No-gi submission grappling · a minimal complete game

The Fundamental Grappling Canon

The shared trunk every grappler needs before style — and the physics under it. Train it diligently against resistance and you will express all fifty invariants. It is also a contract: a written, science-rooted standard you can hold your coaching to.

50 invariants4 bidirectional rivers~2 years · ~400 quality mat-hoursthe floor, not the ceiling
The model

Two axes, one grammar, four rivers

Everything in the game is held by a small number of ideas. Two questions repeat in every phase; one order governs every exchange; and every attack drains into one of four rivers, each of which runs both ways — offence downstream, escape upstream.

Master axis 1 — posture

Seated ⟷ Standing

The same ecological decision, worn from both guard and passing. One idea, both sides of the mat.

Master axis 2 — line

Inside ⟷ Outside

Who owns the inside. Passing picks a side; legs go outside-first. The universal question of control.

ConnectionPositionSubmission Every river runs this loop — reinforced by weight and base. You cannot load a lever whose axis is still free to move.

The four rivers

① Back

Arm-drag / snap-down / body-lock / the pin staircase → face-down back → the strangle.

② Front-headlock

Snap-down & turtle front → chin-strap → the guillotine family.

③ Leg

Shin-to-shin → single-leg-X → outside ashi → the footlock/heel-hook dilemma.

④ Isolation

Guard / pass / pin → isolate a limb → armbar · kimura · triangle · head-and-arm.

The arm drag is the road to the back (river ①); the snap-down drives the head down into the front headlock (river ②). Each river then runs both ways — offence downstream, escape upstream.

The map

The map of the fundamental game

Every fundamental position and how it connects — drawn from your transition graph (51 positions, 125 real transitions), filtered to the trunk. The approach up top (standing → the guard-vs-pass battle), then the four rivers, each a chain of positions ending in its finishes.

① BACK ② FRONT-HEADLOCK ③ LEG ④ ISOLATION / PINS finishes ↓ finishes ↓ finishes ↓ finishes ↓ Standing Arm drag Collar tie Body lock Single leg Sprawl Seated guard Butterfly · Half/Z · DLR Shin-to-shin Shoulder crunch Passing — in / out / conn. Seatbelt Face-down back Front headlock Turtle · 4-point Go-behind Single-leg-X Outside ashi Inside game ⚠ Side control KOB · Mount S / Tech-mount RNC Garrote Rear triangle Armbar Guillotine Ninja D'Arce Anaconda Str. ankle Outside heel Aoki Inside heel Woj Kneebar Calf slicer Toe hold Armbar Kimura Triangle Head-arm N-S choke Choi bar Omoplata Baratoplata Tarikoplata ENTRY GUARD ⇄ PASS
The invariants

The physics — fifty principles

The invariants are the load-bearing principles every technique is an application of. Seventeen are universal — the physics, true in every position, and each shown here with its mechanism and a diagram. Thirty-three are domain principles, grouped by phase. Everything in the curriculum is tagged back to these. Science is the why under every what, never merely asserted.

The 17 universals

INV-01Connection eliminates space and transfers weight

Body-to-body contact at the relevant point (chest-to-chest in pins, chest-to-back on the back, hip-to-hip in leg entanglements) removes the slack a limb or torso needs to move, and rides your weight onto the opponent by gravity rather than muscle. This is what makes control cheap to hold and exhausting to escape. It fails when a practitioner chases grips ahead of connection, or lets the body float during transitions and finishes.

Wspaceweight on your own base Wweight into them
With a gap the top player's weight runs down their own base to the floor; close the gap and it transfers through the contact into the bottom player — no space, and a load to carry.
Neumann, Kinesiology of the Musculoskeletal System
INV-02Inside position controls the outside

Occupying the interior of a joint or limb (underhook, inside knee, inside hook, inside frame) places control nearer the axis of rotation, so the inside dictates what the outside is allowed to do. The advantage is geometric, not muscular, so it scales across body size — a smaller athlete with inside position beats a larger one working outside. It fails when a practitioner accepts outside position and tries to compensate with grip strength.

outside — only the limb moves inside — the whole body turns
A contact on the outside reaches a limb and moves only that limb; a contact on the inside — the centre, under the arm at the hip — turns the whole body, because the centre carries the limbs with it.
Neumann, Kinesiology of the Musculoskeletal System
INV-03Structural resistance must be disrupted before submission

An opponent who keeps aligned, based, connected structure defends through skeletal geometry rather than effort, so their structure must be compromised before a finish is reliable — breaking posture in guard and standing, disrupting the hip and knee line in leg entanglements. Disruption isolates the target joint from its supporting chain so force reaches a diminished structure. The common failure is going straight to the finish against intact structure and blaming strength for the stall.

