{ "entries": [ { "badge_url": "https://proofengine.info/proofs/0-999-with-9s-repeating-forever-is-strictly-less-t/badge.json", "claim": "0.999... (with 9s repeating forever) is strictly less than 1.", "claim_hash": "bfc9a0540c3902d140027c758dc00591e478d558b1b250f3e8a3bc2f1dcfcbee", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/0-999-with-9s-repeating-forever-is-strictly-less-t/", "slug": "0-999-with-9s-repeating-forever-is-strictly-less-t", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/2026-being-divisible-by-2-3-7-11-13-17-proves-it-h/badge.json", "claim": "2026 being divisible by 2, 3, 7, 11, 13, 17 proves it has \"hidden perfect number properties.\"", "claim_hash": "9aabb19e4b78bdf8e3a8f2283e73ceb0ae52a5658e1f3bac4a5b7be52aa3f238", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/2026-being-divisible-by-2-3-7-11-13-17-proves-it-h/", "slug": "2026-being-divisible-by-2-3-7-11-13-17-proves-it-h", "verdict": "DISPROVED" }, { "badge_url": 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"verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/641-divides-2-32-1-exactly/badge.json", "claim": "641 divides 2^{32} + 1 exactly.", "claim_hash": "35826de829f21c5cf3d480f84eb244c8519d1b0a5d682dbf79c2a5d7e31dd4d6", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/641-divides-2-32-1-exactly/", "slug": "641-divides-2-32-1-exactly", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/a-man-on-tiktok-has-solved-the-riemann-hypothesis/badge.json", "claim": "A man on TikTok has solved the Riemann Hypothesis after one week of work.", "claim_hash": "3ad711c5bded6dad2c69c177c454ad5b6b0bb833fb9bc771fd35106e9a28a2e2", "confidence": 1.0, "doi": null, "generated_at": "2026-04-07", "proof_url": "https://proofengine.info/proofs/a-man-on-tiktok-has-solved-the-riemann-hypothesis/", "slug": "a-man-on-tiktok-has-solved-the-riemann-hypothesis", "verdict": "DISPROVED" }, { "badge_url": 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"a-real-number-is-rational-if-and-only-if-its-decim", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/a-venture-capital-fund-investing-50-million-in-25-startups-at-equal-sizes/badge.json", "claim": "A venture capital fund investing $50 million in 25 startups at equal sizes requires at least one 50x return and two 10x returns to achieve a 3x gross multiple.", "claim_hash": "6715696e7ea2f526c3790d1690dd2241b12c36cdeb5e048190946505a0ac733f", "confidence": 1.0, "doi": null, "generated_at": "2026-04-08", "proof_url": "https://proofengine.info/proofs/a-venture-capital-fund-investing-50-million-in-25-startups-at-equal-sizes/", "slug": "a-venture-capital-fund-investing-50-million-in-25-startups-at-equal-sizes", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/activation-of-cannabinoid-receptor-type-2-cb2-on-microglia-has-been-proposed-as/badge.json", "claim": "Activation of cannabinoid receptor type 2 (CB2) on microglia has been proposed as a mechanism for modulating neuroinflammatory pain states, including chronic widespread pain syndromes such as fibromyalgia where central sensitization and microglial activation have been implicated (Cabral & Griffin-Thomas, 2009; Stella, 2010; Chen et al., 2023).", "claim_hash": "7cca5a05189b041ab78e961274cc91f467eb5041c12b6180f2319e0fbc123e36", "confidence": 1.0, "doi": "10.5281/zenodo.20318616", "generated_at": "2026-05-20", "proof_url": "https://proofengine.info/proofs/activation-of-cannabinoid-receptor-type-2-cb2-on-microglia-has-been-proposed-as/", "slug": "activation-of-cannabinoid-receptor-type-2-cb2-on-microglia-has-been-proposed-as", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/adult-brain-neurogenesis/badge.json", "claim": "Critical periods of heightened cortical plasticity close permanently after early development, rendering the adult brain largely incapable of experience-dependent reorganization comparable to juvenile levels.", 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than typical human-written code", "claim_hash": "d06d7bf88965b73a2109df364e3ff33e06510ca0060608452cab33414eb8fe84", "confidence": 0.5, "doi": null, "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/ai-generated-code-has-fewer-security-vulnerabiliti/", "slug": "ai-generated-code-has-fewer-security-vulnerabiliti", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/ai-hallucinations-occur-on-fewer-than-5-of-factual/badge.json", "claim": "AI hallucinations occur on fewer than 5% of factual questions", "claim_hash": "1adb99e104f195615b9be7382282a3d689ce8025a593a30d674d81cd7652313c", "confidence": 1.0, "doi": "10.5281/zenodo.19489820", "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/ai-hallucinations-occur-on-fewer-than-5-of-factual/", "slug": "ai-hallucinations-occur-on-fewer-than-5-of-factual", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/ai-progress-in-capabilities-has-largely-plateaued/badge.json", "claim": "AI progress in capabilities has largely plateaued since late 2024", "claim_hash": "5f3033f91a42ff7bf43bcccd8aa5feb1016c8990100944f5aa2b597f63e47fb3", "confidence": 1.0, "doi": "10.5281/zenodo.19489822", "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/ai-progress-in-capabilities-has-largely-plateaued/", "slug": "ai-progress-in-capabilities-has-largely-plateaued", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/ai-will-replace-over-50-of-white-collar-jobs-by-20/badge.json", "claim": "AI will replace over 50% of white-collar jobs by 2035", "claim_hash": "fcc1f405920dbc8e453a740c931f54af0007489b1d57ac8bee6f4cfbd67296f5", "confidence": 1.0, "doi": "10.5281/zenodo.19489824", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/ai-will-replace-over-50-of-white-collar-jobs-by-20/", "slug": "ai-will-replace-over-50-of-white-collar-jobs-by-20", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/alkaline-water-or-alkaline-diets-meaningfully-improve-health-by-counteracting/badge.json", "claim": "Alkaline water or alkaline diets meaningfully improve health by counteracting body acidity", "claim_hash": "234c86ec1d3c789c9d4fd83a551ef4acc5f74f98a66651ad12228eff2aa9144b", "confidence": 1.0, "doi": "10.5281/zenodo.19489773", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/alkaline-water-or-alkaline-diets-meaningfully-improve-health-by-counteracting/", "slug": "alkaline-water-or-alkaline-diets-meaningfully-improve-health-by-counteracting", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/all-ultra-processed-foods-are-inherently-unhealthy/badge.json", "claim": "All ultra-processed foods are inherently unhealthy and should be avoided completely.", "claim_hash": 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"https://proofengine.info/proofs/artificial-sweeteners-such-as-aspartame-and-sucralose-promote-weight-gain-and/badge.json", "claim": "Artificial sweeteners such as aspartame and sucralose promote weight gain and metabolic disease.", "claim_hash": "fa9341c4212a72f0b989f82e2586de605d564241b6ab150bdc9210108c9c08e5", "confidence": 1.0, "doi": "10.5281/zenodo.19455606", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/artificial-sweeteners-such-as-aspartame-and-sucralose-promote-weight-gain-and/", "slug": "artificial-sweeteners-such-as-aspartame-and-sucralose-promote-weight-gain-and", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/birdsong-traffic-noise-anxiety-depression/badge.json", "claim": "Six minutes of birdsong reduced anxiety with a medium effect size, while six minutes of traffic noise raised depression with the same effect size.", "claim_hash": "b9be738e2c787b90fd70ad56149ec33451e0c104cbb1ae1d5257709a69446c5e", "confidence": 1.0, "doi": null, "generated_at": "2026-04-28", "proof_url": "https://proofengine.info/proofs/birdsong-traffic-noise-anxiety-depression/", "slug": "birdsong-traffic-noise-anxiety-depression", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/bitcoin-is-a-proven-hedge-against-inflation-and-fi/badge.json", "claim": "Bitcoin is a proven hedge against inflation and fiat currency collapse.", "claim_hash": "c95b76db2c43d4de2ce127eba1d99e0bb1ca347ae65d8592c822262f86b3b4e8", "confidence": 0.5, "doi": null, "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/bitcoin-is-a-proven-hedge-against-inflation-and-fi/", "slug": "bitcoin-is-a-proven-hedge-against-inflation-and-fi", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/bulls-charge-because-they-are-enraged-by-the-color/badge.json", "claim": "Bulls charge because they are enraged by the color red.", "claim_hash": "4ea5a77252792bd95f89d7daf3ed23f8927c74a83678a8a9c660ef32ba5e2a33", "confidence": 0.5, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/bulls-charge-because-they-are-enraged-by-the-color/", "slug": "bulls-charge-because-they-are-enraged-by-the-color", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/calories-in-calories-out-is-the-only-thing-that-matters-for-sustainable-weight/badge.json", "claim": "\"Calories in, calories out\" is the ONLY thing that matters for sustainable weight loss.", "claim_hash": "13bdd8874ddcfe04dbb725c6df534561baa01b2a7b739b86c54055dfaa0f2777", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/calories-in-calories-out-is-the-only-thing-that-matters-for-sustainable-weight/", "slug": "calories-in-calories-out-is-the-only-thing-that-matters-for-sustainable-weight", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/carbohydrates-not-dietary-fat-are-the-main-driver/badge.json", "claim": "Carbohydrates, not dietary fat, are the main driver of obesity and type-2 diabetes.", "claim_hash": "c19bc8c73bcd176f539b7291b07608431ada65256d9f7a3fecf31f91e45df657", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/carbohydrates-not-dietary-fat-are-the-main-driver/", "slug": "carbohydrates-not-dietary-fat-are-the-main-driver", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/chicago-shootings-vs-iran-war-kia/badge.json", "claim": "More Americans were killed in Chicago shootings over a four-week period in March 2026 than US service members killed in action in the US-Israel Iran war to date.", "claim_hash": "c2ae713a1cdb308e0b19ccb51129d7fe07e0f990ca151b2ef5233540a557359a", "confidence": 1.0, "doi": null, "generated_at": "2026-04-18", "proof_url": "https://proofengine.info/proofs/chicago-shootings-vs-iran-war-kia/", "slug": "chicago-shootings-vs-iran-war-kia", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/childhood-vaccines-never-placebo-tested/badge.json", "claim": "Childhood vaccines are not properly tested for safety because they were never tested in placebo-controlled clinical trials before approval.", "claim_hash": "ff5259f83b9b5b20605ff2a3ad7093600a6fd0402f04d074cf621c156e251487", "confidence": 1.0, "doi": null, "generated_at": "2026-04-28", "proof_url": "https://proofengine.info/proofs/childhood-vaccines-never-placebo-tested/", "slug": "childhood-vaccines-never-placebo-tested", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/chronic-periodontal-disease-has-been-associated-with-an-increased-risk-of/badge.json", "claim": "Chronic periodontal disease has been associated with an increased risk of atherosclerotic cardiovascular disease in adults, with consensus reviews pointing to systemic inflammation as a biologically plausible mediating mechanism (Tonetti & Van Dyke, 2013; Sanz et al., 2020; Cullinan & Ford, 2013).", "claim_hash": "44f3d51f3be6ac898e4c2a16e105d37111baf1321302bfdc4dde925db3490d36", "confidence": 1.0, "doi": "10.5281/zenodo.20311397", "generated_at": "2026-05-20", "proof_url": "https://proofengine.info/proofs/chronic-periodontal-disease-has-been-associated-with-an-increased-risk-of/", "slug": "chronic-periodontal-disease-has-been-associated-with-an-increased-risk-of", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/co-occurrence-of-lewy-pathology-and-adnc-is-common-30-of-ad-cases-have-lp-50-of/badge.json", "claim": "Co-occurrence of Lewy pathology and ADNC is common (\u226530% of AD cases have LP; \u226550% of DLB cases have ADNC)", "claim_hash": "d1d63374dd17f82f4367ad1d2e0bfbd5f09c039cbf0278f72a331fbb7aeae48d", "confidence": 1.0, "doi": "10.5281/zenodo.19510361", "generated_at": "2026-04-11", "proof_url": "https://proofengine.info/proofs/co-occurrence-of-lewy-pathology-and-adnc-is-common-30-of-ad-cases-have-lp-50-of/", "slug": "co-occurrence-of-lewy-pathology-and-adnc-is-common-30-of-ad-cases-have-lp-50-of", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/cold-plunges-and-ice-baths-significantly-boost-metabolism-via-brown-fat/badge.json", "claim": "Cold plunges and ice baths significantly boost metabolism via brown fat activation and aid long-term fat loss.", "claim_hash": "4c8109cfc487a24e387fc9f1f1ec72f150a1126ef87879a808eff9dd533b5b36", "confidence": 1.0, "doi": "10.5281/zenodo.19455609", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/cold-plunges-and-ice-baths-significantly-boost-metabolism-via-brown-fat/", "slug": "cold-plunges-and-ice-baths-significantly-boost-metabolism-via-brown-fat", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/computers-had-a-hidden-math-glitch-preventing-divi/badge.json", "claim": "Computers had a hidden \"math glitch\" preventing division by zero until it was patched in 2026.", "claim_hash": "8f66105eb80dd6f1d5a79ba8076d0c8e3d955d64e5ed4e8f9165bc2fcd15c0cd", "confidence": 0.5, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/computers-had-a-hidden-math-glitch-preventing-divi/", "slug": "computers-had-a-hidden-math-glitch-preventing-divi", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/consider-a-sector-with-n-2-symmetric-firms-each-endowed-with-l-task-positions/badge.json", "claim": "Consider a sector with N \\geq 2 symmetric firms, each endowed with L task-positions. Each firm i chooses an automation rate \\alpha_i in [0,1], paying wage w per human-staffed task and cost c per automated task, with integration friction cost (k/2) \\cdot L \\cdot \\alpha_i^2 where k > 0. Aggregate sectoral demand is D = A + \\lambda \\cdot w \\cdot L \\cdot [N - (1-\\eta) \\sum_j \\alpha_j], where A > 0 is exogenous demand, \\lambda \\in (0,1] is workers' marginal propensity to consume from wages, and \\eta \\in [0,1) is the fraction of displaced wage income recovered through reemployment. Each firm's revenue is D/N (equal market shares). Define s = w - c > 0 and \\ell = \\lambda(1-\\eta)w > 0. Each firm i maximizes \\pi_i = D/N - wL(1-\\alpha_i) - cL\\alpha_i - (k/2)L\\alpha_i^2. The Nash equilibrium automation rate is \\alpha^{NE} = (s - \\ell/N)/k. The cooperative optimum is \\alpha^{CO} = (s - \\ell)/k. The difference \\alpha^{NE} - \\alpha^{CO} = \\ell \\cdot (1 - 1/N)/k is strictly positive.", "claim_hash": "fae772fc076b9b05e3e393f6678cd97674d15623415b817dd11e7ace33b8a3db", "confidence": 1.0, "doi": null, "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/consider-a-sector-with-n-2-symmetric-firms-each-endowed-with-l-task-positions/", "slug": "consider-a-sector-with-n-2-symmetric-firms-each-endowed-with-l-task-positions", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/contrast-therapy-alternating-sauna-and-ice-bath-is-scientifically-proven/badge.json", "claim": "Contrast