The hot afternoon wind blew construction dust against the two men's faces, but Demetrius didn't blink. Lucius's question, though personal and unexpected in that environment of rigid hierarchy, seemed to have struck a sensitive chord in the Greek master builder's chest. He straightened his posture, wiping the stone dust covering his arms with a dignified gesture.

  "I am proud of my craft, sir," Demetrius replied, his voice firm and laden with rough honesty. "I am proud to see raw stone become a wall, and a wall become shelter or an aqueduct. The sweat of my labor feeds cities and protects families. I like what I do, for building is the only way I know to defy time and death."

  Lucius nodded, satisfied. It was the answer of a man who valued substance over appearance, exactly the kind of ally he needed.

  "Excellent," said Lucius, lowering his voice so only the Greek could hear amidst the noise of hammers and overseers' shouts. "Then listen to me closely, Demetrius. You will have to trust me. You will have to understand my demands, however strange they may seem at first. And most importantly: what I am about to show you, the methods we discuss, and the drawings I make... must not be shared with anyone other than Noble Valerius. Not with your subordinates, nor with other master builders, do you understand me?"

  Lucius held the man's gaze, conveying the gravity of the situation.

  "I will explain some concepts that may seem contrary to tradition, but are based on the nature of things. If everything goes right with this project, if we manage to tame this valley, I give you my word: when I return from the military campaign for which I was summoned, I will personally recommend you to Noble Valerius. I will say success was impossible without your mind and hands. You will be rewarded with gold and prestige, not just the day's wage."

  Demetrius's eyes shone. The promise of direct recognition from a patrician, mediated by this mysterious man who spoke with such authority, was a rare opportunity.

  "I will do my best, sir," Demetrius assured him, bowing his head slightly. "My loyalty is to the work and to those who wish to see it erected."

  "Do we have a place where we can talk in private?" asked Lucius, looking around, uncomfortable with the curious stares of slaves and guard soldiers. "I need to see the maps and make notes away from the wind."

  "Yes, this way," indicated the Greek.

  Demetrius guided Lucius through the labyrinthine construction site, dodging piles of baked bricks and ox carts blocking the path. They arrived at a large tent, made of thick canvas and leather, set up on a wooden platform to avoid the dampness of the swampy ground.

  Upon entering, the contrast with the outside was immediate. The construction noise became a muffled hum. The air inside was warm and smelled of old parchment, wax, and ink. In the center, a sturdy oak table, marked by scars of use and wine stains, was covered with papyrus scrolls, bronze styluses, and wooden rulers.

  Demetrius hurried to organize some scattered scrolls, seeming suddenly conscious of the disorder.

  "Forgive the appearance of the place, sir," said the master builder with an apologetic smile. "It is a field office, not a senatorial library. Dust gets in everywhere, and order is hard to maintain when chaos reigns outside."

  Lucius walked to the table and ran his hand over the rough wood, feeling the real texture of the work.

  "It's fine, Demetrius," said Lucius, turning to him with a relaxed expression. "Don't worry about excessive formalities. I am not a noble. I didn't grow up in marble palaces and am not offended by construction dust. You don't need to be cautious with me, nor measure every word as if speaking to a senator."

  Demetrius paused with a scroll in his hand, confusion stamped on his bearded face. He looked at Lucius's expensive clothes, and then remembered the way Noble Valerius had treated him, as an equal, or even more than that.

  "If you are not noble, sir... what are you?" asked Demetrius, curiosity overcoming prudence. "A tribune? A distant relative of House Valerius? I have never seen a man without patrician blood receive such authority over an imperial project."

  Lucius smiled enigmatically. He knew the truth, "I am an engineer from the future who just invented the wheelbarrow," wasn't an option.

  "I am someone the Master trusts," replied Lucius, maintaining the mystery. "Someone who sees problems and finds solutions. Let's just say my mind serves Rome in a different way. That is all that matters for now."

  He pulled up a wooden stool and sat at the table, clearing a space among the maps.

  "Shall we begin?"

  "Certainly," replied Demetrius, approaching.

  Lucius took a piece of charcoal and a clean sheet of papyrus. With the same didactic clarity he had used with Valerius, he began to draw the valley profile. He explained the inverted siphon concept: the steep descent, the "belly" supported on a low bridge over the swamp, the ascent on the opposite slope, and the hydraulic level recovery. He spoke about pressure, the need to split the flow into multiple smaller pipes to prevent rupture, and using concrete to encase the piping at the lowest point.

  Demetrius listened with absolute attention, eyes fixed on the charcoal dancing on the paper. He asked pointed technical questions about pipe junctions and lead sealing, demonstrating deep practical knowledge. When Lucius finished the explanation, the Greek leaned back, scratching his beard, visibly impressed.

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  "It is bold," admitted Demetrius, shaking his head. "I have heard of siphons in Pergamon, but nothing on this scale. The logic is solid, sir. Avoiding deep foundations in the swamp is a relief to my soul. We lost three months trying to set those stones in the mud."

  However, Demetrius's expression soon clouded with practical reality.

  "But this requires specific materials, and in quantity," he pondered, pointing to the drawing of multiple pipes. "Especially high-quality lead and concrete. It was already a war to get what we have here to start the traditional work. Local quarries are slow and metal supply is rigidly controlled by the provincial treasurer."

  Lucius dropped the charcoal and looked into the master builder's eyes.

  "How many materials do you have in stock exactly? I need to know the real inventory, not what is written in reports for the Emperor."

  Demetrius sighed and went to a side cabinet, from which he took a wax tablet covered in notes.

  "We have a considerable stock of baked bricks, about fifty thousand units, as we were going to erect arcades. We have oak and fir wood, enough for scaffolding and forms. As for cement..." he consulted the tablet, "we have two hundred cartloads of good quality pozzolana, brought from Puteoli, and quicklime in abundance. The problem is lead. We only have enough for the final distribution channels in the city, not to cross a seven-kilometer valley with multiple pipes."

  Lucius frowned, engineer's mind processing the data. Seven kilometers. The total length of the diversion and crossing was enormous.

  "And raw stone? Limestone or tuff?"

  "That we have in abundance. The nearby quarry is rich in travertine, though extraction is slow," replied Demetrius.

  Lucius looked at his own design drawn on the papyrus. The lack of lead was an obstacle, but not insurmountable if he altered the structure's composition. He could make perforated stone pipes or use concrete-reinforced ceramics for lower-pressure parts, reserving lead only for the critical "belly." He needed to calculate. He needed to be sure.

  "Bring me something to write with. More papyrus and ink, if you have it. And I need silence," asked Lucius, his voice taking on a distant, focused tone.

  Demetrius obeyed promptly, bringing a bronze inkwell, sharp reeds, and several rolls of virgin papyrus.

  Lucius dipped the tip of the pen in black ink and began.

  He ignored Roman numerals. For complex engineering calculations, the Roman system was a nightmare of inefficiency. Trying to multiply MDCCXLVIII by XLII was torture he wouldn't impose on himself. Instead, his hand traced symbols that, to Demetrius, looked like sorcery runes or a forgotten foreign alphabet.

  1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

  Demetrius, who watched over Lucius's shoulder at first, frowned, completely confused. He knew the Greek alphabet, knew Roman numbers, even knew some Egyptian and Phoenician symbols he had seen in the port of Corinth. But that... those elegant curves and that empty circle at the end of sequences were alien.

  He saw Lucius align these symbols in columns, draw horizontal lines, and fill the papyrus with frightening speed. Lucius calculated the concrete volume needed for the low bridge: V = Length x Width x Height. He converted Roman units, pes (feet), passus (paces), to a mental standard he mastered, performed operations with the agility of modern mathematics, and then converted the final result back to measures the builders could understand.

  Lucius calculated the tension on the pipe walls for the seven-kilometer drop. If he used ceramic pipes reinforced with a ten-centimeter layer of concrete on the slopes, he would save 80% of the lead. He calculated water flow, friction head loss (using a simplified version of the Hazen-Williams formula in his head), and concrete curing time.

  Time passed. Outside, the sun began to decline, lengthening the shadows of the hoisting machines.

  Demetrius entered and left the tent several times. He went to check a cart unloading, shouted at a lazy overseer, drank water, and returned. Each return, he found Lucius in the same position, hunched over the table, surrounded by papyri covered in "magic symbols" and geometric diagrams. The engineer seemed in a trance, muttering to himself in a language Demetrius didn't understand, scratching out numbers, correcting variables, sweating buckets but seemingly not noticing the heat.

  Three hours passed. The hum of the work began to diminish as the shift end approached.

  When Demetrius entered the tent for the fifth time, bringing a lit lamp as natural light was fading, he found Lucius leaning back on the bench. The engineer held a papyrus up before his eyes, and a smile of tired but triumphant satisfaction illuminated his face.

  "What happened, sir?" asked Demetrius, placing the lamp on the table. "Did you find an error in the design?"

  "Quite the opposite, Demetrius," replied Lucius, turning to him with eyes shining with intellectual excitement. "I found the exact solution. I have here the precise quantity of materials and the definitive schedule for the work."

  Lucius extended the papyrus to the Greek. Although the intermediate calculations were illegible to Demetrius, the final result was written in clear Latin and traditional Roman numerals.

  "Look," pointed Lucius. "By replacing the high arcades with the siphon and using concrete-encased ceramic pipes on the slopes, reserving lead only for the five hundred meters of the valley floor, we will not need to wait for more metal from the imperial treasury. What you have in stock is sufficient if we cast the pipes right here."

  He ran his finger to the document's final line.

  "And the time... By my calculations, considering the current labor force and the use of wheelbarrows for rapid mortar transport, we can complete the seven-kilometer crossing and connection to the city in four months."

  Demetrius took the papyrus, hands trembling slightly. He read the numbers. Then read them again.

  "Four months?" repeated the Greek, voice failing in disbelief. He looked at Lucius as if the man had just said he could fly. "Sir... with all due respect, that is impossible. The original project estimated two years, perhaps three, with foundations in the swamp. Four months? Just to cure the concrete and lay the piping would take double that. No human team can work at that speed."

  He shook his head, skeptical.

  "These numbers... they are dreams, not engineering. If we promise this to Noble Valerius and fail, our heads will roll."

  Lucius stood up, walking to the master builder. He placed a hand on Demetrius's shoulder, squeezing firmly.

  "They are not dreams, Demetrius. It is mathematics. It is efficiency. Roman concrete cures fast if we use the correct ratio of lime and pozzolana. I calculated the exact mix for rapid drying and maximum strength."

  Lucius looked deeply into the Greek's eyes, conveying unwavering confidence.

  "I know it sounds like witchcraft. I know it defies everything you learned in decades on construction sites. But the calculations don't lie. If we organize the men in rotating shifts, if we use the carts for continuous flow and eliminate waiting for large stones, we will do it in four months."

  He paused, letting the weight of responsibility hang between them.

  "You said you trusted your craft. Now, I ask you to trust me. Follow this plan. Follow these quantities. And we will make history in this valley."