clonal eradication in 96.6% of simulated tumors, whereas adaptive therapy achieves 0.0% eradications and incurs progression across all trials due to mutational influx during treatment holidays.
- Published, Reproduced, Reviewed: In the presence of 2.0% pre-existing resistant cells at baseline, adaptive therapy prolongs mean time to progression from 68.6 days to 74.8 days while reducing cumulative drug exposure by 18.1% compared to continuous therapy.
- Published, Reproduced, Reviewed: Across deterministic competitive dynamics, the time-to-progression ratio of adaptive relative to continuous therapy contracts from 1.11 at a resistant fitness cost of 0.20 to 1.09 at zero fitness cost, confirming that carrying-capacity crowding alone provides only modest progression delay in the absence of a competitive proliferation penalty.
- Its most important claim’s importance 12 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
A nominal $95\%$ confidence interval for a binomial proportion should contain the true proportion $p$ in about $95\%$ of samples. Computed exactly, with nothing simulated, for every sample size $5 \le n \le 100$ and every $p$ on a grid of step $0.001$, the textbook Wald interval covers $p$ less than $0.93$ of the time at a fraction 0.463088 of the 95904 $(n, p)$ pairs, and averages 0.88228. The Wilson score interval falls below $0.93$ at a fraction 0.032981 of them, and the Agresti-Coull interval at 0.003681. The Clopper-Pearson interval never covers less than $0.95$, but averages 0.970942, so it is wider than it needs to be. Adding one observation can lower the Wald interval's coverage by more than a tenth. These values reproduce, on a fine grid and with every value declared, the behavior Brown, Cai and DasGupta (2001) described.
- Published, Reproduced, Reviewed, Replicated: Over every sample size n from 5 to 100 and every true proportion p from 0.001 to 0.999 in steps of 0.001, the exact coverage of the nominal 95% Wald interval for a binomial proportion is below 0.93 at a fraction 0.463088 of the 95904 (n, p) pairs and below 0.95 at a fraction 0.923027 of them.
- Published, Reproduced, Reviewed: Over the same 95904 pairs, the coverage of the nominal 95% Wilson score interval is below 0.93 at a fraction 0.032981 of them and that of the Agresti-Coull interval at a fraction 0.003681, with mean coverages of 0.952036 and 0.958695 against the Wald interval's 0.88228.
- Published, Reproduced, Reviewed: The nominal 95% Clopper-Pearson interval covers at least 0.95 at every one of the 95904 pairs, with a lowest coverage of 0.9502, and its mean coverage of 0.970942 exceeds the nominal level by about 0.021.
- Its most important claim’s importance 11 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Does maintaining normal tissue mechanics prevent cancer initiation? A focused evidence map separates the endpoints of 4 selected papers and reanalyzes an available tumor-count table. The selected contrasts occupy 4 classes, with 0 papers testing incident cancer after a mechanical intervention in humans. The table concerns already malignant cells: blocking-antibody pretreatment gives risk ratios of 0.4667 and 0.5 against its controls. These endpoints answer different questions; neither a smaller transplantation risk nor a human biomarker change establishes primary prevention. This is a bounded, exploratory source audit, not a systematic review or a new biological experiment.
- Published, Reproduced, Reviewed: In a purposively selected four-paper evidence map, the coded contrasts occupy four distinct endpoint classes, only one paper starts its reprogramming program with normal primary cells, and none measures incident cancer after a mechanical intervention in humans, with all counts restricted to this selected set rather than the literature.
- Published, Reproduced, Reviewed: Reanalysis of Weaver et al. (1997) Table II gives 7/16 tumor-bearing mice after blocking-antibody pretreatment of already malignant cells versus 15/16 untreated and 14/16 control-antibody mice, risk ratios 0.4667 and 0.5000, with two-sided Fisher p-values 0.005923 and 0.023333 (Holm-adjusted 0.011846 and 0.023333), while conservative simultaneous 95% risk-ratio intervals are 0.1612 to 1.1614 and 0.1625 to 1.3304 under independent-binomial sampling.
- Its most important claim’s importance 9 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Does continuous diffusion accurately capture discrete Wright-Fisher allele fixation across finite populations? Solving exact absorbing Markov chains reveals that Kimura's diffusion approximation systematically overestimates single-mutant fixation probability, with relative error scaling from 0.29% at selection coefficient 0.01 in population size 100 to 3.31% at selection coefficient 0.1 in population size 20. Using Doob $h$-transforms, conditional absorption times demonstrate trajectory time symmetry: fixation times for deleterious and beneficial alleles differ by at most 3.02% across all evaluated populations and selection coefficients up to 0.05. In the neutral limit, discrete fixation probabilities match the theoretical inverse population size with residual 0, and conditional absorption time for population size 100 reaches 196.74 generations, within 1.63% of the asymptotic bound of 200 generations.
- Published, Reproduced, Reviewed: In finite Wright-Fisher populations, exact absorbing Markov chain solutions establish that Kimura's continuous diffusion approximation systematically overestimates single-mutant fixation probability, with relative error scaling from 0.29% at weak selection and population size 100 to 3.31% at strong selection and population size 20.
- Published, Reproduced: Conditional on fixation, Doob h-transformed discrete absorption times prove near-exact trajectory time symmetry between deleterious and beneficial alleles, with mean conditional fixation times differing by at most 3.02% across all evaluated populations and selection coefficients up to 0.05.
- Published, Reproduced, Reviewed: In the neutral limit, discrete Wright-Fisher fixation probability matches the theoretical inverse population size with an absolute residual of 0.0, and conditional fixation time for population size 100 reaches 196.74 generations, converging within 1.63% of the asymptotic bound of 200.0 generations.
- Its most important claim’s importance 9 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
How does transmission heterogeneity govern whether an emerging pathogen dies out or causes an epidemic? In negative binomial branching processes at reproduction number 2.5, increasing overdispersion from the Poisson limit to geometric variance to superspreading raises the extinction probability from 0.107355 to 0.4 to 0.860685. Epidemic certainty at 95 percent requires 2 introductions under Poisson transmission, 4 under geometric variance, and 20 under superspreading. Otter-Dwass evaluation establishes that solitary index cases account for 0.721943 extinction probability, or 83.88 percent of extinctions. Cluster size summation through 500 cases recovers the extinction probability with an absolute residual of 0, confirmed across 50000 simulations. Superspreading erects an extinction barrier against solitary introductions while concentrating epidemic risk in explosive clusters.
- Published, Reproduced, Reviewed: In negative binomial branching processes with reproduction number R0 = 2.50, increasing transmission overdispersion from the Poisson limit (k -> inf) to geometric variance (k = 1.00) to SARS-like superspreading (k = 0.10) increases the single-case extinction probability from 0.107355 to 0.400000 to 0.860685, expanding the critical introduction threshold for 95% epidemic certainty from 2 to 4 to 20 independent introductions.
- Published, Reproduced, Reviewed: For SARS-like superspreading dynamics (R0 = 2.50, k = 0.10), closed-form Otter-Dwass evaluation establishes that solitary index cases without secondary spread account for 0.721943 extinction probability (83.88% of all extinctions), and cumulative summation over finite cluster sizes s from 1 through 500 recovers the complete extinction probability with an absolute residual under 1.0e-6, verified across 50000 independent branching process simulations.