INV-04Force angle determines leverage, not size

Joint torque is force times the perpendicular distance from the axis to the line of force, so the angle of application — not the applicant's strength — sets the rotational effect. A correct angle turns modest force into a clean finish; a poor angle bleeds force into tissue and demands strength to compensate. It fails when a practitioner adds force to a bad angle instead of reading the resistance as a signal to change the angle.

axisFFd₁d₂
Torque is force times its distance from the axis. The same force does more turning the farther from the joint it acts — the reason control at the end of a limb beats a grip up by the joint.
Hall, Basic Biomechanics · Hamill, Knutzen & Derrick
INV-05Frames redirect perpendicular; fail when opposing directly

A frame (shin, forearm, knee, elbow) placed straight into the path of force becomes a wall that holds only if it is stronger than the force; angled to the force it redirects it laterally for far less strength. This is how a smaller athlete structures against a larger one. The dominant failure is the push-back reflex — straightening the frame into direct opposition as pressure rises, reintroducing the strength contest.

load along itholds load across itcollapses
A frame is a strut. Loaded along its length the skeleton carries it for almost nothing; loaded across its length it bends and only muscle resists — so it collapses. Set a frame so their force runs along the bone and is sent past you.
Nordin & Frankel, Basic Biomechanics of the Musculoskeletal System
INV-06Base is weight distribution over the support point

Base is a structural condition — weight distributed over support points (feet, knees, seat) — not a property of the person, so disrupting or removing a loaded support point destabilises the structure regardless of the mass above it. This is why efficient sweeps and takedowns attack the support point rather than pushing the mass. It fails by engaging the mass instead of the support point, or by disrupting the point but pausing before the structure falls.

basecentre of mass forcepast the edge — it topples
Balance holds while the centre of mass stays over the base. Drive it past the edge and the line of gravity falls outside the base: nothing holds it up. A sweep is that, applied to a person.
Hall, Basic Biomechanics
INV-07Connection is the prerequisite for all control

Control cannot begin until connection exists; distance is not neutral, because a committed attacker at range has revealed a trajectory the defender can still react to — the cost of commitment falls on the attacker until contact closes it. The correct order is close distance, connect, then attack; grips without connection are not control. It fails through premature grips and through treating reconnection after a disruption as a minor detail.

INV-08Positional advantage is the prerequisite for submission

Position → control → submission is the progressive reduction of the opponent's options, not a stylistic convention: position restricts escape, control isolates and unsupports the target, submission applies force to a target whose options are already few. Skipping the order doesn't remove the requirements — it concentrates them at the finish as maximal resistance. The test is the state achieved, not rigid step-order. It fails through the urgent opportunistic submission and through abandoning position while finishing.

PositionIsolateFinish
A finish depends on what comes before it: a position that fixes the axis and connects, then the slack removed and the limb cut off, and only then the finish. Reach for the last step early and it has nothing to act on.
INV-09Joints against natural range reach danger faster

A joint attacked along its natural plane (an armbar hyperextending the elbow) travels through a detectable range before ligaments load, giving warning time to tap; a joint attacked across its range (rotational force on the knee via a heel hook) reaches danger almost immediately with little warning. This is why heel hooks, toe holds, and kneebars are treated as elevated risk — a classification the mechanics inform and rulesets formalise. For rotational knee attacks the tap must come at "starting to apply," and the attacker must lower finishing speed accordingly.

range of motionlimitpast here, the joint failsjoint
A joint is strong through its natural range — the muscles guard it. At and past the end of that range the load shifts to ligament, capsule, and bone. A lock drives the joint there; the tap concedes before the tissue does.
Nordin & Frankel, Basic Biomechanics of the Musculoskeletal System
INV-10Space is contested — neither player owns the space they create

Space created between two grapplers belongs to whoever acts on it first, not to whoever made it — a frame that opens distance for your escape opens the same distance for their re-advance. So space must be used in the same motion as its creation; every beat between creating and using it is a beat the opponent can take it. 50/50 is the extreme case. It fails through the two-step "create then exploit" model, and through trusting a defensive frame that only temporarily keeps the opponent away.

