corpus.blog
41554 blogs · [ { "id": "01a087a8-75b4-73a1-80a1-7bb3a4ac15d9", "title": "A Conjecture That Was False by One Exponential", "url": "https://monogate.org/blog/false-by-one-exponential", "published_at": "2026-08-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a523d2de", "title": "Eight Circles, Except When There Are Seven", "url": "https://monogate.org/blog/eight-circles-except-when-seven", "published_at": "2026-08-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a5d2310a", "title": "Two Things We Didn't Close, and Exactly Why", "url": "https://monogate.org/blog/two-open-questions-pinned-down", "published_at": "2026-07-22T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a6bf5947", "title": "Periodicity Is Enough — Every Nonconstant Periodic Function Is Out of EML's Reach", "url": "https://monogate.org/blog/periodicity-is-enough", "published_at": "2026-07-22T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a7a1fb85", "title": "The Axiom You Can't See — A Machine-Checked Trust Boundary, and the False One It Caught", "url": "https://monogate.org/blog/the-axiom-you-cannot-see", "published_at": "2026-07-10T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a7d10270", "title": "A Model for the Axioms — MachLib's Reals, Weighed Against Mathlib", "url": "https://monogate.org/blog/a-model-for-the-axioms", "published_at": "2026-07-08T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a81750d6", "title": "Finiteness of Zeros for Any Exponential-Type Chain, Machine-Checked", "url": "https://monogate.org/blog/zeros-any-exponential-chain", "published_at": "2026-07-04T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a8e80904", "title": "Climbing the Exponential Tower — a Machine-Checked Depth-3 Khovanskii Bound", "url": "https://monogate.org/blog/climbing-the-exponential-tower", "published_at": "2026-07-01T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a97dc4dd", "title": "We Injected a Fault and the Safety Proof Held", "url": "https://monogate.org/blog/we-injected-a-fault-and-the-proof-held", "published_at": "2026-06-30T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3a9c0e437", "title": "We Put the Proof on a Real FPGA", "url": "https://monogate.org/blog/equivalence-on-real-silicon", "published_at": "2026-06-29T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3aa97a427", "title": "Oscillation Is a Compact Torus", "url": "https://monogate.org/blog/oscillation-is-a-compact-torus", "published_at": "2026-06-24T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3aaf650e8", "title": "Stress-Testing the eFrog → Forge Pipeline", "url": "https://monogate.org/blog/stress-testing-the-pipeline", "published_at": "2026-06-18T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ab88eb41", "title": "Two Independent Routes to the SingleExp Khovanskii Bound", "url": "https://monogate.org/blog/two-routes-to-the-khovanskii-bound", "published_at": "2026-06-17T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3abc918df", "title": "The Dashboard the Verification Needed", "url": "https://monogate.org/blog/the-dashboard-the-verification-needed", "published_at": "2026-06-14T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ac889b52", "title": "A Constructive Khovanskii Reduction — the SingleExp (eˣ) Case", "url": "https://monogate.org/blog/constructive-khovanskii", "published_at": "2026-06-14T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ad23e4f1", "title": "The EML Advantage Lab", "url": "https://monogate.org/blog/eml-advantage-lab", "published_at": "2026-05-28T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ad553aa2", "title": "Why EML Optimization Lives on the Boundary", "url": "https://monogate.org/blog/why-eml-optimization-lives-on-the-boundary", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ad700fe8", "title": "The Third Proof-Carrying Rescue", "url": "https://monogate.org/blog/third-proof-carrying-rescue", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ad8fc37c", "title": "The Second Proof-Carrying Rescue", "url": "https://monogate.org/blog/second-proof-carrying-rescue", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3adfdefb6", "title": "Proof-Carrying Rescue Suite v0", "url": "https://monogate.org/blog/proof-carrying-rescue-suite-v0", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ae05df60", "title": "Proof-Carrying