BlawkOps — Radicals

What is a radical

A radical is a named tuple of constraints that defines a BJJ position. Two layers, two primitives.

Radical = Frames + CONs
             |        |
             |        |-- required  (must exist)
             |        |-- forbidden (must not exist)
             |        '-- forbidden_bilateral (must not both exist)
             |
             '-- facing, ground state

Frames

Global spatial facts about the two bodies. Four types:

FacingOpposed FacingAligned OnGround(X) NotOnGround(X)

CON

One wrapping contact between two limb axes. 9 independent fields:

Attacker role part sign dir

Axis role part sign dir

Wrap helicity

Two primitives, one data type for contacts, three quantifiers over it.

Defense lines

Guard players defend through three barriers. Each level cleared brings the passer closer to a dominant position.

Level 3

Feet

OGRD — DLR, SLX, RDLR, LSSO, OMOP

First line of defense. Feet and legs create distance, hooks, and entanglements.

Level 2

Knees

HGRD

Feet cleared. One knee entangles the opponent's leg — half guard.

Level 1

Hips

CGRD

Last barrier. Both legs wrap the torso, feet locked. Closed guard.

Level 0

Passed

MNT, SCTR, BCTR, TRTL

Guard passed. Dominant positions: mount, side control, back control, turtle.

Structural distance

How it works

Each radical is defined by frame constraints and CON primitives. A CON has 9 independent fields: attacker role, part, sign, direction; axis role, part, sign, direction; helicity.

Distance = number of fields that differ. One field change = one structural edit.

Adding a contact

An unmatched CON costs 9 — the number of independent fields. Going from no contact to a specific contact means specifying all 9 fields from nothing.

The chain

Each step is exactly one field change:

DLR →helicity SLX →ax_part LSSO →ax_dir OMOP

Distance matrix — 7 fundamental positions

	MNT	SCTR	BCTR	CGRD	OGRD	HGRD	TRTL
MNT	·	29	13	12	20	13	35
SCTR	29	·	27	39	30	24	18
BCTR	13	27	·	19	31	24	29
CGRD	12	39	19	·	30	23	43
OGRD	20	30	31	30	·	9	30
HGRD	13	24	24	23	9	·	26
TRTL	35	18	29	43	30	26	·

Distance matrix — open guard subtypes

	OGRD	DLR	SLX	RDLR	LSSO	OMOP
OGRD	·	11	11	11	11	11
DLR	11	·	1	1	2	3
SLX	11	1	·	2	1	2
RDLR	11	1	2	·	3	4
LSSO	11	2	1	3	·	1
OMOP	11	3	2	4	1	·

Transitions

Pass / Advance

OGRD→HGRD, OGRD→SCTR, HGRD→SCTR, CGRD→SCTR, CGRD→MNT, SCTR→MNT, SCTR→BCTR, TRTL→BCTR

Recover / Escape

SCTR→HGRD, SCTR→OGRD, SCTR→TRTL, MNT→OGRD, MNT→HGRD, BCTR→TRTL, BCTR→OGRD, TRTL→OGRD

Close guard

OGRD→CGRD, HGRD→CGRD

Lateral (subtype switch)

DLR↔SLX, DLR↔RDLR, SLX↔LSSO, LSSO↔OMOP