INV-11The underhook controls the hip on that side

An underhook connects upper body to torso to hip, so it steers the opponent's hip on the same side and controls the direction their body can move; movement toward the underhook side is fluid while movement away meets resistance. This is why the underhook battle in half guard is effectively the pass-versus-escape decision. It fails when the underhook is shallow (in position but not transmitting force to the hip), or won on one side while the free hip re-angles the body.

INV-12Rotation around a fixed point creates leverage

Every leverage technique pairs a structural anchor that does not move (the elbow on the hip brace, the knee in a heel hook, the posted hand under a sweep) with rotation around it — move the fixed point and the same force produces no pressure, leaving a strength contest. Identifying the fixed point is understanding the technique, and defenders escape by eliminating it (pulling the elbow off the brace, straightening the arm) rather than out-muscling the rotation.

INV-13Destabilisation precedes control

A balanced opponent can generate organised defensive force in any direction, so balance must be removed before control is possible; destabilised, they can only react. This is the key equaliser against strength — a heavier opponent keeps that advantage only while their base is intact. It applies to finishes too (taking the hip off-line before a heel-hook rotation). It fails by attempting control before destabilising, or by achieving only momentary destabilisation and not acting inside the window.

INV-14Limb isolation requires removing it from the defensive system

A gripped limb is still connected through shoulder, lat, trunk, and hip to the whole body's defensive resources; true isolation severs that chain so the submission attacks a disconnected segment, not the full body's resistance. In the armbar that means elbow over the hip, knees on the shoulder, and the arm crossed and extended — all three, not merely gripping the arm. It fails by confusing holding with isolating, and by letting partial isolation degrade as the segment reconnects.

linked — the chain meets the load isolated — the limb alone
Linked to the chain, a limb borrows the whole body's strength to meet a load. Cut off from it, the same limb meets the load alone — one joint, one set of muscles. A submission is the deliberate making of the right-hand picture.
Hamill, Knutzen & Derrick, Biomechanical Basis of Human Movement — shared with INV-15
INV-15Segmenting the body prevents unified defence

The body defends as a coordinated whole, so controlling its sections with separate, independent mechanisms stops them communicating force and reduces resistance to what isolated segments produce alone. The requirement is independence — a single grip on two parts connects them, whereas separate controllers on upper and lower body (seatbelt plus hooks, the crucifix's two-arm split) mean neither segment frees the other. It fails when one control is lost, or is loose enough to transmit force between the segments it should separate.

INV-16Escape mechanics require creating space before moving through it

A pinned player cannot move into space that does not yet exist, so every escape is two ordered stages — create space (bridge, frame, push), then move through it (shrimp, hip escape, re-engage) — and reversing the order fails no matter how fast. Skipping space-creation drives the movement into the opponent's body, which absorbs it and often re-loads a tighter pin. Because space is contested, the window must be closed quickly. It fails through premature movement and through partial space followed by hesitation.

INV-17Structural loading

Structural load is force delivered through a position, body weight, or skeletal path that arrives beyond the reach of the opponent's muscles — body weight at a joint's end-range, where the muscles are already maxed and have no counter. This is distinct from a strength advantage: once load is placed through the skeletal path, equalising the muscle equation doesn't equalise the outcome. It shows up wherever weight beats leverage, and in deep grips (seatbelt depth, not strength). It fails by loading in the plane the muscles are built for, or achieving the position without committing weight through it.

muscle answers strength irrelevant
A muscle can resist a load it is positioned to meet. Deliver the load straight down the aligned skeleton — or at end-range where the muscle is already maxed — and it arrives where no muscle can answer. Then position, not force, decides it.
Nordin & Frankel, Basic Biomechanics of the Musculoskeletal System

The 33 domain invariants

Grouped by phase. These are applications of the universals to a specific part of the game; the curriculum tags to both.

Standing / takedowns
INV-ST01Destabilising requires controlling the secondary leg

A displaced opponent doesn't fall — they rebalance by stepping with the secondary leg (the one not bearing load). A takedown that ignores that leg (rather than trapping, loading, or angling it out of its recovery step) produces a scramble, not a finish, because their fastest recovery tool is left free.