Rescue Status", "url": "https://monogate.org/blog/proof-carrying-rescue-status", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ae27b55c", "title": "How to Read the Rescue Suite", "url": "https://monogate.org/blog/how-to-read-the-rescue-suite", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3af15bf83", "title": "The Fourth Proof-Carrying Rescue", "url": "https://monogate.org/blog/fourth-proof-carrying-rescue", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3afb6ad20", "title": "The First Proof-Carrying Rescue", "url": "https://monogate.org/blog/first-proof-carrying-rescue", "published_at": "2026-05-26T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3afbda9dc", "title": "One Operator, All of Applied Mathematics", "url": "https://monogate.org/blog/one-operator", "published_at": "2026-04-27T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3afffbaf2", "title": "Hear the Math: When Equations Become Sound", "url": "https://monogate.org/blog/hear-the-math", "published_at": "2026-04-27T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b037b7d5", "title": "The Equation That Counts Physics", "url": "https://monogate.org/blog/dynamics-counter", "published_at": "2026-04-27T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b0903996", "title": "How Claude and I Built a Research Program in Two Weeks", "url": "https://monogate.org/blog/built-with-claude", "published_at": "2026-04-27T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b0b3aa0b", "title": "Which Way Does the Transform Go?", "url": "https://monogate.org/blog/which-way-does-the-transform-go", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b0c0e3cb", "title": "What We Got Wrong", "url": "https://monogate.org/blog/what-we-got-wrong", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b1b80100", "title": "Two Boundaries of ELC", "url": "https://monogate.org/blog/two-boundaries", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b2745993", "title": "Planck Radiation Is ELC-Native (No Trig Needed)", "url": "https://monogate.org/blog/planck-elc-native", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b36d80f2", "title": "The Oscillation Boundary", "url": "https://monogate.org/blog/oscillation-boundary", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b3cd7b36", "title": "When Olympiad Problems Produce EML Trees", "url": "https://monogate.org/blog/olympiad-meets-eml", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b4c691be", "title": "FMA Is the Only Primitive That Matters", "url": "https://monogate.org/blog/fma-staircase", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b5426638", "title": "Why EAL and EXL Share the Multiplier 4.3164206…", "url": "https://monogate.org/blog/conjugacy-explained", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b5eeda63", "title": "Only the Multiplicative F16 Operators Are Chaotic", "url": "https://monogate.org/blog/chaos-multiplicative-operators", "published_at": "2026-04-23T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b69caea8", "title": "The ReLU–Softplus Error is Exactly ln(2)/β", "url": "https://monogate.org/blog/relu-softplus-exact-error", "published_at": "2026-04-22T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b783c8f5", "title": "Every Log Branch Has Its Own Attractor", "url": "https://monogate.org/blog/lambert-log-branch-attractors", "published_at": "2026-04-22T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b878839d", "title": "Hyperbolic Functions Preserve ELC (And Why Trig Doesn't)", "url": "https://monogate.org/blog/hyperbolic-preserves-elc", "published_at": "2026-04-22T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b9457866", "title": "The Exp-Log Duality at Fixed Points", "url": "https://monogate.org/blog/exp-log-duality-at-fixed-points", "published_at": "2026-04-22T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3b976f459", "title": "Why tan(1) Controls Everything", "url": "https://monogate.org/blog/tan1-obstruction", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ba18ba1c", "title": "The SuperBEST Table Is Complete", "url": "https://monogate.org/blog/superbest-complete", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3ba9faa71", "title": "16 Operators: The Complete exp-ln