therapy alternating sauna and ice bath is scientifically proven superior for recovery and longevity.", "claim_hash": "9cb5e49ff4df931201d6e343ee078075516791b7b5b99967680864303c1d3d25", "confidence": 1.0, "doi": "10.5281/zenodo.19489779", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/contrast-therapy-alternating-sauna-and-ice-bath-is-scientifically-proven/", "slug": "contrast-therapy-alternating-sauna-and-ice-bath-is-scientifically-proven", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/covid-19-vaccines-killed-20-000-to-60-000-people-in-germany-as-claimed-in-dr/badge.json", "claim": "COVID-19 vaccines killed 20,000 to 60,000 people in Germany (as claimed in Dr. Helmut Sterz's March 19, 2026 parliamentary testimony and amplified by Elon Musk on April 12).", "claim_hash": "4425aded2bc07ab2c39cb4ec35b2b136022e452105f942d4b72310bbd060c312", "confidence": 1.0, "doi": null, "generated_at": "2026-04-19", "proof_url": "https://proofengine.info/proofs/covid-19-vaccines-killed-20-000-to-60-000-people-in-germany-as-claimed-in-dr/", "slug": "covid-19-vaccines-killed-20-000-to-60-000-people-in-germany-as-claimed-in-dr", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/cracking-your-knuckles-regularly-causes-arthritis/badge.json", "claim": "Cracking your knuckles regularly causes arthritis later in life.", "claim_hash": "3a926aa5ab94ffe133ef332acec5dbacb6e9f23666866ef14f332cd1ad9541bf", "confidence": 0.5, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/cracking-your-knuckles-regularly-causes-arthritis/", "slug": "cracking-your-knuckles-regularly-causes-arthritis", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/current-ai-systems-have-already-achieved-artificia/badge.json", "claim": "Current AI systems have already achieved Artificial General Intelligence (AGI).", "claim_hash": "91959925115d7e6c73c5f57c2404014009d2ff1990002c51c1111bf4bba1c318", "confidence": 1.0, "doi": "10.5281/zenodo.19489830", "generated_at": "2026-04-06", "proof_url": "https://proofengine.info/proofs/current-ai-systems-have-already-achieved-artificia/", "slug": "current-ai-systems-have-already-achieved-artificia", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/current-ai-systems-in-2026-have-near-zero-hallucinations-and-human-level/badge.json", "claim": "Current AI systems in 2026 have near-zero hallucinations and human-level reasoning across most domains.", "claim_hash": "b57390b0bbc632016fc89cd51ee60688b1e4c0a58609003e782ec4f6632da358", "confidence": 1.0, "doi": "10.5281/zenodo.19489832", "generated_at": "2026-03-31", "proof_url": "https://proofengine.info/proofs/current-ai-systems-in-2026-have-near-zero-hallucinations-and-human-level/", "slug": "current-ai-systems-in-2026-have-near-zero-hallucinations-and-human-level", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/current-global-warming-is-primarily-driven-by-natu/badge.json", "claim": "Current global warming is primarily driven by natural climate cycles rather than human CO2 emissions.", "claim_hash": "e80ce941412545f69c2591abc5e2b8fd92525374c78667b42580fe53a337c7ce", "confidence": 1.0, "doi": "10.5281/zenodo.19455633", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/current-global-warming-is-primarily-driven-by-natu/", "slug": "current-global-warming-is-primarily-driven-by-natu", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/daily-low-dose-aspirin-reduces-the-risk-of-recurrent-non-fatal-myocardial/badge.json", "claim": "Daily low-dose aspirin reduces the risk of recurrent non-fatal myocardial infarction in patients with prior cardiovascular disease, per the Antithrombotic Trialists' Collaboration meta-analysis.", "claim_hash": "94328a8ae4a2916e3849ed20de012fe1d700b9e34cd7148b9a84d66c50709723", "confidence": 1.0, "doi": "10.5281/zenodo.20315066", "generated_at": "2026-05-20", "proof_url": "https://proofengine.info/proofs/daily-low-dose-aspirin-reduces-the-risk-of-recurrent-non-fatal-myocardial/", "slug": "daily-low-dose-aspirin-reduces-the-risk-of-recurrent-non-fatal-myocardial", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/daily-mindfulness-meditation-for-10-minutes-increa/badge.json", "claim": "Daily mindfulness meditation for 10 minutes increases hippocampal volume by at least 1% within one month.", "claim_hash": "a1fad98533c21e3428c3b8b98a69fd12453f506194af36cba5b883284a0c038f", "confidence": 0.5, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/daily-mindfulness-meditation-for-10-minutes-increa/", "slug": "daily-mindfulness-meditation-for-10-minutes-increa", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/dark-energy-constitutes-more-than-68-of-the-univer/badge.json", "claim": "Dark energy constitutes more than 68% of the universe's total energy density according to the Planck 2018 legacy release.", "claim_hash": "28f33c87b778f9a312cd4fd1f3f107373679b0b33d1f11c501bee4a03fb0a012", "confidence": 0.5, "doi": "10.5281/zenodo.19455666", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/dark-energy-constitutes-more-than-68-of-the-univer/", "slug": "dark-energy-constitutes-more-than-68-of-the-univer", "verdict": "PROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/deepfake-videos-are-now-indistinguishable-from-rea/badge.json", "claim": "Deepfake videos are now indistinguishable from real footage to the average human eye.", "claim_hash": "c0330c569b9619b02ad7a949ed863f01bbf39989abe26aad17fcbb1b79173e76", "confidence": 1.0, "doi": "10.5281/zenodo.19489834", "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/deepfake-videos-are-now-indistinguishable-from-rea/", "slug": "deepfake-videos-are-now-indistinguishable-from-rea", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/detox-diets-and-juice-cleanses-actually-remove-tox/badge.json", "claim": "Detox diets and juice cleanses actually remove toxins from the body.", "claim_hash": "37343365fe657c728fe4ec2b170b7b207c3b64d05f91dc200475631749b4287e", "confidence": 1.0, "doi": "10.5281/zenodo.19489781", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/detox-diets-and-juice-cleanses-actually-remove-tox/", "slug": "detox-diets-and-juice-cleanses-actually-remove-tox", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/discrete-time-rescaling-yields-exp1/badge.json", "claim": "For a correctly specified discrete-time spike train model with conditional spike probabilities p_k, define A_m = sum_{k=tau_{m-1}+1}^{tau_m-1} -log(1-p_k) and R_m = A_m - log(1 - U_m * p_{tau_m}), where U_m ~ Uniform(0,1) independently. Then R_m are i.i.d. Exp(1), equivalently Z_m = 1 - exp(-R_m) are i.i.d. Uniform(0,1).", "claim_hash": "ae3cc621cf7f720f49f58043a219522499136d3f105b8a39ca4ecb98b2c4cf49", "confidence": 1.0, "doi": "10.5281/zenodo.19646034", "generated_at": "2026-04-19", "proof_url": "https://proofengine.info/proofs/discrete-time-rescaling-yields-exp1/", "slug": "discrete-time-rescaling-yields-exp1", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/earth-will-lose-gravity-for-exactly-7-seconds-on-a/badge.json", "claim": "Earth will lose gravity for exactly 7 seconds on August 12, 2026, causing 40 million deaths.", "claim_hash": "be21e663d955927162cc872659c77d00648469d2909e421dba4065a15c4e63b6", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/earth-will-lose-gravity-for-exactly-7-seconds-on-a/", "slug": "earth-will-lose-gravity-for-exactly-7-seconds-on-a", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/eating-eggs-significantly-raises-ldl-cholesterol-a/badge.json", "claim": "Eating eggs significantly raises LDL cholesterol