Recaps

Li Mo investigated Thomas's murder, using Anna's vision and forensic deductions to identify clues and preserve fingerprints. The evidence pointed toward the docks, where Li Mo suspected a larger plot involving Matthew, Professor Bryce's tide research, and the military blockade, so he hurried back to the academy to find Bryce.

• Anna performed a ritual at Thomas's room and saw a tall person in a dark trench coat kill him after Thomas tried to hide something in the wardrobe.
• Wayne and Sheriff Sanders reasoned that Thomas knew his killer and had taken something dangerous enough to be killed over.
• Li Mo deduced that the killer was tall, heavy, left-handed, and connected to large steam freighters, then lifted fingerprints from the wardrobe for comparison.
• Li Mo learned that Helen had last been seen running toward the sealed-off docks and connected the docks to Thomas's murder and the unusual interest in Professor Bryce's tide research.
• Li Mo suspected Matthew and the people behind him planned an operation at the docks based on the autumn equinox tides, and he hurried to find Professor Bryce.

Li Mo questioned Professor Bryce about Helen’s disappearance and used Focus mode to infer that the Empress had sealed the docks to prepare a secret autumn equinox attack involving a powerful Mystical Artifact. He concluded Helen may have witnessed someone spying on the docks and left to find her, while Professor Bryce begged him to keep his deductions secret.

• Wayne reported that Matthew was absent, and Li Mo told Anna and Wayne to wait while he spoke to Professor Bryce alone.
• Professor Bryce revealed that he had reported their tidal findings to the Empress’s envoy and that the Empress had asked for Li Mo by name.
• Li Mo told Professor Bryce that Helen had gone missing after running toward the docks, and Bryce admitted she would not be harmed by the people inside the docks but might have been endangered on the way there.
• Li Mo used Focus mode to deduce that the Empress had ordered the dock lockdown for a secret autumn equinox attack using a Mystical Artifact, and that the blockade had caused the town’s cotton shortage and factory crisis.
• Li Mo inferred that Helen might have witnessed someone secretly gathering information near the docks and hurried off to find her, while Professor Bryce warned him not to share his guesses.

Li Mo prepared flashbangs with Anna and Wayne, then searched the road to the docks for evidence of Helen’s disappearance. Anna’s ritual revealed that Helen had been abducted and taken toward the birch woods, and the three set out at night to rescue her.

• Li Mo bought chemicals and showed Anna and Wayne how to make flash powder, then gave each of them a flashbang.
• Li Mo, Anna, and Wayne searched the road to the docks, where Li Mo found a button from Helen’s coat beside an extinguished gas lamp.
• Anna used Ember Rewind and saw Helen struggle with a man who knocked her unconscious and carried her toward the birch woods to the west.
• Li Mo told Anna and Wayne to rest while Anna recovered, then laid out a plan to rescue Helen and avoid confronting the killer.
• After night fell, Anna checked her revolver, Wayne drew his cane sword, and Li Mo led the group toward the woods.

Li Mo, Anna, and Wayne rescued Helen from a hidden cellar and escaped her kidnapper by reaching the military-controlled docks. After Helen recovered, she recognized the kidnapper in a newspaper advertisement for Dr. Morris’s clinic.

• Li Mo followed faint footprints through the woods, and Anna used a ritual to locate a concealed cellar where they found the unconscious Helen.
• The kidnapper arrived as the group left the cellar, but Li Mo, Anna, and Wayne used flashbangs and gunfire to escape with Helen.
• Li Mo led them to the docks, where soldiers brought them inside the secured perimeter and gave them a place to wait.
• Helen woke, thanked Anna and Li Mo for rescuing her, and blushed when she addressed Li Mo.
• Helen recognized the kidnapper in Wayne’s newspaper as Dr. Morris, the bloodletting practitioner who had visited Li Mo’s house.

Li Mo identified Doctor Morris as the killer and told Sheriff Sanders where to search for him. The Empress's envoy thanked Li Mo and invited him to study in the capital after his entrance exams, while Li Mo agreed without revealing his reluctance to become involved in the war.

• Li Mo, Anna, and Wayne concluded that Doctor Morris had killed Thomas and kidnapped Helen, and Wayne suspected Matthew's family might be connected.
• The Empress's red-haired envoy thanked Li Mo for helping the kingdom and invited him to study mathematics and physics in the capital after his entrance exams.
• Commander Carter offered Li Mo help from the troops stationed at the docks, and a messenger announced that Sheriff Sanders was waiting outside.
• Li Mo told Sheriff Sanders that Morris was the killer and that Helen had been found in a cellar in the birch grove, prompting the sheriff to send officers and hounds after Morris.
• On the carriage ride to town, Wayne lamented missing that the envoy was linked to the Empress, then teased Li Mo and Anna about their closeness while Helen rejected his offer of comfort.

