Arhan Chaudhary ArhanChaudhary

DR bounding: errata, and what the full BFS settles

Goes with the write-up "Judging a DR by hand: what the full BFS says", but reads on its own. The write-up has the measurements and the full tables.

November 2026. A name with a date is a link to that message on the FMC solvers Discord (#fmc-theory or #fmc-discussion). Docs and sheets are listed with links at the end.

What everything below is measured against:

A full BFS of the DR group ⟨U, D, R2, L2, F2, B2⟩: the optimal DR-move finish of all 19,508,428,800 DR states, done in Rust on the group reduced by the 16 symmetries that keep the U/D axis. "Optimal" below means that (same as nissy's drudfin) unless it says otherwise. It matches Joba's per-subset distribution in every cell and nissy on 40 random DRs, and it's the same in every entry as the table Lean has proven optimal (next but one bullet).
The 216 NISS@1qt cases (FakeMMAP's: 12 corner cases × 3 M-slice patterns × 3 S-slice patterns × E-parity, each case being 3,072 of the 663,

Keybase proof

I hereby claim:

I am arhanchaudhary on github.
I am archandstarch (https://keybase.io/archandstarch) on keybase.
I have a public key ASCwCpPniMU2uwlUKUw_jDz9lwZ2lyULttFh8wLUfHIahgo

To claim this, I am signing this object:

Programming

	NOTE: all instruction counts ignore the initial and final SIMD register load instructions

	AVX2 composition: 5 instructions, averaging 700M/sec on an Intel Xeon E5-2667 v3
	AVX2 inversion: 26 instructions, averaging 175M/sec on an Intel Xeon E5-2667 v3
	ARM64 composition: 19 instructions, averaging 870M/sec on an Apple M4
	ARM64 inversion: 48 instructions, averaging 400M/sec on an Apple M4

	#include <jni.h>
	#include "Main.h"

	JNIEXPORT jobject JNICALL Java_Main_getSecret(JNIEnv *env, jobject obj, jobject secretObj)
	{
	jclass cls = (*env)->GetObjectClass(env, secretObj);
	jfieldID field_id = (*env)->GetFieldID(env, cls, "secret", "Ljava/lang/Object;");
	jobject secret = (*env)->GetObjectField(env, secretObj, field_id);
	return secret;
	}

	import re
	import webbrowser
	import requests
	import PyPDF2
	import io

	url = input("Enter the study guide URL: ")
	url_raw = requests.get(url).content
	url_contents = ''
	with io.BytesIO(url_raw) as open_pdf_file: