I started with a ship full of max-level veterans, and I'm just a complete noob.

The dark gold lettering faded into the pages, and Jiang Ming saw the graph paper on his lap again. The numbers on both sides of the crease had not changed, but the arrangement had added a line that could be traced.

He drew the central axis along the fifth item, and paired the first ten frequency points from the left and right ends toward the middle, with the first item corresponding to the tenth item, the second item corresponding to the ninth item, and folding them inward in sequence.

4.93 and 5.44 are on either side, 5.48 and 5.17 are in the second group, and 5.07 and 4.81 form the third group.

After the chaotic jumps on the surface undergo positive and negative flips, they begin to oscillate around the same baseline, and each set of deviations can find a residual value in the opposite direction on the opposite side.

"You broke down the timing sequence?"

Fang Xudong reached for the paper, but Jiang Ming pressed down on the center axis with a pencil, preventing the fold from moving.

"The temporal sequence is still there; we only unfold the reflections that have exceeded the boundary."

"Cryptanalysis must preserve the order of events. If you force the first and tenth items together, you can only achieve artificial symmetry."

Jiang Ming did not look up, but continued to separate the dwell time according to odd and even digits, putting four seconds, six seconds and eight seconds into one column, and the remaining values ​​into another column.

Fang Xudong saw that he neither used a slide rule nor applied ready-made formulas, but simply drew two intersecting geometric lines on the paper, and his hand was already reaching for the paper.

Old Sun leaned against the car door, switched the socket wrench to his right hand, and glanced at him.

Let him calculate.

"Master Sun, this isn't a machined part; you can't find the password by touch."

"Your three sets of books are all useless now. Let the people who didn't get the books try them out first."

Fang Xudong withdrew his hand and stood behind Jiang Ming, his rebuttal left unfinished.

Jiang Ming set 4.8 MHz as the zero point, normalized the bandwidth to 800 kHz, and then folded back along the boundary each time the part that crossed the upper or lower limit.

If the frequency wheel does not reappear from the bottom edge after reaching the top edge, it will change direction and return along the mirror path.

The second and third items appear to be discontinuous from the outside, but when the mirror is unfolded, they are located adjacent to each other on the same diagonal line.

Jiang Ming removed the base frequency and eliminated the fixed bias caused by the odd and even capacitor groups. The slope of the broken line finally fell between 0.413 and 0.415.

He added the three sets of errors together, divided them again by the effective range, and left a decimal on the paper.

0.414.

Fang Xudong looked at the three numbers, first multiplied them by the bandwidth, and then compared them with the dwell time in groups.

"This number cannot form an integer gear ratio."

"It shouldn't have been an integer ratio in the first place."

Jiang Ming wrote the square root of 2 next to 0.414, then subtracted 1. The two numbers completely overlapped under the current mechanical error.

The backup frequency hop does not use thermal noise. It uses dual capacitors to charge and discharge to create a continuous ramp, and then uses the square root of two minus one as the step ratio. When it reaches the edge of the frequency band, it mirrors back.

The square root of two cannot be fully represented by a finite number of gears. The designer approximates the cycle with a multi-stage resistor and a cam cycle, which will not repeat in short sequences and is unlikely to produce visible cycles in long-term operation.

Dwell time plays another role; each change in its length determines whether to use a forward capacitor bank or a reverse capacitor bank in the next step. From the receiver's perspective, the frequency points appear to be in three layers of disorder.

Fang Xudong picked up a pencil and recalculated the sixth to tenth items in the blank space. The error after expansion all fell within one channel width.

"It treats the two ends of the frequency band as a mirror; however much it jumps out, it bounces back from the boundary by the same amount."

"We also need to add odd-even group reversal; without this layer, the third item won't match."

Lu Qinghe was still tracking the eleventh frequency hopping. After hearing what the two people were saying, he locked the receiver frequency to the edge of the current bright band.

"Could you give it a push?"

Jiang Ming substituted the tenth item into the expansion formula, determined the next time the reverse capacitor group would take over based on the switching noise interval, and then advanced along the mirror line by 0.41 four units.

He drew three intersections on the paper with the pencil, and then tapped the last point where the pencil landed.

"4.92 MHz, then 5.33, and then 5.08."

"Three consecutive jumps?"

"The step seed is the square root of two minus one, the dwell order is not changed, and all three jumps are in place."

Lu Qinghe placed her hand on the knob but did not turn it immediately.

The current bright band is at 5.26 MHz. Based on the recorded pattern of change, it would not be surprising if the next hop falls to any position. 4.92 is just one of the eighty channels.

