The asker is hand-crafting a minimal ELF64 executable in NASM, laying out the ELF header and a single PT_LOAD program header that maps a tiny amount of code at virtual address 0x1000. Producing an ELF that runs is a classic golf exercise (see a.out minimizers by Brian Raiter and others), but the Linux kernel loader has become significantly stricter over the years, and small deviations that were once tolerated now yield opaque failures like ENOEXEC, SIGKILL before _start, or a bare "cannot execute" message.

What makes it interesting is that the ELF spec permits a lot, but fs/binfmt_elf.c in the kernel enforces additional invariants that aren't obvious from reading the spec. A few common culprits for "single small segment" failures:

• Page-alignment congruence: The kernel requires p_vaddr % p_align == p_offset % p_align. If your file offset for the segment isn't congruent to 0x1000 modulo the page size, the kernel refuses to mmap it. Many hand-golfed ELFs place the segment at file offset 0 and virtual address 0x1000 — that only works if p_align is 0x1000 and both offsets share a page-remainder of zero, which means the ELF header itself must live inside the mapped segment.
• Missing PT_LOAD covering the ELF header: Related to the above — the de facto convention is that the first PT_LOAD starts at file offset 0 so the ELF header and program headers are mapped along with code.
• mmap_min_addr: On modern kernels the sysctl vm.mmap_min_addr is usually 65536. A segment at va = 0x1000 is below that threshold and will fail to map for an unprivileged process.
• Non-zero segment size but p_filesz < sizeof(headers): If p_memsz or p_filesz underflows what you're actually reading, the loader silently bails.

Diagnostic approach:

1. Run strace -f ./tiny 2>&1 | head — look for the execve return value. EINVAL almost always points to alignment; EACCES to mmap_min_addr.
2. Enable kernel loader diagnostics: dmesg after the failed exec often prints "requested but not required" or "bad ELF" messages from load_elf_binary.
3. Use readelf -l and check that VirtAddr and Offset match modulo Align.
4. Compare against Raiter's "A Whirlwind Tutorial on Creating Really Teensy ELF Executables" — his 45-byte binary works precisely because it satisfies the congruence rule by piling everything into one overlapping segment.

Without the actual error message the answer is speculative, but 9 times out of 10 for this pattern it's the p_offset ≡ p_vaddr (mod p_align) constraint biting.