Li Mo and his companions returned Helen safely to her father after rescuing her from Doctor Morris, and Mr. Green swore an oath to support Li Mo. Still traumatized, Helen came to stay at Li Mo’s house, where Anna arranged for all three of them to sleep together.

• Li Mo told Mr. Green that Doctor Morris had kidnapped Helen and that he, Anna, and Wayne had rescued her from the western birch forest.
• Mr. Green thanked Li Mo and swore by the twin moons to support him and never criticize him again.
• Helen asked to sleep at Li Mo’s house with Anna, but Li Mo persuaded her to stay home and talk with her father.
• Li Mo planned a seven-day Mathematics Salon and considered sending his generator paper to the Capital Royal Academy of Sciences.
• Mr. Green brought Helen back to Li Mo’s house after she panicked when the lights went out and begged for Anna.
• Anna bathed Helen and proposed that she, Helen, and Li Mo share a bed, with Anna sleeping between them.

Li Mo learned that Isaac Oliver had manipulated the raw cotton shortage to threaten Li En’s factory, and he planned to use the crisis to move the mill into a new line of business. After Li Mo and his companions returned to Puxiu Academy, Charles Bowen asked him to help Matthew impress Helen.

• Li Mo reassured Helen after she spent the night with Anna, then explained to Li En how Doctor Morris had been exposed and captured.
• Li En told Li Mo that Isaac Oliver had secretly bought up raw cotton and withheld shipping notices to cripple rival workshops.
• Li Mo said his improved spinning machines would free up factory space and hinted that he would reveal a more profitable business plan over the weekend.
• Li Mo, Anna, Helen, and Wayne left for school, where Wayne read news about Morris’s capture, the cotton shortage, and the northern war.
• At Puxiu Academy, Charles Bowen asked Li Mo to help Matthew put on a show in front of Helen.

Li Mo uncovered Charles Bowen’s supposed occult organization as a student-run middleman scheme and refused to help Matthew stage a rescue for Helen. He then announced a mathematics salon where he planned to present the epsilon-delta definition of limits.

• Charles Bowen explained that Matthew had hired his organization to stage a crisis so he could impress Helen, and Li Mo used his focus state to expose the group’s lies and methods.
• Li Mo refused Charles’s offer of up to seven pounds, warning him not to upset Helen and threatening to tell Sheriff Sanders about the organization.
• Li Mo noticed that Helen seemed better than the night before but still lowered her head when she sensed him looking at her.
• Li Mo announced a mathematics salon that afternoon, promising to replace vague intuitions about calculus with rigorous definitions.
• When students doubted him, Li Mo declared that Mr. Harrison would applaud his plan to present the epsilon-delta definition of limits.

Li Mo finished a paper on a self-excited DC generator, then began his lawn salon to present a rigorous definition of limits in calculus. As skeptical teachers and students watched, Matthew waited for the occultists he had paid, unaware that Charles had come to return his money.

• Matthew taunted Li Mo about the salon and looked forward to winning back the fifteen gold pounds he had paid an occult organization.
• Li Mo asked Wayne to set up a blackboard and chairs, then worked through the day to finish his generator paper.
• Professor Bryce reviewed Li Mo's paper, found no obvious flaws, and agreed to study it further before submitting it to the Royal Academy of Sciences.
• Wayne prepared the lawn, and Mr. Harrison invited teachers to attend Li Mo's salon.
• Li Mo arrived with Anna and faced a crowd of doubters, while Matthew waited for the occult organization and Charles came to return Matthew's money.
• The academy bell rang, and Li Mo began the salon by addressing the audience.

Li Mo presented a rigorous definition of limits and proved that a function approaching a finite limit was locally bounded, surprising the teachers and students with material beyond their syllabus. He then posed a control problem about preventing oscillations in steam-engine governors, leaving the class to solve it.

• Li Mo introduced the epsilon-delta definition of a function limit and explained how it replaced ambiguity with precise inequalities.
• Li Mo used the triangle inequality to prove that a function with a finite limit was locally bounded, then carefully filled in steps that had confused the students.
• Mr. Harrison stood and praised Li Mo's detailed proof, prompting the students to applaud while Matthew regretted losing his chance to show off.
• Li Mo described oscillations in centrifugal governors at Mendel Port and textile mills and wrote a cubic characteristic equation for the system.
• Li Mo asked the class to find necessary and sufficient conditions for the system's characteristic roots to have negative real parts and to calculate the required mechanical damper threshold.

Li Mo finished his mathematics salon after Matthew’s attempt to show off ended in an awkward escape, then announced another lecture for the next day. Afterward, Li Mo found Helen waiting alone in the classroom and offered to walk her home.

• Matthew confidently went to the blackboard expecting the Goddess of the Moon to reveal the answer, but fled after nothing happened and pretended to be ill.
• Li Mo wrote the critical damping threshold, concluded the salon, and announced a lecture on continuity, the intermediate value theorem, and the Cauchy convergence criterion for the next day.
• Wayne teased Matthew about whether he had understood Li Mo’s lecture by asking what was special about 1729, leaving Matthew confused.
• Wayne invited Li Mo and Anna to the teahouse, but Li Mo returned to the classroom and found Helen sitting alone because she was afraid to go home by herself.
• Li Mo offered to walk Helen home, and Helen shyly took one of his fingers and thanked him.

Li Mo left the tea room after hearing doubts about the war and wondered who had arrived at the sealed port. The Empress secretly came to Mondel after the Great Sage died, then decided to disguise herself and join Li Mo’s class.

• Li Mo treated Wayne, Anna, and Helen to tea, where Anna asked about the Cauchy convergence criterion he had written on the blackboard.
• A cloth merchant and a fur merchant argued over the war’s progress, and Wayne told Li Mo that the official reports seemed unreliable.
• The Empress arrived secretly at Mondel’s military docks and met Caroline at the governor’s private residence.
• The Empress told Caroline that the Great Sage had died after making a final prophecy that the key to turning the war around lay in Mondel.
• Caroline reported Li Mo’s recent achievements, and the Empress ordered the Black-Robed Court Guards to disguise her so she could join his class as a transfer student.

Li Mo investigated the strange noises in Helen's bedroom and traced them to a loose ventilation valve connected to the house's smoke-extraction system. After he stopped the noise, Mr. Green realized Helen had feelings for Li Mo and considered bringing them together.

• Helen told Li Mo that strange scraping and whistling noises had haunted her bedroom for half a month, so he went with her and Anna to investigate.
• Li Mo discovered that the noises came from the flue and a loose ventilation valve, then quieted it by wedging a coin into the valve's worn slide rail.
• Helen thanked Li Mo, and Mr. Green escorted Li Mo and Anna to the gate as they left.
• Mr. Green asked Helen how she felt about Li Mo and considered helping bring them together after her embarrassed reaction.

Li Mo studied the firestone’s activation and discovered that linseed oil prevented it from reacting, while Anna mistook his distracted replies for a demand that she sleep with him naked. Anna agreed and joined him in bed, leaving Li Mo to realize from the unfamiliar sensation against his back that she had taken off her clothes.

• Li Mo observed the miniature globe without seeing any change, then tested the firestone and found that rubbing it with any part of his body could activate it.
• Li Mo found that rubbing the firestone in linseed oil produced no reaction, and he excitedly recorded the result while Anna watched with concern.
• Anna urged Li Mo to rest, but his absent-minded agreement led her to assume he wanted her to sleep naked with him.
• Anna darkened the room and climbed into bed with Li Mo, who realized from the feel against his back that she was not wearing clothes.

Li Mo and Anna stayed awake together as he explained advanced calculus problems, then woke to awkward tension after another embarrassing night. Meanwhile, Li En planned to use his social connections to pressure Oliver, and Li Mo walked to school with Anna and Helen after accepting a breakfast box Helen's father had prepared.

• Li Mo explained tests for oscillatory integrals and singularities to Anna until they fell asleep.
• Li Mo woke up naked again, and Li En told him he would use the town ladies' connections to prompt an investigation of Oliver and restrict his bank credit.
• Li Mo and Anna left for school, and Li Mo told Li En they had met Mrs. Turner at the Egret Tea Room.
• Green presented Li Mo with a breakfast box he claimed Helen had made, leaving Helen mortified.
• Li Mo accepted the breakfast and walked to school with Anna and Helen while Green congratulated himself on matchmaking.

Anna confronted Li Mo over his misunderstood agreement from the previous night, then chased him down the street after giving him a three-step head start. As Helen joined their run and smiled, an unfamiliar carriage carrying a new transfer student watched the group pass.

