docs(debt): cite the bundled libc.prx for _Mtx_trylock, strdup and strndup

docs/dev/debt/libc.md

@@ -10,7 +10,7 @@
 - [fdopen](../../../core/libs/prx/libc/src/FileAndHeap.cpp) (libc) validates descriptor access modes as FreeBSD 11.4 [fdopen.c](https://github.com/freebsd/freebsd-src/blob/8c639945a44588f6cfdddfb057bb5aad88735da0/lib/libc/stdio/fdopen.c) does: a requested mode incompatible with a descriptor not opened for both reading and writing returns null with `EINVAL`, leaving the descriptor open. Windows reads the handle's granted access through the same host helper as `fcntl(F_GETFL)`; a closed descriptor returns null with `EBADF`. Console behavior is unverified.
 - [scriptingGetMem, scriptingFreeMem](../../../core/libs/prx/libc/src/ApplicationHeap.cpp) (libc) - runtime allocator hooks for Unity titles. The allocation signature `(alignment, size)`, minimum alignment 16 and null result for a non-power-of-two alignment follow [KytyPS5](https://github.com/KytyPS5/KytyPS5/blob/df5b9b92be7dfd463b47756b707d6d356a9f0550/src/libs/libKernel.cpp); the free hook's one-pointer signature follows [Raeen's recorded contract](https://github.com/Whoisraeen/Raeen/blob/2db56923204b89719916b95e29c2f3c4e1d9f90b/docs/unity-dlsym-blocker.md). Both use libc's own guest heap, not the title's registered allocator. A title that ships its own `libc.prx` (Metal Gear Solid Master Collection, PPSA18194) has already initialized that allocator, and reaching it from here would run its initializer a second time. That title's IL2CPP runtime looks up only `scriptingGetMem`, by name from `Il2cppUserAssemblies.prx`, and asks it for 256 KiB blocks aligned to 4 KiB. Which console library exports the hooks is unknown, and there is no console measurement. Allocation failure and sizes that overflow return null.
 
-- [_Mtx_trylock](../../../core/libs/prx/libc/src/Threads.cpp) (libc, NID `k6pGNMwJB08`) - returns busy for a non-recursive mutex already owned by the caller, assumed to match `_Mtx_lock`'s ownership handling; exact console behavior is unverified.
+- [_Mtx_trylock](../../../core/libs/prx/libc/src/Threads.cpp) (libc, NID `k6pGNMwJB08`) - returns busy for a non-recursive mutex already owned by the caller. The `libc.prx` that titles ship (read from disassembly of PPSA13934's copy, 0x5cf0, not measured on a console) passes its argument to `scePthreadMutexTrylock` and returns 0 for success, `_Thrd_busy` (3) for `SCE_KERNEL_ERROR_EBUSY` and `_Thrd_error` (4) for any other error, so busy for an owned non-recursive mutex comes from the kernel mutex there; this libc keeps its own owner and count instead, and its result for a kernel error other than busy is not compared.
 - [nearbyintf](../../../core/libs/prx/libc/src/Math.cpp) (libc, NID `c+4r-T-tEIc`) rounds with the MXCSR rounding mode, as the console's `libSceLibcInternal.sprx` does in a payload process on a PS5 (firmware 13.60): with the x87 mode set to upward and MXCSR to nearest it rounded 2.5 to 2, and with MXCSR upward to 3, and the four modes gave the results the host gives. The console also raised `FE_INEXACT` for those inexact inputs, which the host's `nearbyintf` does not; whether it does for exact inputs was not measured
 - [__std_find_trivial_unsized_N](../../../core/libs/prx/libc/src/VectorAlgorithms.cpp) (libc) - matches the `libc.prx` bundled with PPSA08427 (disassembly, and that binary run side by side on random inputs): when nothing matches between `first` and the end of its 32-byte-aligned block, the console rescans that whole block without masking and so can return a match up to 31 bytes before `first`
 - [_Thrd_sleep](../../../core/libs/prx/libc/src/Threads.cpp) (libc, NID `jfRI3snge3o`) follows the Dinkumware threads library shipped with [Visual C++ 2013](https://github.com/adityaramesh/concurrency_runtime/tree/master/VS2013_SP2/crt/src/thr) (`xtime.c`) and C11 Annex K, without console verification. It reads a 16-byte xtime (64-bit seconds and nanoseconds) on the guest `CLOCK_REALTIME`, normalizes the nanoseconds and sleeps through `nanosleep` on POSIX, retrying on `EINTR`, or high-resolution waitable timers on Windows; a null xtime or one whose normalization overflows throws. Guest thread cancellation is not integrated with this wait. The console's `_Thrd_sleep` (disassembled from a title's `libc.prx`) also takes an optional `xtime*` of remaining time and returns `int`; here the sleep is never cut short, so it returns 0 and leaves the remaining time untouched.
@@ -50,7 +50,7 @@
 - [strerror_s and strerrorlen_s](../../../core/libs/prx/libc/src/WideConversion.cpp) (libc) follow [C11 K.3.7.4.2 and K.3.7.4.3](https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf), using the existing FreeBSD error messages and unknown-error formatting. Truncation writes an ellipsis when capacity exceeds 3; constraint failures leave the destination untouched and invoke the registered guest-ABI handler. The console's `RSIZE_MAX` (`SIZE_MAX >> 1` here), nonzero returns (`EINVAL` 22 for constraints, `ERANGE` 34 for truncation), handler arguments and default abort behavior are unverified. Messages remain in the C locale, and guest errno is preserved.
 - [getw and putw](../../../core/libs/prx/libc/src/BinaryWordIo.cpp) (libc) follow FreeBSD 11.4 [getw.c](https://github.com/freebsd/freebsd-src/blob/8c639945a44588f6cfdddfb057bb5aad88735da0/lib/libc/stdio/getw.c) and [putw.c](https://github.com/freebsd/freebsd-src/blob/8c639945a44588f6cfdddfb057bb5aad88735da0/lib/libc/stdio/putw.c): one 32-bit little-endian word, `getw` returns -1 for EOF or an error, and `putw` returns 0 on success or -1 on error while holding the stream lock. They use the existing host-backed streams, so buffering and error timing follow the host CRT. Null streams throw and closed streams return -1 with `EBADF`, as existing byte I/O does. Console behavior is unverified. A payload process on a PS5 (firmware 13.60) gave the same results: two words written little-endian, -1 with end of file after them and for a 2-byte file, and -1 with the error flag for `putw` on a read-only stream
 - [vsnwprintf_s](../../../core/libs/prx/libc/src/FormattingWide.cpp) (libc) - `va_list` counterpart of `snwprintf_s` (C11 K.3.9.1.3): truncates to the buffer and returns the full length, with the same constraints and argument checks
-- [strndup and strdup](../../../core/libs/prx/libc/src/AllocatingStrings.cpp) (libc) return null with `errno` set to `EINVAL` (22) when `source` is null, preventing a host segfault on invalid guest input. POSIX.1-2008 and FreeBSD 11.4 libc leave `strndup(NULL)` and `strdup(NULL)` undefined (faulting); exact console behavior on hardware is unverified.
+- [strndup and strdup](../../../core/libs/prx/libc/src/AllocatingStrings.cpp) (libc) return null with `errno` set to `EINVAL` (22) when `source` is null, preventing a host segfault on invalid guest input. POSIX.1-2008 and FreeBSD 11.4 libc leave `strndup(NULL)` and `strdup(NULL)` undefined (faulting). The `libc.prx` that titles ship has no null check either (read from disassembly of PPSA13934's copy, not measured on a console): `strdup` (0x6b440) calls `strlen` and `strndup` (0x6b650) calls `strnlen` on the source before allocating, so both fault on a null source there, except `strndup(NULL, 0)`, whose `strnlen` reads nothing and which returns an empty copy; here it returns null with `EINVAL`.
 - [snprintf_s and vsnprintf_s](../../../core/libs/prx/libc/src/Formatting.cpp) (libc) - follow C11 K.3.5.3.5 and K.3.5.3.12 with `RSIZE_MAX` assumed to be `SIZE_MAX >> 1`, as `snwprintf_s` does: a null buffer or format, `size` of 0 or above `RSIZE_MAX`, any `%n` and a null `%s`, `%ls` or `%S` argument return a negative value and set `buffer[0]` to zero when the buffer and size allow it; otherwise the output is truncated to the buffer and the full length is returned. A violation only returns: the constraint handler is not invoked, and the console's error value is unverified. Not confirmed on a PS5 title
 - [vsscanf_s](../../../core/libs/prx/libc/src/Formatting.cpp) (libc) - returns the count of items converted before an undersized `%s`/`%c`/`%[` destination (0 when it is the first), not EOF. Not confirmed on a PS5 title
 - [setlocale](../../../core/libs/prx/libc/src/StdioExtras.cpp) (libc) knows only the "C" locale, as the `libc.prx` that titles ship does: it ignores the category, returns "C" for a null, empty or "C" name and a null pointer for any other, "POSIX" included, without setting `errno`. Checked by running the copies bundled with PPSA07923 and PPSA13934 side by side for categories -40 to 79 and 2^30, not measured on a console.