Census", "url": "https://monogate.org/blog/sixteen-operators", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bb15aa58", "title": "recip(x) Is 1 Node — ELSb Closes the Gap", "url": "https://monogate.org/blog/recip-one-node", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bb857cf4", "title": "The SuperBEST Cost of Quantum Mechanics", "url": "https://monogate.org/blog/quantum-costs", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bbe1eb3c", "title": "The SuperBEST Cost of Geometry", "url": "https://monogate.org/blog/geometry-costs", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bc1ac15f", "title": "EML Meets Neural Networks", "url": "https://monogate.org/blog/eml-neural-networks", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bc9a475d", "title": "Negation in Two Nodes — For All Real x", "url": "https://monogate.org/blog/eml-negation", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bc9b72bf", "title": "The Exact Depth Spectrum of EML", "url": "https://monogate.org/blog/depth-spectrum", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bd3014fb", "title": "The Cost Theory Is Complete", "url": "https://monogate.org/blog/cost-theory-complete", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bd62bba1", "title": "Predicting SuperBEST Cost from Equation Structure", "url": "https://monogate.org/blog/cost-theory", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bdac6e27", "title": "The SuperBEST Cost of Everything", "url": "https://monogate.org/blog/cost-of-everything", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3be80d401", "title": "What If tan(1) Were Constructible?", "url": "https://monogate.org/blog/conditional-tan1", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bf1d2203", "title": "Why exp(+x) Means Complete: The Structural Theorem for exp-ln Operators", "url": "https://monogate.org/blog/completeness-characterization", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bf841d72", "title": "SuperBEST Node Costs: Chemistry and Biology", "url": "https://monogate.org/blog/chembio-costs", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3bfb575c6", "title": "The SuperBEST Cost of Calculus", "url": "https://monogate.org/blog/calculus-costs", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c090d710", "title": "General Addition in 2 Nodes: The Last Gap Closes", "url": "https://monogate.org/blog/add-gen-2n", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c10c0805", "title": "214 Equations: The SuperBEST Cost of Science", "url": "https://monogate.org/blog/157-equations", "published_at": "2026-04-20T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c149507f", "title": "The Tight Zeros Bound: How Many Zeros Can an EML Tree Have?", "url": "https://monogate.org/blog/tight-zeros-bound", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c2173732", "title": "The Operator Zoo: Which exp-ln Gates Are Complete?", "url": "https://monogate.org/blog/operator-zoo", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c2aca544", "title": "We Found a Faster Multiplication: 3 Nodes", "url": "https://monogate.org/blog/mul-gap-closed", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c378d6d6", "title": "Fourier Beats Taylor by 100x in EML Node Count", "url": "https://monogate.org/blog/fourier-beats-taylor", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c40364a8", "title": "Timbre Is EML Node Count", "url": "https://monogate.org/blog/eml-sound", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c4d5ae98", "title": "The EML Self-Map Has No Fixed Points", "url": "https://monogate.org/blog/eml-no-fixed-points", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c5b1f689", "title": "EML Generates the Exponential Mandelbrot Set", "url": "https://monogate.org/blog/eml-fractals", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c5b25848", "title": "Is the EML Closure Dense in ℂ?", "url": "https://monogate.org/blog/eml-closure-density", "published_at": "2026-04-19T00:00:00+00:00" }, { "id": "01a087a8-75b4-73a1-80a1-7bb3c698e92f", "title": "The Completeness Trichotomy: EML, EMN, and Everyone Else", "url": "https://monogate.org/blog/completeness-trichotomy", "published_at": "2026-04-19T00:00:00+00:00" } ] posts Claim your blog
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2026

A Conjecture That Was False by One Exponentialoriginal ↗