• Wayne escorted Helen ahead after Anna asked to speak privately with Li Mo.
• Anna accused Li Mo of agreeing to sleep with her undressed, and Li Mo explained that he had been absentmindedly brushing her off while working.
• Li Mo told Anna that she had misunderstood and complained that her attempt to seduce him had kept him from sleeping well.
• Anna handed Li Mo her schoolbag, counted to three, and chased him as Wayne ran after them and Helen followed.
• Helen began jogging with the group and smiled as Puxiu Academy students discussed her and the arriving transfer student.
• A luxurious carriage with an unfamiliar family crest traveled down the street, and a girl with cool black eyes watched the group from behind its curtain.

Li Mo and his companions arrived at Puxiu Academy just in time for the morning assembly, where he stopped Lawrence and the other students from bullying Perry over his late father’s missing top hat. After Li Mo received special treatment from the prefect for arriving after the bell, a note addressed to him was passed through the auditorium’s assembled students.

• Anna stopped hitting Li Mo at the school gates, and Wayne warned them they had only minutes to reach the auditorium before the assembly doors closed.
• In the cloakroom, Perry confronted Lawrence over his missing top hat, and Lawrence admitted taking it while other students joined in mocking Perry.
• Li Mo told Lawrence to return the hat and stop bullying Perry, so Lawrence had an underling retrieve it; Perry thanked Li Mo and hurried to the auditorium.
• Wayne discovered his walking stick was missing, and Li Mo helped him find it before they hurried to the assembly as the bell rang.
• The prefect punished two late first-year boys but let Li Mo enter without penalty, then directed him to Class One’s column.
• Students passed a note addressed to Li Mo through the auditorium, and Wayne handed it to him.

Li Mo received new privileges and widespread respect after his mathematics salon, while planning to investigate how Mystical Rituals drew energy. On his way to class, he recognized a silver emblem on a girl’s coat as the one he had seen on the Scarlet Moon and avoided confronting her by using Matthew’s excuse.

• Li Mo read notes asking to buy his calculus notes, inquire about the steam-engine salon, and attend the salon, while Colin confirmed Li Mo was exempt from attendance requirements.
• At the morning assembly, the dean encouraged students to attend the lawn salons, and Li Mo briefly activated Focus while wondering how Mystical Rituals drew energy.
• Anna and Helen remarked on the unusual politeness they had received, and Wayne explained that Li Mo’s salon and new school privileges had impressed the students.
• Li Mo noticed a girl walking past him without acknowledging him and saw a silver emblem on her coat that matched the emblem he had seen on the Scarlet Moon.
• When the girl turned and asked if something was wrong, Li Mo felt pressured and said, “Damn... why did it have to be now...?”

Li Mo saw a mysterious symbol on a Puxiu Academy girl's jacket that Anna and Wayne could not see, and decided to investigate by becoming her friend. Meanwhile, Matthew tried to recover from his public embarrassment and planned to impress an incoming transfer student with political talk.

• Li Mo questioned the girl about her jacket indirectly after seeing a symbol on it, but Wayne and Anna said they had seen no design.
• Li Mo returned to class, where his classmates greeted him warmly and Lily offered cookies for him and Anna.
• Matthew arrived late and endured classmates teasing him about his failed lawn salon performance, then claimed family business would keep him from the next salon.
• Matthew heard that a girl from out of town was transferring into Class One and decided to impress her by discussing politics.

Li Mo met the new transfer student, Estelle Xi, and invited her to his mathematics salon. When Matthew boasted that his family had hoarded cotton using advance military intelligence, Estelle questioned him and Li Mo offered to show her an improved spinning machine.

• Mr. Harrison introduced Estelle Xi as a new student in Class One, seated her beside Li Mo, and directed her to ask him for help with her studies.
• Estelle asked Li Mo a mathematics question, agreed to attend his afternoon salon, and asked him to call her Xiao Xi.
• Matthew introduced himself to Estelle and boasted that his family had stockpiled Mondel Town's raw cotton after learning of the northern sea blockade, driving prices up and hurting local workshops.
• Estelle questioned Matthew about whether his father knew he was revealing the family's actions, while Li Mo sensed her anger.
• Li Mo described an improved spinning machine that could use far less cotton and produce stronger, finer thread, and Estelle asked whether it had been built.
• Li Mo said he would take Estelle to the factory to see the machine after the salon.

Estelle drew Matthew into revealing his family’s corrupt dealings while Anna and Wayne stayed with them. At the observatory, Li Mo rejected Lydia’s attempt to win his silence and suggested Professor Bryce had known about her offer to sell assessment questions all along.