and heart-disease risk.", "claim_hash": "82106e2c8594fac2c2315c2d21587375e093a9bdf427630ffd33bbe8122a8348", "confidence": 1.0, "doi": "10.5281/zenodo.19489785", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/eating-eggs-significantly-raises-ldl-cholesterol-a/", "slug": "eating-eggs-significantly-raises-ldl-cholesterol-a", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/eating-the-same-calories-late-at-night-leads-to-significantly-more-weight-gain/badge.json", "claim": "Eating the same calories late at night leads to significantly more weight gain and fat storage than earlier in the day.", "claim_hash": "69246fabace3c9d872d19f4e238f23f47f2bb81a0ed30d1c18cfaa11192892ef", "confidence": 1.0, "doi": "10.5281/zenodo.19455611", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/eating-the-same-calories-late-at-night-leads-to-significantly-more-weight-gain/", "slug": "eating-the-same-calories-late-at-night-leads-to-significantly-more-weight-gain", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/electric-vehicles-have-a-larger-lifetime-carbon-fo/badge.json", "claim": "Electric vehicles have a larger lifetime carbon footprint than gasoline cars when manufacturing and battery disposal are included.", "claim_hash": "a38e92261d45116b15b92810eab63fbc17008b59dce6250711c4f099c06777d2", "confidence": 0.5, "doi": "10.5281/zenodo.19455637", "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/electric-vehicles-have-a-larger-lifetime-carbon-fo/", "slug": "electric-vehicles-have-a-larger-lifetime-carbon-fo", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/eml-calculator-closure/badge.json", "claim": "Every elementary function that appears on a standard scientific calculator \u2014 including +, \\times, \\div, exponentiation x^y, \\sin, \\cos, \\tan, \\sqrt{x}, \\log_{10}, \\pi, e, i, and their compositions and inverses \u2014 can be realised as a finite binary tree of the operator \\mathrm{eml}(a, b) = e^{a} - \\ln b whose leaves are the constant 1 and the input variables. Each construction is verified to machine precision at multiple test points on its natural domain.", "claim_hash": "c423c438d5cd17ed2aede85cd041eee3da52104dc180cb58f72fd648b707615d", "confidence": 1.0, "doi": "10.5281/zenodo.19635623", "generated_at": "2026-04-17", "proof_url": "https://proofengine.info/proofs/eml-calculator-closure/", "slug": "eml-calculator-closure", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/eml-k17-multiplication-tree/badge.json", "claim": "The binary operator eml is defined by the expression \\text{eml}(a, b) = \\exp(a) - \\ln(b). There exists a finite binary tree consisting solely of eml operations, whose 9 leaves are drawn from \\{1, x, y\\}, such that the tree evaluates exactly to x \\times y. The tree has K = 17 tokens (8 eml operations and 9 leaves), and the identity holds for all complex x and y (in the algebraic setting where \\ln \\circ \\exp is the identity).", "claim_hash": "765e9ee03813e8a9c3068bc519e72782130932d4dbc9825bf52512a0d22a1134", "confidence": 1.0, "doi": "10.5281/zenodo.19635621", "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/eml-k17-multiplication-tree/", "slug": "eml-k17-multiplication-tree", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/eml-k19-addition-tree/badge.json", "claim": "The binary operator eml is defined by the expression \\text{eml}(a, b) = \\exp(a) - \\ln(b). There exists a finite binary tree consisting solely of eml operations, whose 10 leaves are drawn from \\{1, x, y\\}, such that the tree evaluates exactly to x + y. The tree has K = 19 tokens (9 eml operations and 10 leaves), and the identity holds for all real x and y (and formally for all complex x, y in the algebraic setting where \\ln \\circ \\exp is the identity).", "claim_hash": "96a9cb80abd60e6cd7bbe93e19d36720686ac735c463d5a6cc2a946114daa0d9", "confidence": 1.0, "doi": "10.5281/zenodo.19635620", "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/eml-k19-addition-tree/", "slug": "eml-k19-addition-tree", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/eml-pi-and-i-from-1/badge.json", "claim": "Using only the eml operator applied to the constant 1 (and allowing complex intermediates), there exist finite expressions that evaluate exactly to the mathematical constant \\pi and to the imaginary unit i. These expressions can be verified by symbolic simplification or by numerical evaluation that matches the known values \\pi \\approx 3.1415926535\\ldots and i^2 = -1 to machine precision.", "claim_hash": "65ad4c6ac6a65a79af0f57ff59d9572a98d7decad5a89111cf151673f883427d", "confidence": 1.0, "doi": "10.5281/zenodo.19635622", "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/eml-pi-and-i-from-1/", "slug": "eml-pi-and-i-from-1", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/eml-triple-nesting-recovers-ln-x/badge.json", "claim": "The binary operator eml is defined by the expression \\text{eml}(a, b) = \\exp(a) - \\ln(b) (where exp is the exponential function and ln is the principal branch of the natural logarithm). For every real x > 0, the nested expression \\text{eml}(1, \\text{eml}(\\text{eml}(1, x), 1)) equals the natural logarithm \\ln(x).", "claim_hash": "046e703c6bd6479775ff9fe2df254f96d8308976d6eef13eac3220ef757201f6", "confidence": 1.0, "doi": "10.5281/zenodo.19635615", "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/eml-triple-nesting-recovers-ln-x/", "slug": "eml-triple-nesting-recovers-ln-x", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/extreme-weather-events-hurricanes-wildfires-floods/badge.json", "claim": "Extreme weather events (hurricanes, wildfires, floods) have become dramatically more frequent and intense solely because of climate change.", "claim_hash": "4714abe2261598eb4780cade9612bee92a7498c146ec050b65c72b3c108cb7dd", "confidence": 1.0, "doi": "10.5281/zenodo.19489838", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/extreme-weather-events-hurricanes-wildfires-floods/", "slug": "extreme-weather-events-hurricanes-wildfires-floods", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/fewer-than-20-percent-of-the-positive-integers-fro/badge.json", "claim": "Fewer than 20 percent of the positive integers from 1 to 1000 are prime.", "claim_hash": "086e40b7200fd5bb5e7012a605ed8e9fdb5519b934402ca71e435c2682acc061", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/fewer-than-20-percent-of-the-positive-integers-fro/", "slug": "fewer-than-20-percent-of-the-positive-integers-fro", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/for-any-triangle-with-sides-a-b-c-where-a-b-c-then/badge.json", "claim": "For any triangle with sides a, b, c where a^2 + b^2 = c^2, the angle opposite c is exactly 90 degrees, AND the converse also holds.", "claim_hash": "e188d52003cc238f58c42e70411335f630c27d36b9dee8770947ab3cf40d2da0", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/for-any-triangle-with-sides-a-b-c-where-a-b-c-then/", "slug": "for-any-triangle-with-sides-a-b-c-where-a-b-c-then", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/frequent-sauna-use-4-to-7-times-per-week-dramatically-lowers-risk-of-heart/badge.json", "claim": "Frequent sauna use 4 to 7 times per week dramatically lowers risk of heart disease, dementia, and all-cause mortality.", "claim_hash": "bf4131791c0d0d0ab046383c622cc8fb66f09ae2063923d05008271d3a2c35a4", "confidence": 