19 Aug 2026
Eight Circles, Except When There Are Sevenoriginal ↗
19 Aug 2026
Two Things We Didn't Close, and Exactly Whyoriginal ↗
22 Jul 2026
Periodicity Is Enough — Every Nonconstant Periodic Function Is Out of EML's Reachoriginal ↗
22 Jul 2026
The Axiom You Can't See — A Machine-Checked Trust Boundary, and the False One It Caughtoriginal ↗
10 Jul 2026
A Model for the Axioms — MachLib's Reals, Weighed Against Mathliboriginal ↗
8 Jul 2026
Finiteness of Zeros for Any Exponential-Type Chain, Machine-Checkedoriginal ↗
4 Jul 2026
Climbing the Exponential Tower — a Machine-Checked Depth-3 Khovanskii Boundoriginal ↗
1 Jul 2026
We Injected a Fault and the Safety Proof Heldoriginal ↗
30 Jun 2026
We Put the Proof on a Real FPGAoriginal ↗
29 Jun 2026
Oscillation Is a Compact Torusoriginal ↗
24 Jun 2026
Stress-Testing the eFrog → Forge Pipelineoriginal ↗
18 Jun 2026
Two Independent Routes to the SingleExp Khovanskii Boundoriginal ↗
17 Jun 2026
The Dashboard the Verification Neededoriginal ↗
14 Jun 2026
A Constructive Khovanskii Reduction — the SingleExp (eˣ) Caseoriginal ↗
14 Jun 2026
The EML Advantage Laboriginal ↗
28 May 2026
Why EML Optimization Lives on the Boundaryoriginal ↗
26 May 2026
The Third Proof-Carrying Rescueoriginal ↗
26 May 2026
The Second Proof-Carrying Rescueoriginal ↗
26 May 2026
Proof-Carrying Rescue Suite v0original ↗
26 May 2026
Proof-Carrying Rescue Statusoriginal ↗
26 May 2026
How to Read the Rescue Suiteoriginal ↗
26 May 2026
The Fourth Proof-Carrying Rescueoriginal ↗
26 May 2026
The First Proof-Carrying Rescueoriginal ↗
26 May 2026
One Operator, All of Applied Mathematicsoriginal ↗
27 Apr 2026
Hear the Math: When Equations Become Soundoriginal ↗
27 Apr 2026
The Equation That Counts Physicsoriginal ↗
27 Apr 2026
How Claude and I Built a Research Program in Two Weeksoriginal ↗
27 Apr 2026
Which Way Does the Transform Go?original ↗
23 Apr 2026
What We Got Wrongoriginal ↗
23 Apr 2026
Two Boundaries of ELCoriginal ↗
23 Apr 2026
Planck Radiation Is ELC-Native (No Trig Needed)original ↗
23 Apr 2026
The Oscillation Boundaryoriginal ↗
23 Apr 2026
When Olympiad Problems Produce EML Treesoriginal ↗
23 Apr 2026
FMA Is the Only Primitive That Mattersoriginal ↗
23 Apr 2026
Why EAL and EXL Share the Multiplier 4.3164206…original ↗
23 Apr 2026
Only the Multiplicative F16 Operators Are Chaoticoriginal ↗
23 Apr 2026
The ReLU–Softplus Error is Exactly ln(2)/βoriginal ↗
22 Apr 2026
Every Log Branch Has Its Own Attractororiginal ↗
22 Apr 2026
Hyperbolic Functions Preserve ELC (And Why Trig Doesn't)original ↗
22 Apr 2026
The Exp-Log Duality at Fixed Pointsoriginal ↗
22 Apr 2026
Why tan(1) Controls Everythingoriginal ↗
20 Apr 2026
The SuperBEST Table Is Completeoriginal ↗
20 Apr 2026
16 Operators: The Complete exp-ln Censusoriginal ↗
20 Apr 2026
recip(x) Is 1 Node — ELSb Closes the Gaporiginal ↗
20 Apr 2026
The SuperBEST Cost of Quantum Mechanicsoriginal ↗
20 Apr 2026
The SuperBEST Cost of Geometryoriginal ↗
20 Apr 2026
EML Meets Neural Networksoriginal ↗
20 Apr 2026
Negation in Two Nodes — For All Real xoriginal ↗
20 Apr 2026
The Exact Depth Spectrum of EMLoriginal ↗
20 Apr 2026
The Cost Theory Is Completeoriginal ↗
20 Apr 2026
Predicting SuperBEST Cost from Equation Structureoriginal ↗
20 Apr 2026
The SuperBEST Cost of Everythingoriginal ↗
20 Apr 2026
What If tan(1) Were Constructible?original ↗
20 Apr 2026
Why exp(+x) Means Complete: The Structural Theorem for exp-ln Operatorsoriginal ↗
20 Apr 2026
SuperBEST Node Costs: Chemistry and Biologyoriginal ↗
20 Apr 2026
The SuperBEST Cost of Calculusoriginal ↗
20 Apr 2026
General Addition in 2 Nodes: The Last Gap Closesoriginal ↗
20 Apr 2026
214 Equations: The SuperBEST Cost of Scienceoriginal ↗
20 Apr 2026
The Tight Zeros Bound: How Many Zeros Can an EML Tree Have?original ↗
19 Apr 2026
The Operator Zoo: Which exp-ln Gates Are Complete?original ↗
19 Apr 2026
We Found a Faster Multiplication: 3 Nodesoriginal ↗
19 Apr 2026
Fourier Beats Taylor by 100x in EML Node Countoriginal ↗
19 Apr 2026
Timbre Is EML Node Countoriginal ↗
19 Apr 2026
The EML Self-Map Has No Fixed Pointsoriginal ↗
19 Apr 2026
EML Generates the Exponential Mandelbrot Setoriginal ↗
19 Apr 2026
Is the EML Closure Dense in ℂ?original ↗
19 Apr 2026
The Completeness Trichotomy: EML, EMN, and Everyone Elseoriginal ↗
19 Apr 2026