Date: 202109
Location: ZZZ.ARTCC, US
Flight conditions: VMC
Light: Daylight
Aircraft: Cessna 425/441 Conquest I/Conquest II
Operator: Air Carrier
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Commercial; Flight Crew Flight Instructor
Human factors: Workload; Communication Breakdown; Human-Machine Interface; Situational Awareness
Anomaly: ATC Issue All Types; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Overcame Equipment Problem; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Became Reoriented
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: In the event that occurred on Date a crossing restriction was assigned to my aircraft to cross ZZZZZ 10nm SW at 10;000 [feet]. I set that in my preselect on my altimeter and on the Garmin. Initially I missed the altitude at first and he repeated 10;000. I read back ZZZZZ 10nm SW 10;000. I reconfirmed with the passenger who decided to sit in the front with me and he confirmed that is what he heard (I also have his contact information). I began to get the plane into its descent to meet the restriction. I set the plane to meet its descent altitude right at 10000; 10 nm SW of ZZZZZ. At this point it had already been VFR conditions and turbulent through FL180. As I passed 15;000 I began noticing we were not going to make it over the mountain according to the chart and the visual out of the cockpit window. I leveled at around 13;500 to 13;800 (with Visual Separation). Again I had visual separation during the entire situation. Then I began to try and question ATC; I called 4-5 times several on Center and I believe twice on 121.5 (guard). I finally got the controllers attention when he ask probably perplexed at how low we had become. I read him back the crossing instructions he assigned over the radio; after confirming it; he apologized and stated if I could keep my own obstruction clearance; I confirmed I could; then assigned an immediate climb to 15;000 which I gladly executed. He had also in-between that claimed he assigned 16;000 (sounding unsure to me). I continued in bound and today the situation was avoided. Landed safely at ZZZ1 with no alert systems being activated.In this situation I should have caught the issue in the initial stages of the decent. I had ZZZ1 weather playing as the plane was descending and got it. In the descent as stated this is when I noticed the mountains becoming very close and compelled me to level off. I again tried to reach Center; I might have been too low for his receiver to hear me. I also tried Guard with no luck. Fortunately I finally got a hold of him. In this instance I could have leveled off soon instead of setting the auto pilot so meticulously maybe getting fixated on aviating. However; I do know the rules 'Aviate; Navigate; Communicate'. I aviated and then caught this situation happening in the Navigating Phase.As for ATC their Job is just as important as mine. I reconfirmed the altitude and crossing restriction. However; the error in altitude (if it was 16;000) was not caught. It also sounded like on Center that he became a little over saturated himself. I was not focused on it but he seemed [inundated] with multiple frequencies and more aircraft than a controller could handle by themselves. It sounded like some delay occurred somewhere. He apologized which initially made me wonder where the error occurred. I know his job is stressful and busy. I hope he submits a report on his end to see his perspective if anything were to come of this.As for correcting the situation I believe confirming altitudes and crossing restrictions is important. But in the mountains more than ever. From now on I will be double confirming my crossing restrictions and verifying plates before any descent is made to verify the crossing altitude.As for ATC I am not a controller and I know their worst fear would be to lose a plane. I know he was busy and probably [inundated]. But both sides keeping their ears peeled is ever more important.The Important thing is the situation was corrected and nobody was harmed. I used my skills to the best of my ability and I know the controller was giving his best too.




Synopsis: Air Carrier Captain reported a CFIT event due to a miscommunication between Captain and Air Traffic Controller regarding an erroneous crossing restriction in mountainous terrain area. The altitude was clarified and the flight landed safely.