• Li Mo left for the observatory to study nearly ten years of observation ephemerides and asked Anna to get to know Estelle.
• Estelle encouraged Matthew to talk, and he revealed how his family profited from a blockade order, improper bank loans, and plans to overcharge the Quartermaster’s Office.
• Estelle recorded the names of Matthew’s family’s contacts as he prepared to disclose more about their tax evasion.
• Lydia begged Li Mo not to tell Professor Bryce she had offered to buy assessment questions and offered to do whatever he wanted in return.
• Li Mo told Lydia Professor Bryce might have known about her offer as a screening method, then went inside and left her stunned.

Li Mo analyzed ten years of lunar observations and discovered that the Red Moon behaved like a massless celestial oscillator, then connected its harmonic frequency to the energy-absorbing silver threads of a Mystical Artifact. He suspected that an opposing phase could interrupt the artifact’s ritual and asked Professor Bryce for tools to test his theory.

• Professor Bryce gave Li Mo ten years of orbital records for the Silver Moon and the Red Moon.
• Li Mo confirmed the Silver Moon’s orbit and found that the Red Moon’s distance, orbital period, and lack of gravitational effects contradicted ordinary celestial mechanics.
• Li Mo analyzed the Red Moon’s data and determined that its orbital motion followed a stable fundamental frequency and its harmonics.
• Professor Bryce told Li Mo that he had accidentally activated a Star-Track Resonance Time Calibration Instrument that would run for forty-eight hours and consume an ounce of Star Silver Powder.
• Li Mo observed the artifact’s silver threads and found that their energy-absorption rhythm nearly matched the Red Moon’s harmonic frequency.
• Li Mo proposed disrupting the artifact’s resonance with an opposing half-wave phase and asked Professor Bryce to fetch a vernier caliper, a brass probe, and linseed oil.

Li Mo experimented on a time calibrator to disrupt its ritual, accidentally caused an explosion, and then discovered how to reverse the energy flow back to the Red Moon. He concealed the discovery from Professor Bryce by triggering another small blast, leaving the professor terrified by Li Mo’s smoke-covered appearance.

• Li Mo used linseed oil and a brass probe to weaken the calibrator’s silver threads, but the trapped energy caused an explosion that injured his cheek and knocked Professor Bryce down.
• Li Mo analyzed the explosion and calculated how to reverse the energy flow through the silver threads instead of merely blocking them.
• Li Mo inserted three probes at calculated positions and successfully sent energy from the calibrator back to the Red Moon.
• Li Mo realized others must not learn that he could stop Mystical Rituals, then withdrew a probe and caused a smaller explosion to conceal his discovery.
• Professor Bryce searched the smoke for Li Mo and found him gathering Star Silver Powder while grinning and laughing eerily.

After an explosion destroyed the Star-Track Resonance Time Calibration Instrument, Li Mo began developing a quicker method for calculating higher-order Mystical Artifacts before rushing to the academy’s second math salon. He opened the salon with a lecture on continuity, the intermediate value theorem, and convergence criteria, while Estelle watched him with her usual composure.

• Li Mo gathered the surviving Star Silver Powder, and Professor Bryce told him to take the damaged instrument to the Moonfall Artifact Workshop for repairs.
• Li Mo began calculating a standardized Red Moon Harmonic Order Reduction Quick Reference Table to simplify future reverse-engineering work.
• Wayne told Estelle stories about Li Mo’s achievements on the way to the salon, but Anna redirected their conversation to watches.
• Li Mo arrived late and disheveled at the crowded salon, where Anna wiped the dried blood from his cheek.
• Li Mo began his second salon lecture on continuity, the intermediate value theorem, and convergence criteria, and he wondered whether he could astonish Estelle.

Toby sold bread and barley water at Puxiu Academy’s second Mondel Academic Salon, where Li Mo delivered a mathematics lecture that drew enthusiastic applause. After the salon, Harrison introduced Li Mo to Arthur Kent, a visiting council member with an important proposal, leaving Li Mo curious about what Kent wanted.

• Toby sold bread and barley water to the crowd gathered for Li Mo’s lecture at Puxiu Academy.
• Li Mo explained continuity, the intermediate value principle, and sequence convergence during the salon.
• The audience applauded Li Mo, who announced that the salon would continue the following afternoon.
• Li Mo noticed Estelle’s reserved reaction and wondered about her family background.
• Harrison introduced Li Mo to his friend Arthur Kent, who praised the lecture and hinted at an important proposal.