1.0, "doi": "10.5281/zenodo.19455616", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/frequent-sauna-use-4-to-7-times-per-week-dramatically-lowers-risk-of-heart/", "slug": "frequent-sauna-use-4-to-7-times-per-week-dramatically-lowers-risk-of-heart", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/glp-1-drugs-like-ozempic-cause-unavoidable-major-muscle-loss-and-ozempic-face/badge.json", "claim": "GLP-1 drugs like Ozempic cause unavoidable major muscle loss and \"Ozempic face\" even with exercise and high protein intake", "claim_hash": "9611e0604061eabc274440f4bf910aec5608126d3436e6a11dfb601e169e1c15", "confidence": 1.0, "doi": "10.5281/zenodo.19489787", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/glp-1-drugs-like-ozempic-cause-unavoidable-major-muscle-loss-and-ozempic-face/", "slug": "glp-1-drugs-like-ozempic-cause-unavoidable-major-muscle-loss-and-ozempic-face", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/grounding-or-earthing-through-barefoot-contact-with-the-earth-measurably/badge.json", "claim": "Grounding or earthing through barefoot contact with the Earth measurably reduces inflammation and improves recovery and sleep.", "claim_hash": "2047aac2bd1934c6ac9e62b84a9e857ecfef7d198300e2ad94ff76c78d2d6a27", "confidence": 1.0, "doi": "10.5281/zenodo.19455619", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/grounding-or-earthing-through-barefoot-contact-with-the-earth-measurably/", "slug": "grounding-or-earthing-through-barefoot-contact-with-the-earth-measurably", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/hair-and-fingernails-continue-to-grow-for-days-aft/badge.json", "claim": "Hair and fingernails continue to grow for days after a person dies.", "claim_hash": "bca1568000373cb37baa5156c5671cf04d0cf946c51496959abf4a87e24601b1", "confidence": 0.5, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/hair-and-fingernails-continue-to-grow-for-days-aft/", "slug": "hair-and-fingernails-continue-to-grow-for-days-aft", "verdict": "DISPROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/heavier-objects-fall-faster-than-lighter-objects-e/badge.json", "claim": "Heavier objects fall faster than lighter objects even in a perfect vacuum.", "claim_hash": "76c81b72a29bb74c588d48e32904465260144a78e0a1dcfdc0286a1200dbc3fb", "confidence": 1.0, "doi": "10.5281/zenodo.19489864", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/heavier-objects-fall-faster-than-lighter-objects-e/", "slug": "heavier-objects-fall-faster-than-lighter-objects-e", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/high-protein-diets-above-1-6-g-kg-body-weight-damage-kidneys-in-healthy-people/badge.json", "claim": "High-protein diets above 1.6 g/kg body weight damage kidneys in healthy people.", "claim_hash": "0f6b961971fb506d94d6f3c85f52ba7056b8a23016f10ea40f627104589f69be", "confidence": 1.0, "doi": "10.5281/zenodo.19489789", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/high-protein-diets-above-1-6-g-kg-body-weight-damage-kidneys-in-healthy-people/", "slug": "high-protein-diets-above-1-6-g-kg-body-weight-damage-kidneys-in-healthy-people", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/higher-atmospheric-co2-is-beneficial-plant-food-wi/badge.json", "claim": "Higher atmospheric CO2 is beneficial \"plant food\" with no net negative effects.", "claim_hash": "5290d4ef6e6acaa8f33d288cc9b267c3c945a865944367adc6734992503b2704", "confidence": 1.0, "doi": "10.5281/zenodo.19455640", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/higher-atmospheric-co2-is-beneficial-plant-food-wi/", "slug": "higher-atmospheric-co2-is-beneficial-plant-food-wi", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/hippocampal-damage-leads-to-anterograde-amnesia-fo/badge.json", "claim": "Hippocampal damage leads to anterograde amnesia for new episodic memories and does not impair skill learning or retrograde memories from early life.", "claim_hash": "78474571ec1448e1ba883a8700c721caaf53362e45417418ba6eae592bd297c3", "confidence": 0.5, "doi": "10.5281/zenodo.19455652", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/hippocampal-damage-leads-to-anterograde-amnesia-fo/", "slug": "hippocampal-damage-leads-to-anterograde-amnesia-fo", "verdict": "PROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/humans-use-only-10-of-their-brain-at-any-one-time/badge.json", "claim": "Humans use only 10% of their brain at any one time.", "claim_hash": "c4d94b0292e432065fccb163ff6365d4f279e4ad4e8aa51ba406071de27f9a96", "confidence": 1.0, "doi": "10.5281/zenodo.19600322", "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/humans-use-only-10-of-their-brain-at-any-one-time/", "slug": "humans-use-only-10-of-their-brain-at-any-one-time", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/if-a-company-raises-5-million-in-series-a-at-a-25-million-post-money-valuation/badge.json", "claim": "If a company raises 5 million in Series A at a 25 million post-money valuation and exits at $500 million seven years later, the annualized return to the Series A investor exceeds 40% before dilution.", "claim_hash": "731863cc4e82d11c6a0148ef16d86251e131efb0d51146e1d56b1b6de3a16d41", "confidence": 1.0, "doi": null, "generated_at": "2026-04-08", "proof_url": "https://proofengine.info/proofs/if-a-company-raises-5-million-in-series-a-at-a-25-million-post-money-valuation/", "slug": "if-a-company-raises-5-million-in-series-a-at-a-25-million-post-money-valuation", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/in-venture-capital-the-top-10-of-investments-generate-more-than-75-of-total/badge.json", "claim": "In venture capital, the top 10% of investments generate more than 75% of total portfolio returns, following a power law distribution.", "claim_hash": "fbd46bee715307ef6db3d368f29f7e333284fb60f35c547a13e12ea5150445a2", "confidence": 0.5, "doi": null, "generated_at": "2026-04-08", "proof_url": "https://proofengine.info/proofs/in-venture-capital-the-top-10-of-investments-generate-more-than-75-of-total/", "slug": "in-venture-capital-the-top-10-of-investments-generate-more-than-75-of-total", "verdict": "SUPPORTED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/infinite-economic-growth-is-possible-on-a-finite-p/badge.json", "claim": "Infinite economic growth is possible on a finite planet.", "claim_hash": "2e335972891fa16b5ace427e568c65ffa0d91916ab091c1b05720cc86eb333b1", "confidence": 0.5, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/infinite-economic-growth-is-possible-on-a-finite-p/", "slug": "infinite-economic-growth-is-possible-on-a-finite-p", "verdict": "PROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/infonce-lower-bounds-mutual-information/badge.json", "claim": "Let (X,Y) ~ p(x,y). For each contrastive training instance, sample one positive Y_1 ~ p(y|X) and N-1 negatives Y_2,...,Y_N iid ~ p(y), conditionally independent given X. Let i* be the index of the positive, uniformly distributed over {1,...,N}. For any measurable scoring function s(x,y), define L_N(s) = - E[ log( exp(s(X,Y_{i*})) / sum_j exp(s(X,Y_j)) ) ]. Then log N - L_N(s) is a lower bound on I(X;Y). The Bayes-optimal score is s*(x,y) = log(p(y|x)/p(y)) + c(x), where c(x) is arbitrary. Under the standard multi-sample setup, the resulting InfoNCE lower bound tightens as N increases.", "claim_hash": "52a6a7faa4f69233efc0e03768231203da0d40ffa1ed93e8f047410a1ee548e1", "confidence": 1.0, "doi": "10.5281/zenodo.19645782", "generated_at": "2026-04-18", "proof_url": "https://proofengine.info/proofs/infonce-lower-bounds-mutual-information/", "slug": "infonce-lower-bounds-mutual-information", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/intermittent-fasting-is-scientifically-proven-supe/badge.json", "claim": "Intermittent fasting is scientifically proven superior to other diets for fat loss and longevity.", "claim_hash": "e3ec4bc9d5fecc14f50172e366c36000d3beb336f748eb6c65fcff864ffe9d06", "confidence": 1.0, "doi": "10.5281/zenodo.19489791", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/intermittent-fasting-is-scientifically-proven-supe/", "slug": "intermittent-fasting-is-scientifically-proven-supe", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/lectins-in-nightshades-like-tomatoes-and-potatoes-and-grains-cause-widespread/badge.json", "claim": "Lectins in nightshades like tomatoes and potatoes and grains cause widespread inflammation and leaky gut.", "claim_hash": "9a87d40846336e6e94f7f66b94e0277f7154085280b4a003c27bc2489f3c13d9", "confidence": 1.0, "doi": null, "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/lectins-in-nightshades-like-tomatoes-and-potatoes-and-grains-cause-widespread/", "slug": "lectins-in-nightshades-like-tomatoes-and-potatoes-and-grains-cause-widespread", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/lightning-never-strikes-the-same-place-twice/badge.json", "claim": "Lightning never strikes the same place twice.", "claim_hash": "8d2ddb21285065248e59b2dbbcf8615cfd016ae72f20c35bb581d4a7eca14540", "confidence": 1.0, "doi": "10.5281/zenodo.19489858", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/lightning-never-strikes-the-same-place-twice/", "slug": "lightning-never-strikes-the-same-place-twice", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/local-cepheid-variable-measurements-of-the-hubble/badge.json", "claim": "Local Cepheid-variable measurements of the Hubble constant exceed 72 km s\u207b\u00b9 Mpc\u207b\u00b9 while the 2018 Planck CMB inference yields a value below 68 km s\u207b\u00b9 Mpc\u207b\u00b9.", "claim_hash": "6fc7649ebc9b8200d38fc4dd59134277a22707698564a92c10eb1c2c8fb814f2", "confidence": 0.5, "doi": "10.5281/zenodo.19455673", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/local-cepheid-variable-measurements-of-the-hubble/", "slug": "local-cepheid-variable-measurements-of-the-hubble", "verdict": "PROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/math-washing-a-spreadsheet-presenting-empirical-observations-as-universal/badge.json", "claim": "Presenting empirical spreadsheet observations as universal theorems violates the hypothetico-deductive method as defined by mainstream philosophy of science.", "claim_hash": "531831a4aac552457a8bf06e613206f8d970b84bdb7d214239e603d8f415324b", "confidence": 1.0, "doi": null, "generated_at": "2026-04-07", "proof_url": "https://proofengine.info/proofs/math-washing-a-spreadsheet-presenting-empirical-observations-as-universal/", "slug": "math-washing-a-spreadsheet-presenting-empirical-observations-as-universal", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/microplastics-ingestion-from-food-water-and-air-is-currently-causing-major/badge.json", "claim": "Microplastics ingestion from food, water, and air is currently causing major declines in human fertility and hormone disruption.", "claim_hash": "3084b41cf1586886faa26cc78bfd671767cdd860987a1c2364e639499932ebeb", "confidence": 1.0, "doi": "10.5281/zenodo.19455620", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/microplastics-ingestion-from-food-water-and-air-is-currently-causing-major/", "slug": "microplastics-ingestion-from-food-water-and-air-is-currently-causing-major", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/mouth-taping-during-sleep-greatly-improves-sleep-quality-and-reduces-sleep-apnea/badge.json", "claim": "Mouth taping during sleep greatly improves sleep quality and reduces sleep apnea.", "claim_hash": "753c638721e7e6908534e8e52057413cbf7312c7ca777047c2edc15248205642", "confidence": 1.0, "doi": "10.5281/zenodo.19455621", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/mouth-taping-during-sleep-greatly-improves-sleep-quality-and-reduces-sleep-apnea/", "slug": "mouth-taping-during-sleep-greatly-improves-sleep-quality-and-reduces-sleep-apnea", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/multivitamins-and-most-supplements-provide-meaningful-health-benefits-for-the/badge.json", "claim": "Multivitamins and most supplements provide meaningful health benefits for the general healthy population.", "claim_hash": "50dde78a9f6c33653cda89d667adce6380a1a954d373029ac4ecc56141a0f948", "confidence": 1.0, "doi": "10.5281/zenodo.19489795", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/multivitamins-and-most-supplements-provide-meaningful-health-benefits-for-the/", "slug": "multivitamins-and-most-supplements-provide-meaningful-health-benefits-for-the", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/napoleon-bonaparte-stood-shorter-than-the-average/badge.json", "claim": "Napoleon Bonaparte stood shorter than the average Frenchman of his era.", "claim_hash": "d20885922a5192718e6c03979b9c94b5ade0b29424802fff6fb51acfb363e5e8", "confidence": 1.0, "doi": null, "generated_at": "2026-04-16", "proof_url": "https://proofengine.info/proofs/napoleon-bonaparte-stood-shorter-than-the-average/", "slug": "napoleon-bonaparte-stood-shorter-than-the-average", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/natural-sugars-in-fruit-are-healthy-while-added-su/badge.json", "claim": "Natural sugars in fruit are healthy while added sugars are poison (in equivalent amounts).", "claim_hash": "476a2c1d3787a5261014f5c7aeb4bb8758193e7b85e5240cc96795266eb263d5", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/natural-sugars-in-fruit-are-healthy-while-added-su/", "slug": "natural-sugars-in-fruit-are-healthy-while-added-su", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/nuclear-power-is-the-safest-form-of-electricity-generation-with-the-lowest/badge.json", "claim": "Nuclear power is the safest form of electricity generation with the lowest death rate per TWh produced.", "claim_hash": "9cb6e9d8dc476e60d875463c1b6cd51cca8b39660bc64c12f575aaba4848b5cd", "confidence": 1.0, "doi": "10.5281/zenodo.19455641", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/nuclear-power-is-the-safest-form-of-electricity-generation-with-the-lowest/", "slug": "nuclear-power-is-the-safest-form-of-electricity-generation-with-the-lowest", "verdict": "UNDETERMINED" }, { "badge_url": "https://proofengine.info/proofs/nuclear-power-is-too-dangerous-to-be-a-major-part/badge.json", "claim": "Nuclear power is too dangerous to be a major part of any clean-energy future.", "claim_hash": "fc579d2ff2bd4b72c1e7dbb4d722c0ab534b888414d22d7c0a3615464acf2dad", "confidence": 1.0, "doi": "10.5281/zenodo.19489842", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/nuclear-power-is-too-dangerous-to-be-a-major-part/", "slug": "nuclear-power-is-too-dangerous-to-be-a-major-part", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/over-80-of-the-brain-s-neurons-are-located-in-the/badge.json", "claim": "Over 80% of the brain's neurons are located in the cerebellum.", "claim_hash": "ad11d520944585b349fc3ee444f708fd450efe346986dfdeb89739cf7f074dda", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/over-80-of-the-brain-s-neurons-are-located-in-the/", "slug": "over-80-of-the-brain-s-neurons-are-located-in-the", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/poisson-spike-train-loglik-concave/badge.json", "claim": "Consider a spike-train encoding model where spikes are generated by an inhomogeneous Poisson process with intensity lambda_t = f(eta_t), eta_t = x_t^T beta + h_t^T gamma + b, with convex parameter space for theta = (beta, gamma, b). If f is positive, convex, and log-concave, then the log-likelihood is concave in theta. Therefore every local maximum is global, ML fitting is a convex optimization problem, and the same holds for MAP inference under any log-concave prior on theta.", "claim_hash": "9c7237f28874d690ee8f4ef7dcb0f2dfe0f5541d8103e0495afc9dabbc4c46b4", "confidence": 1.0, "doi": "10.5281/zenodo.19645244", "generated_at": "2026-04-18", "proof_url": "https://proofengine.info/proofs/poisson-spike-train-loglik-concave/", "slug": "poisson-spike-train-loglik-concave", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/potential-games-fip-and-pure-nash/badge.json", "claim": "Let G be a finite strategic-form game. (A) If G admits a generalized ordinal potential P, then every better-response path is finite, G has the finite improvement property, and G admits a pure Nash equilibrium. (B) If G admits an exact potential P, then every global maximizer of P is a pure Nash equilibrium.", "claim_hash": "391a7485ef22ef7e6df9df1a921d77e679531873bff3d1108b08cce6748da9f7", "confidence": 1.0, "doi": null, "generated_at": "2026-04-28", "proof_url": "https://proofengine.info/proofs/potential-games-fip-and-pure-nash/", "slug": "potential-games-fip-and-pure-nash", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/quantum-entanglement-enables-the-transmission-of-u/badge.json", "claim": "Quantum entanglement enables the transmission of usable information faster than the speed of light when the distant parties pre-agree on a measurement basis.", "claim_hash": "53ddc25a6072fdf2ffedf0e9710554cf23c81f1b0d289b9c34ca1b0fdf1a20df", "confidence": 1.0, "doi": "10.5281/zenodo.19489844", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/quantum-entanglement-enables-the-transmission-of-u/", "slug": "quantum-entanglement-enables-the-transmission-of-u", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/red-light-therapy-at-660-850-nm-significantly-reduces-wrinkles-boosts-collagen/badge.json", "claim": "Red light therapy at 660-850 nm significantly reduces wrinkles, boosts collagen, and improves skin health.", "claim_hash": "06213e59b7979510d9c6a992b5ab19dc8d25d150384b78d2c8ac4355355ac8cb", "confidence": 1.0, "doi": "10.5281/zenodo.19455625", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/red-light-therapy-at-660-850-nm-significantly-reduces-wrinkles-boosts-collagen/", "slug": "red-light-therapy-at-660-850-nm-significantly-reduces-wrinkles-boosts-collagen", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/renewable-energy-solar-wind-can-replace-fossil-fue/badge.json", "claim": "Renewable energy (solar + wind) can replace fossil fuels without major grid upgrades or backups.", "claim_hash": "810b7bfa8980fafe2d1d07ee9c5a9cb4873fc2f1a6853d766367e7dbec96b187", "confidence": 1.0, "doi": "10.5281/zenodo.19455644", "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/renewable-energy-solar-wind-can-replace-fossil-fue/", "slug": "renewable-energy-solar-wind-can-replace-fossil-fue", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/seed-oils-canola-sunflower-soybean-corn-oil-are-to/badge.json", "claim": "Seed oils (canola, sunflower, soybean, corn oil) are toxic and a primary cause of modern chronic inflammation and disease.", "claim_hash": "e1403b0743e813151b0b4376755f0739c3cb93e052055bf5826a6165913880fd", "confidence": 1.0, "doi": "10.5281/zenodo.19489797", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/seed-oils-canola-sunflower-soybean-corn-oil-are-to/", "slug": "seed-oils-canola-sunflower-soybean-corn-oil-are-to", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/sequoia-capital-manages-over-100-billion-in-assets-under-management-aum-with-an/badge.json", "claim": "Sequoia Capital manages over $100 billion in assets under management (AUM), with an average fund multiple exceeding 4x net returns to investors.", "claim_hash": "c61952ae0df5065fa5a2b7e02746752943d681827a5223336f52e50acb904aa9", "confidence": 1.0, "doi": null, "generated_at": "2026-04-08", "proof_url": "https://proofengine.info/proofs/sequoia-capital-manages-over-100-billion-in-assets-under-management-aum-with-an/", "slug": "sequoia-capital-manages-over-100-billion-in-assets-under-management-aum-with-an", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/smartphone-screens-deliver-80-100-lux-vs-sunlight-100-000-lux-posing-negligible/badge.json", "claim": "Smartphone screens deliver ~80-100 lux (vs. sunlight ~100,000 lux), posing negligible blue-light risk for retinal damage or macular degeneration, but evening use suppresses melatonin via ipRGCs/melanopsin and delays sleep onset by up to 90 minutes.", "claim_hash": "b443b93fbe431e5b3d7d849a2d11c2fe2965756b35b5625290c17f49015c948f", "confidence": 1.0, "doi": "10.5281/zenodo.19455628", "generated_at": "2026-04-06", "proof_url": "https://proofengine.info/proofs/smartphone-screens-deliver-80-100-lux-vs-sunlight-100-000-lux-posing-negligible/", "slug": "smartphone-screens-deliver-80-100-lux-vs-sunlight-100-000-lux-posing-negligible", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/sunscreen-is-more-dangerous-due-to-chemical-absorption-and-vitamin-d-blocking/badge.json", "claim": "Sunscreen is more dangerous due to chemical absorption and vitamin D blocking than moderate sun exposure.", "claim_hash": "fa944d61c38d3e2d8ba562ef6fbc9dabbdefdc22d2068743fa01d6f94e2bb078", "confidence": 1.0, "doi": "10.5281/zenodo.19489799", "generated_at": "2026-04-01", "proof_url": "https://proofengine.info/proofs/sunscreen-is-more-dangerous-due-to-chemical-absorption-and-vitamin-d-blocking/", "slug": "sunscreen-is-more-dangerous-due-to-chemical-absorption-and-vitamin-d-blocking", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/thank-god-2026-has-no-square-root-is-mathematically-meaningful/badge.json", "claim": "\"Thank God 2026 has no square root\" is mathematically meaningful", "claim_hash": "fdbfca4269ac53be235f8b252cff0ee654179e3b2fec12f506216b46dca8d1aa", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/thank-god-2026-has-no-square-root-is-mathematically-meaningful/", "slug": "thank-god-2026-has-no-square-root-is-mathematically-meaningful", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/the-100000th-prime-number-is-exactly-1299709/badge.json", "claim": "The 100000th prime number is exactly 1299709.", "claim_hash": "7b75b86f3120711ea6470a5ab8017dc9c2d66e7e08a07bbbbc19919389afe387", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-100000th-prime-number-is-exactly-1299709/", "slug": "the-100000th-prime-number-is-exactly-1299709", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/the-2005-israeli-disengagement-from-gaza-removed-e/badge.json", "claim": "The 2005 Israeli disengagement from Gaza removed every settlement and military outpost AND resulted in Hamas winning the January 2006 parliamentary elections followed by its complete takeover of the territory in 2007.", "claim_hash": "a7ca9634ee37256fad2d49b9229d099b1fdd24f7215cc67595a43c19b9e968c1", "confidence": 0.5, "doi": "10.5281/zenodo.19455674", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-2005-israeli-disengagement-from-gaza-removed-e/", "slug": "the-2005-israeli-disengagement-from-gaza-removed-e", "verdict": "PROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/the-adult-human-brain-has-approximately-86-billion/badge.json", "claim": "The adult human brain has approximately 86 billion neurons and an average of 7,000 synapses per neuron, resulting in a total synaptic count exceeding 6 \u00d7 