INV-ST02Hip access is the functional goal of all single-leg attacks

The leg is only the entry; the hip is the target, because reaching the hip line puts you on the opponent's centre of mass and removes their sprawl. Leg control without hip access is a limb they defend around by sprawling and circling — the sprawl works precisely by keeping your head below hip height.

INV-ST03Hands to the mat = advantage; hips to the mat = takedown

A destabilised opponent passes through a hands-down stage (recoverable, advantageous but not the finish) before a hips-down stage (the completed takedown). The two need different follow-ups — hands requires continued pressure and a conversion; hips requires immediate pinning. Treating a hands position as finished lets them recover.

INV-ST04Level change is the prerequisite for penetration

Penetration works by getting the hips below the opponent's centre of mass so you drive up through the base; without level change the shot is a horizontal lunge that leaves the head exposed at hip height, exactly where the sprawl lands. The level change must be continuous with the entry, not a telegraphed squat.

INV-ST05Kuzushi is sustained loading of the leg you intend to remove

Kuzushi is a held condition, not a moment: the target leg must stay loaded long enough for the reap/sweep/trip to land, or the opponent rebalances in the gap. Sustained loading is what pairs with INV-ST01 — it fixes the leg to be removed while the secondary leg is occupied.

INV-ST06Bent-over posture is functionally equivalent to mid-throw

Spine angle sets hip mobility; once the spine tips past roughly 60° forward the hips can no longer change level, rotate, or recover base — the exchange is effectively already lost. This is why competent standing offence treats posture-breaking (collar tie, snap-down, front headlock) as the entry, not the finish, and why head height is a false proxy for posture.

Guard — bottom
INV-G01The foot line determines whether the guard engages

The bottom player's feet, held between or at the line of the passer's knees, are the guard's outermost barrier — they force the passer to address the guard rather than walk through it. The line is spatial, not grip-dependent; when the feet retract, drop, or drift outside the knees, the passer advances freely.

INV-G02The guard must face the passer

Guard is information-dependent: the bottom player's head and hands must orient at the passer to read and frame against passes, and orientation interposes the frames between the bodies. Turning away presents the back — a surface with no framing ability — which is why leg-drag and back-take passes are completed by the bottom player's own rotation away from pressure.

INV-G03Elbow connections control the passer's weight

The passer's weight distributes through the arms; connections at the inside or outside of the elbows redirect it and deny stable passing positions, with the elbow the optimal fulcrum. At least one connection is a partially intact guard; losing both simultaneously is the functional definition of being passed.

INV-G04Hand posts create offensive opportunities

Forcing the top player to post a hand to the mat commits their passing capacity to base and flips the dynamic from defensive to offensive guard; a posted hand is also an isolated limb open to kimura, omoplata, or wrist attack. The destabilisation must come first — attacking a stable, both-hands-free top player skips the step that creates the post.

INV-G05Hip mobility is the guard's engine

Every guard action — sweeps, recovery, submissions, foot-line placement, distance — originates in hip movement, so a flattened bottom player has the whole system switched off even before the guard is technically passed. Hip freedom doubles as a real-time gauge of guard health; the counter to compression is preserving hip angle early, not recovering it after flattening.

Passing
INV-P01Clear the feet before advancing

The feet are the guard's first line of resistance; the passer must neutralise them (redirect, pin, or angle past) before advancing, or they pass through the frames and hooks rather than around them. Clearance must be complete first — a partial clearance followed by a committed advance is worse than none, because weight is now committed into a re-engaging guard.

INV-P02Advance to and hold the knee line

Passing is two stages: after clearing the feet, hold the knee line — the zone of knee shields, frames, and half-guard hooks — before advancing to the hips. Treating the knee line as a corridor to rush rather than a checkpoint lets the bottom player re-insert a knee shield mid-advance and stall or reverse the pass.

INV-P03The pass is complete when connections are broken

A pass is defined by the state of the bottom player's connections, not the passer's geography: reaching side control while they retain an underhook or hip connection is not a pass. Completion is bilateral — connections broken and the bottom player pinned at once — and connection-breaking must be fast enough that one cannot be re-established before the next is addressed.