"How much longer?"

"There are three seconds left on the current frequency. Set the receiver to 4.92 and reduce the bandwidth to 6 kHz."

Lu Qinghe turned the frequency scale to 4.92, then lowered the intermediate frequency bandwidth, leaving only a narrow dark area on the oscilloscope.

At the mine control console, the technical supervisor flipped through the newly output tape. The backup frequency hopping device had completed a full cycle, and all switching was within the design tolerance.

He placed the enamel mug next to the frequency meter, and the steam from the coffee spread along the instrument glass.

"Are the North and West gullies still sending telegrams?"

"Each carrier was captured twice, each lasting less than three seconds, making it impossible to establish a connection."

"Keep pushing the power into the two channels until they run into their own people in the dark."

The technical supervisor sat back in his chair and checked each item on the control panel with his fingers. The backup system had not been directly impacted by the source lightning bolt, nor did it have any fixed coupling frequency that could be used for reverse calculation.

As the second hand on the mound crossed the third mark, the noise in the speaker rose first, then a brief pause appeared when the capacitors were being switched.

A bright band appeared on the right side of the oscilloscope, and its point of intersection was exactly on the 4.92 MHz mark.

Lu Qinghe's pre-installed narrowband receiver opened the path before the interference power was fully applied, and the carrier wave of the distant transmitter pierced through the gap.

"Beigou Company calling command post! Beigou Company calling command post! Please respond!"

A hoarse shout burst from the loudspeaker, and everyone in the carriage turned to the receiver at the same time.

Lu Qinghe grabbed the microphone and tuned the transmitter to 4.92 MHz, taking advantage of the few seconds of gap before the enemy station had finished gaining up after switching stations to respond.

"Mound received. Report location and casualties."

"We encountered crossfire on the east side of the second fork in the road. There are wounded in the second platoon. There is no contact with the west gully direction. The people in the mine are retreating to the central high ground!"

As the interference bands began to thicken, Lu Qinghe switched the receiver to 5.33 MHz ahead of time, following the next frequency point written down by Jiang Ming.

The enemy station then jumped in, and she once again beat them to the punch before the switch could happen. The carrier of Beigou Company 1 switched synchronously from the previous frequency point, and the sound was cut off by only half a sentence.

The command post communications officer also understood the preset pattern and switched the main station to 5.33 MHz, as Director Wang ordered to connect to the channel.

"The first company of Beigou shall maintain its firepower and shall not cross the No. 3 stone marker. The second battalion is to your southwest; the artillery shall not fire."

"Received. We can hold out for another twenty minutes. Please restore long-distance communication as soon as possible!"

The third preset target was set to 5.08 MHz, and the enemy's signal light appeared on time. Radar base No. 3 and outpost No. 4 also jumped into the narrow gap.

The communication network that had been cut up was reconnected, and each time it could only take advantage of the brief intervals when the enemy's gain was not yet fully deployed, but it was enough to transmit location and action commands.

Fang Xudong stood behind the receiver, holding a slide rule, his gaze moving along the mirrored lines on the graph paper. Every point on the paper was verified on the oscilloscope.

He applied three different teaching models and ultimately judged the equipment as physically random. However, Jiang Ming dissected the random surface and found the irrational numbers hidden behind the mirror in the frequency switching noise.

"Square square root of two minus one, where have you seen this frequency hopping method before?"

Jiang Ming wrote down the next frequency points for Lu Qinghe, his pencil never stopping.

"I've never seen this before; I just calculated it."

Fang Xudong's hand was still on the slide rule, but he didn't ask any further questions. The clear chain of derivation on the paper had already silenced all doubts.

Once communications were restored, the command post checked the coordinates of Beigou and Xigou step by step, and the two red flags on the map finally began to move forward.

Just then, a confidential clerk rushed into the earthen house and handed the newly received coded telegram to Director Wang.

Director Wang only read the first two lines before picking up the walkie-talkie and asking Tuqiu to switch to a separate, secure channel.

Following Jiang Ming's calculations of the frequency hopping table, Lu Qinghe rushed to the next frequency switching gap and connected the command post's signal to the vehicle.

"Jiang Ming and Fang Xudong, stay here. The rest of you, continue your work." Director Wang's voice cut through the background noise, without any pause between words. "The Lanzhou surveillance team just sent an urgent telegram: Meng Dechang has escaped surveillance and his whereabouts are unknown."

Jiang Ming is writing the fourth preset frequency.

The pencil tip suddenly pierced through the graph paper and struck the metal sheet of the shockproof box.