10^14.", "claim_hash": "3e5e5a3f63e2c305c83a7d92660af5ad1c0f62823d110e7224cf025698f6828f", "confidence": 1.0, "doi": "10.5281/zenodo.19455665", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-adult-human-brain-has-approximately-86-billion/", "slug": "the-adult-human-brain-has-approximately-86-billion", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/the-assertion-that-no-arab-state-has-ever-recogniz/badge.json", "claim": "The assertion that no Arab state has ever recognized Israel is false because Egypt signed a peace treaty in 1979, Jordan in 1994, and four additional states joined the Abraham Accords by 2023.", 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"UNDETERMINED" }, { "badge_url": "https://proofengine.info/proofs/the-average-person-swallows-eight-spiders-per-year/badge.json", "claim": "The average person swallows eight spiders per year while sleeping.", "claim_hash": "c4ce2f0d9749b4f92d055c86e3b5a7f10162d707a8a90067cff0a5eb1cb7d11b", "confidence": 1.0, "doi": "10.5281/zenodo.19489854", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-average-person-swallows-eight-spiders-per-year/", "slug": "the-average-person-swallows-eight-spiders-per-year", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/the-binary-operator-defined-by-text-eml-a-b-exp-a-ln-b-satisfies-text-eml-x-1/badge.json", "claim": "The binary operator defined by \\text{eml}(a, b) = \\exp(a) - \\ln(b) satisfies \\text{eml}(x, 1) = \\exp(x) for every complex number x.", "claim_hash": "ff25a115386390a7de133a68c568ba6c6e85df3be6ffc73fb16342bf17b1fb18", "confidence": 1.0, "doi": "10.5281/zenodo.19635614", "generated_at": 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"verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/the-correlation-between-human-brain-volume-and-int/badge.json", "claim": "The correlation between human brain volume and intelligence is r = 0.4", "claim_hash": "68c167372faa4da4277ea1c58d666ba7c0f05dc197bdae25d3eb631b06403b7f", "confidence": 1.0, "doi": "10.5281/zenodo.19455657", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-correlation-between-human-brain-volume-and-int/", "slug": "the-correlation-between-human-brain-volume-and-int", "verdict": "PARTIALLY VERIFIED" }, { "badge_url": "https://proofengine.info/proofs/the-failure-rate-for-venture-backed-startups-is-70-within-10-years-lower-than/badge.json", "claim": "The failure rate for venture-backed startups is 70% within 10 years, lower than the commonly cited 90% for all startups.", "claim_hash": "e00339994d8c9da20662e6c938db27addd17170a289342e02a4dfefda3154b6f", "confidence": 1.0, "doi": null, "generated_at": 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"the-infinite-sum-from-n-1-to-infinity-of-1-n-2-equ", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/the-integer-1-is-a-prime-number/badge.json", "claim": "The integer 1 is a prime number.", "claim_hash": "88c4634e60b5e9746bc0faaf6b8b298f914b2858ff77566f560dd997e43b72ee", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-integer-1-is-a-prime-number/", "slug": "the-integer-1-is-a-prime-number", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/the-israeli-settler-population-in-the-west-bank-an/badge.json", "claim": "The Israeli settler population in the West Bank and East Jerusalem surpassed 700,000 by December 2023 per the Israeli Central Bureau of Statistics, representing more than 20 percent growth since 2010.", "claim_hash": "c2ad89e5bc7cb3f0bc0f2ff47918682417811fe58201ff458a4a08302b2a8c52", "confidence": 0.5, "doi": "10.5281/zenodo.19455677", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-israeli-settler-population-in-the-west-bank-an/", "slug": "the-israeli-settler-population-in-the-west-bank-an", "verdict": "PROVED (with unverified citations)" }, { "badge_url": "https://proofengine.info/proofs/the-mean-neutron-lifetime-measured-in-beam-experim/badge.json", "claim": "The mean neutron lifetime measured in beam experiments is more than 1 second shorter than the lifetime obtained from ultracold-neutron bottle experiments.", "claim_hash": "f22704b4275ddea3bd79f5c40a196b1db24d24b02281eee849505ce0ec2e0516", "confidence": 1.0, "doi": "10.5281/zenodo.19489848", "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-mean-neutron-lifetime-measured-in-beam-experim/", "slug": "the-mean-neutron-lifetime-measured-in-beam-experim", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/the-paper-goh-ac-gill-is-wallace-anastomosis-in-complex-dissections-eur-urol/badge.json", "claim": "The paper 'Goh AC, Gill IS. Wallace anastomosis in complex dissections. Eur Urol Focus. (2024) 11:80\u20138' does not exist.", "claim_hash": "df370bb1079b027a0b495335dd325012c6586a7ceb4f264341231ffcbe495238", "confidence": 1.0, "doi": "10.5281/zenodo.20318631", "generated_at": "2026-05-20", "proof_url": "https://proofengine.info/proofs/the-paper-goh-ac-gill-is-wallace-anastomosis-in-complex-dissections-eur-urol/", "slug": "the-paper-goh-ac-gill-is-wallace-anastomosis-in-complex-dissections-eur-urol", "verdict": "SUPPORTED" }, { "badge_url": "https://proofengine.info/proofs/the-pattern-matching-limitations-identified-in-gsm-noop-are-practically/badge.json", "claim": "The pattern-matching limitations identified in GSM-NoOp are practically surmountable when LLMs are allowed to offload formal reasoning steps to code execution.", "claim_hash": "400f55eb42b8e76fb07c3f870956f665cdaab24f6bfe0caac2fb247c22407a09", "confidence": 1.0, "doi": "10.5281/zenodo.19467525", "generated_at": "2026-04-08", "proof_url": 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(1 + \u221a5)/2", "claim_hash": "c3b4680568dd13fa3b6c0bee9424987212decd5d6b071f58d6b1823d795f33a3", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-positive-root-of-x-x-1-0-is-exactly-1-5-2/", "slug": "the-positive-root-of-x-x-1-0-is-exactly-1-5-2", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/the-pyramid-of-giza-was-built-by-slaves/badge.json", "claim": "The Pyramid of Giza was built by slaves.", "claim_hash": "25fd077ed4e2e79ee93f3375c09baa9fd2a2d933277247e0e16b742ad5c83e0d", "confidence": 1.0, "doi": "10.5281/zenodo.19489860", "generated_at": "2026-03-29", "proof_url": "https://proofengine.info/proofs/the-pyramid-of-giza-was-built-by-slaves/", "slug": "the-pyramid-of-giza-was-built-by-slaves", "verdict": "DISPROVED" }, { "badge_url": "https://proofengine.info/proofs/the-schwarzschild-radius-of-the-sun-calculated-via/badge.json", "claim": "The Schwarzschild radius of the Sun calculated via rs = 2GM/c\u00b2 with 2022 CODATA values for G, solar mass, and c lies strictly between 2.95 km and 2.96 km.", "claim_hash": "3415c54ac98d53cda52804fc59a7336cd5d9565fb63cef80cced3139ba91aa3d", "confidence": 1.0, "doi": null, "generated_at": "2026-04-06", "proof_url": "https://proofengine.info/proofs/the-schwarzschild-radius-of-the-sun-calculated-via/", "slug": "the-schwarzschild-radius-of-the-sun-calculated-via", "verdict": "PROVED" }, { "badge_url": "https://proofengine.info/proofs/the-st-petersburg-paradox-has-a-finite-expected-va/badge.json", "claim": "The St. Petersburg paradox has a finite expected value that a rational person should be willing to pay.", "claim_hash": "183bf223cf9fe53db1800831fcf001c25524aa6f227e62b8c4128c6b3811b424", "confidence": 1.0, "doi": null, "generated_at": "2026-03-28", "proof_url": "https://proofengine.info/proofs/the-st-petersburg-paradox-has-a-finite-expected-va/", "slug": "the-st-petersburg-paradox-has-a-finite-expected-va", "verdict": "DISPROVED" }, { 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