INV-P04Passing and pinning are the same task

Most passes fail after arrival, in the pause where the passer relaxes to switch from "passing" to "pinning" — that gap is the recovery window. The passing drive must flow seamlessly into pinning weight with no drop in pressure or grip; against fast recovery the size of that gap is the whole contest.

Pinning
INV-PIN01Underhooks with chest contact cover the hips

Chest-to-chest with underhooks controls torso and hip at once: the underhooks pull the shoulder girdle to the mat, and the shoulder-to-hip chain denies the hip movement that starts every escape. The control is multiplicative — chest without underhooks leaves framing arms; underhooks without chest leaves bridging space; shallow underhooks break the chain even when contact looks solid.

INV-PIN02Chest contact without hip coverage fails

Chest contact is necessary but insufficient; the hip is the hinge of the escape system, so an uncovered hip lets the bottom player turn in, insert a knee, or stand up without moving your chest. Coverage comes from diagonal weight (near shoulder to far hip), not vertical weight that merely feels heavy — and the sequence is hip-first, chest-second.

INV-PIN03Flattening to the back removes frame capacity

Defensive capacity sits on a gradient: a bottom player on their side keeps both framing arms, the diagonal bridge, and knee insertion, whereas flat-on-back loses hip elevation and one arm's leverage. Flattening is therefore a continuous top-position goal and the rationale for the whole turtle breakdown — remove base point by point until flat, then attack. This is why face-down is the true objective of back control.

INV-PIN04Double underhooks are the highest control state in a pin

Double underhooks in loaded chest contact remove both framing arms at once, leaving only an unassisted hip bridge — a self-securing position that costs the top player the least effort and offers submissions the least resistance. Every single-underhook position is a stepping stone toward it; double underhooks without chest loading is nominal, not functional, because the hip is uncovered.

Scrambles
INV-SC01Greater hip height holds the structural advantage

In minimally-connected exchanges the player with greater relative hip/centre-of-mass height has gravity as a free resource while the lower player works upward against it. Height is comparative and momentary — it must be used immediately (which is why the wrestle-up is high-value); achieving height and pausing lets the opponent close the differential.

INV-SC02The opponent's downward pressure creates offensive entries

When the bottom player threatens height, the opponent's correct response — downward pressure — commits their weight and creates the entry: forward weight opens sweeps, downward weight opens leg entries. The scramble game is dilemma-based, not sequence-based: the height threat is a trigger to read their commitment, not a goal to complete blindly.

INV-SC03First connection dictates the scramble direction

Scrambles are structured by connection priority: the first meaningful contact sets the direction and makes its establisher the actor, not the reactor. The connection must be to a force-transmitting point (hip, leg, back, elbow) — connecting first to a low-value wrist or sleeve does not win directional initiative, and initiative still needs the fluency to convert it.

INV-SC04Re-connecting on your own terms holds the scramble initiative

Disconnection is a resource: whoever chooses when and where contact resumes is functionally making first connection in the new exchange. A deliberate disconnection with a predetermined, superior reconnection point (the guard pull is the clearest case) keeps initiative; an uncontrolled disconnection cedes the terms to the opponent.

Leg entanglements
INV-LE01Inside space control determines the entanglement

Every entanglement turns on the contested space between the attacker's hip and the defender's hip; when the attacker's hip occupies it, the defender's leg physically cannot extract. Inside space is geometric, not grip-based (the leg expression of inside-position-controls-outside) — the most common failure is the hip retreating out of the space while reaching for the heel, freeing the leg despite an intact grip.

INV-LE02Heel exposure is determined by position, not grip

Which heel is exposed follows from leg configuration, which follows from position — the grip is the last step, not the chooser. A practitioner cannot pick a heel independent of the position held, and a defender hides a heel only by changing configuration, never by gripping their own foot.

INV-LE03Connection throughout prevents escape

The leg-entanglement application of "connection eliminates space": extraction is almost never strength, but a moment of lost connection — usually the hip floating out during the heel-grip reach. The correct sequence is hip first, body contact second, grip third; transitions between entanglements are the second major leak point.

INV-LE04The foot is the handle; the knee is the target

A heel hook is a knee attack: force travels heel → ankle → tibia → knee, and the knee (held immobile by the entanglement) is where the ligaments load. Cranking the foot without whole-body rotation produces a resistible ankle crank; inconsistent force that suddenly reaches the knee is the dangerous failure — controlled body mechanics are both more effective and safer.

