The Courtyard House: Xu Damao's Aunt is the Queen of Women

"Has Ximing passed away? Alas, heaven is jealous of talent!"

A look of sorrow appeared on Qian Lao's face as he deeply regretted Zu Hongjie's tragic fate.

Xi Ming is Zu Hongjie's courtesy name!

Liu Hao was puzzled: Did Old Qian know Uncle Hong?

"Uncle-Master, Uncle Hong was well taken care of by my father in his later years, and his mental state recovered a lot. After my father passed away, Uncle Hong was depressed and soon followed him."

Mr. Qian nodded, and without wasting any time, picked up a black briefcase with a mechanical combination lock from the ground, entered the password to open it, and took out two large stacks of documents.

He looked at Liu Hao, his tone becoming serious.

"Liu Hao, I've come to see you today not for any other reason than that the country has encountered some trouble."

When he spoke of the word "nation," the gentleness in his eyes vanished instantly, replaced by a heavy and unwavering sense of mission.

Liu Hao subconsciously sat up straight, his expression becoming serious.

"Senior Uncle, please tell me. As long as it's within my power, I will do it without hesitation."

Mr. Qian admired it even more.

No beating around the bush, no affectation, no stage fright – that's what makes someone capable of handling big things.

"Okay, before I ask you to help me solve some difficult problems, I need to test you a little. Do you mind?"

I don't mind at all, I'd be happy to.

I, Liu Hao, am going to prove today that I knew calculus before I was fourteen!

"Master, please examine me."

"I don't ask about abstract concepts or textbook rules."

Old Qian's voice was calm, yet it gave Liu Hao an invisible sense of pressure, making him a little nervous.

"I only ask about the real problems that are currently hindering our progress. Tell me your thoughts, calculations, and reasonings honestly. Right is right, and wrong is wrong. Don't worry about who I am."

Liu Hao took a deep breath, his expression more serious than ever before.

"Okay, I understand."

"For the first question, start with math, which is what you're best at."

Professor Qian tapped his fingers lightly on the table and said, "Ye Xi solved the Poincaré conjecture, and you provided crucial support in terms of topological structure. I ask you, what is the most fundamental criterion for determining whether a three-dimensional simply connected closed manifold is homeomorphic to a sphere? What is the essential difference between the path you gave Ye Xi and Smel's high-dimensional proof?"

This problem represents the most cutting-edge mathematical core in the world, and even most mathematicians struggle to understand it.

Liu Hao answered almost without hesitation.

"There is only one core principle: all closed curves in a manifold can be continuously contracted to a single point, and there are no singular homology classes. Smail uses high-dimensional handle-body decomposition and the h-coordinate theorem. When n≥5, the degrees of freedom are large enough and the obstacles disappear."

"But three dimensions won't work; the space is too tight. We have to use the approach of geometricization and curvature flow. The path I gave Ye Xi was to first decompose the manifold into standard blocks, and then use metric deformation to round each block back, avoiding high-dimensional tools and directly pinning the tightness and simple connectivity in three-dimensional space."

Qian Lao's eyes narrowed slightly. This was not memorization; this was a true understanding of the underlying logic.

"In just one sentence, you've clarified a division that has plagued the world for decades."

Qian Xuesen continued, "Since you can navigate the three-dimensional Poincaré model, could you also conveniently build the framework for the three-dimensional manifold geometrization conjecture?"

Liu Hao thought for a few seconds and said, "Yes, and I've already built it. All eight geometric structures are listed, the decomposition theorem is complete, existence, uniqueness, and cutting and splicing rules are all there. I just haven't explained them to Sister Xi yet."

Old Qian's heart skipped a beat; this time, he was truly shocked.

The Geometry Conjecture is a grander and more fundamental program than the Poincaré Conjecture, with Poincaré being just one of its corollaries.

He paused for two seconds, then continued to press for answers.

"Complete? You say complete? Where's the rigor in the proof? Torus decomposition, hyperbolic structure, spherical structure, Euclidean structure—how are they unified under a single set of invariants?"

"Use homology, homotopy, volume, curvature, end structure, and five sets of invariants to lock the system."

Liu Hao was already in the zone, speaking at a moderate pace.

"Each geometry corresponds to a set of rigid features that do not overlap, intersect, or omit each other. Any compact three-dimensional manifold must have one of these features, and it is unique."

"A one-sentence conclusion?"

"In three-dimensional topology, there are ultimately only eight shapes."

Old Qian gave Liu Hao a deep look; Liu Hao was far more capable than he had imagined.

He didn't stop, but went straight from mathematics into physics.

"Let's leave the math for now. I'll ask you the most crucial question in aerospace engineering: the trajectory of a missile during its boost phase. Considering Earth's rotation, gravitational anomalies, and aerodynamic asymmetry, can you provide an analytical solution instead of numerical iteration?"

"able."

Liu Hao nodded.

Mr. Qian took out a stack of white paper and a Yong Sheng 201 fountain pen and pushed them in front of Liu Hao.

Write out the equation.

Liu Hao picked up his pen and started writing without any hesitation.

"In a geocentric inertial frame of reference, dr/dt = v, dv/dt = P/m + D + G, m = m0 - ∫ṁdt, where P is the thrust, D is the drag, and G is the gravitational force, including spherical harmonic corrections."

"Decoupling in-plane and out-of-plane projection, linearization under small deviations yields the deviation propagation matrix, and direct integration gives the analytical expression for the landing point deviation."

Old Qian also got into the zone and asked with a frown.

"What is the magnitude of the lateral deflection caused by the Coriolis force? How does the sign of the deflection change depending on the firing direction?"

"In the Northern Hemisphere, shots fired eastward tend to deviate to the right, shots fired westward tend to deviate to the left, shots fired southward tend to deviate to the west, and shots fired northward tend to deviate to the east. The range is in the hundreds of kilometers, while the range is in the tens to hundreds of meters, which cannot be ignored."

"Which is dominant: thrust eccentricity or wind disturbance?"

"Low-level winds dominate, while high-level thrust eccentricity dominates."

Liu Hao answered fluently without pausing for a moment.

Mr. Qian smiled. This Liu Hao not only has a strong talent for mathematics, but his knowledge of aerospace ballistics is also at an expert level.

He went a step further, tackling the most critical issues directly to test Liu Hao's limits.

"Hypersonic reentry, aerodynamic heating, where is the peak heat flux density? Give me a formula for stagnation point heat flux that can be directly used in warhead design."

Liu Hao opened the paper and began writing as he spoke.

"The classic formula q ∝ √ρ · V³, with correction coefficients for non-equilibrium air, is applicable in engineering as q_w = K ·√(ρ_∞ / R_n) · V_∞³. K includes chemical non-equilibrium, vibrational excitation, ablation, wall temperature ratio, and the peak value is not at the stagnation point, but at the beginning of the laminar transition zone, where heat transfer is strongest."

Mr. Qian was stunned; Liu Hao's ideas had greatly inspired him.

"Turning point criterion? What do you use?"

"Mach number, Reynolds number, wall roughness, and pressure gradient coupling criterion."

"Give me a simplified version."

"Re_tr / Ma^α = C, α≈1.2~1.5, C is determined experimentally."

Old Qian stared at Liu Hao: "From which book did you learn all this?"

Where can I find it in the book?

These were all deduced from system bugs.

"Senior Uncle, you should know that no publicly available textbook in China explains reentry heating, transition criteria, and ballistic analytical solution in such detail. I derived it myself."

Liu Hao is frank, straightforward, upright, and full of confidence.

The system and I are bound by soul; I am the system, and the system is me—no problem!