INV-LE05The hip controls the line of the leg

The hip is the structural root of the leg, so the real contest is the hip, not the foot: the chain runs hip → leg line → heel exposure → available submission. Attackers who build from the heel backward work against this order; defenders who fight the heel grip instead of repositioning the hip defend from the wrong end of the chain.

Submissions
INV-S01Strangles require compression on both sides of the neck at once

A strangle interrupts blood flow, which requires simultaneous bilateral carotid compression; one-sided pressure only produces resistible discomfort or a windpipe choke. The two pressure points need not share a source (forearm + bicep, thigh + the opponent's own shoulder), and the fix for an "almost there" choke is bilateral firmness via angle and depth, not squeezing harder.

INV-S02The target limb must be isolated before the submission completes

The body defends joints via the core and opposite limb; a limb still connected to that system is fighting total-body strength, not the joint's structural limit. Isolation (crossing the armbar arm past centreline, breaking the kimura clasp, controlling the wrist) is the condition without which the submission cannot finish — forcing before isolation invites reversals.

INV-S03The secondary anchor must be controlled or removed

Every submission has a primary target and a secondary anchor — the base point (posting hand, mat, grip pull, knee rotation) the opponent multiplies resistance from. Attacking the primary alone against an intact anchor manufactures the illusion of a "tough opponent"; removing the anchor drops resistance to the real limit and closes their reversal launch point.

INV-S04Arm-out strangles apply force directly; arm-in must compensate

The pathway from choking surface to carotid is the key variable: with no arm inside, force travels a short direct line; with the opponent's arm inside it must transmit through the arm, lengthening the path. An arm-in strangle is not failed but less efficient — the fix is tighter geometry (higher forearm, closer triangle, precise angle), not more raw force.

INV-S05Joint submissions require loading the joint to its structural limit

A tap is a warning that precedes structural failure; loading speed governs the warning window, and fast application can reach the limit before the opponent can register and tap. This runs both ways: application speed is a genuine competition finishing variable, and the same mechanic makes fast application in training dangerous. A submission held below the limit will not finish a resisting opponent.

Safety — because speed can outrun the tap on joint locks, in training apply progressively and tap early; save explosive application for competition only, if at all.
Standing — the entry
A handful of high-value areas, not a takedown collection. The finish is individualised; the goal is to afford opportunities.

Stance and defensive awareness first, then five areas that all read the same rule — hands to the mat is an advantage, hips to the mat is a takedown (INV-ST03). The arm drag is the road to the back; the snap-down stuffs the head into the front headlock.

Stance & distanceneutral base

The neutral start — staggered feet, bent knees, straight back, hands up — and the management of long / tie-up / clinch range. Its job is to steer the opponent toward one of two destinations (onto their hands, or onto their hips) and to make first contact on your terms.

Sprawlescape · takedown defence

The primary takedown defence: as they shoot, drive the hips down-and-back and throw the legs behind their arms so the level change reaches empty space, chest driving over their upper back. It's defence that becomes offence immediately — a good sprawl lands you in the top front headlock with the opponent face-down, straight into the Front-headlock river.

Arm dragentry → the back

Grip the wrist and tricep (or a Russian-tie 2-on-1) and pull the whole arm across their centreline so the torso must rotate to follow; step behind in the same motion to convert arm control into hip control. A Back-river entry — to the rear body lock, a single-leg, or direct back exposure. Works standing and seated.

Collar tie & snap-downposition → the front headlock

The collar tie (single or double) is the standing control position; the snap-down is the technique from it — a short, explosive downward-and-forward pull that drives posture past the recovery angle. Head stuffed and they post their hands / turtle → the front headlock and its guillotine family. The road to the back is a different door (the arm drag); the snap-down's job is the front.

Body lock (front & rear)control

One grip, worn from front, side, and behind. Front: arms clasped low around the hips, chest-to-chest — but trap one arm or neither, never both: locking both arms in makes the position easier to escape, not harder. Dictate the finish (trip the far leg, lift-and-dump, or break to four-point). Rear: the standing equivalent of having the back — locked at the navel line, chest-to-back, hip-to-hip, chin over the shoulder — feeding the rear breakdown chain to back exposure and the strangle.

Single legentry · takedown

Level-change below the centre of mass, penetrate to the outside of the near leg, and drive the shoulder into the hip — hip access, not the leg grip, is the requirement, because a shoulder on the hip makes the sprawl impossible. Finishes (run-the-pipe, cut-the-corner, single-to-double) all address the secondary leg. Also the universal recovery when other shots stall.

Other takedownsentry · finish individualised

Beyond the single leg: the double leg (level change, penetrate, drive through both legs), the uchi-mata (a hip-and-leg throw off the collar tie or an underhook), the ankle pick (off a reaching post or a collar tie), and the knee tap (a reactive trip off forward pressure). Which one a player finishes is individualised — the goal is to afford the shot from the five areas, not to drill a fixed list.

Russian tie (2-on-1)clinch control · platform

Two hands on one of the opponent's arms — near hand on the wrist, far hand above the elbow to keep it straight — two control points against zero defence on that side. A platform, not a move: the isolated arm is the handle the arm drag (to the back), snap-down (to front headlock), single leg, double leg, and ankle pick all run from, chosen by the reaction. Learn the grip and the pull-toward-your-hip angle, then the arm-drag as the first exit — grip and movement are one action, never a static hold.

Inside triptakedown · from the clinch

A clinch takedown that hooks your near leg inside the opponent's stance against the back of their near leg, then trips it out while the upper body drives the same way. No level change or shot needed: the leg removes the base while the clinch drive tips their weight over that disappearing leg — both at once, or they re-plant. Run it from the over-under as a single "fall together," timed to their weight transfer, and follow to side control or top half. (Judo's ko-uchi-gari.)

Outside triptakedown · from the clinch

The mirror of the inside trip — the near leg steps to the outside of their near foot, hooks behind the calf, and reaps it inward while the upper body drives out and back, rotating them over their own leg. It needs an outside angle first (over-under, body lock, or a wide defensive stance) and low contact at the ankle/calf, not a high push at the knee. Learn it paired with the inside trip so the two are a dilemma; its powerful version is judo's o-soto-gari.

Guard pullentry to the ground

A deliberate choice to start on the bottom — not a failed takedown — holding a grip and dropping into a chosen guard while pulling the opponent down with you. Decide the destination first: seated guard is the modern no-gi default (immediate sweeps, wrestle-up, leg-entanglement access), with butterfly, half, or SLX as alternatives. It only works with a maintained connection through the descent and against a ground game you can beat — a gripless or destination-less pull just gives away top. Pull to seated, timed to their weight coming forward, and train the pull and the first attack as one.

Guard — bottom
Retain, sweep, and enter the legs. Seated-vs-standing is the master decision; shin-to-shin is the gate to the Leg river.

The guards are chosen to punish a passer who kneels or drops their hands to the mat, the scramble tools (arm drag, snap-down) are the same as standing, and retention is a skill in its own right. The job on the bottom is never to be comfortable — it's to make the top player pay for their posture.

Seated guardretention · hub

The default open-guard platform: sit upright, feet active at or inside the knee line, head and hands forward. No submissions of its own — its value is as a mobile hub that reaches butterfly, single-leg-X, shin-on-shin, and DLR in a movement or two. Arm drags and snap-downs punish a passer who reaches or leans in.

Shoulder crunchguard · entry

A permanent fixture of the modern no-gi meta, so it's fundamental, not fringe: the bottom player crunches the passer's posture down over one shoulder, a compact frame-and-control that stalls the pass and opens back-takes, leg entries, and the crab-ride / truck. Reached from seated guard and the shin-to-shin exchange.

Closed guardguard · offensive control

Not a place to hide — an offensive control platform. Ankles locked behind the opponent's back, the bottom player owns the posture: break it down, climb the shoulders, and attack. The modern no-gi version is aggressive — off broken posture it threatens the guillotine, the kimura and arm-drag to the back, the hip-bump and flower / pendulum sweeps, and the omoplata / triangle / armbar off any posted or over-committed arm. Posture is the whole game: head down, you attack; head up, you sweep or climb. A passive closed guard that only holds is a stall, not a safe place.

Butterfly guardsweep · hub

Both hooks inside the thighs and an underhook on one side, played upright to punish a passer who kneels or drops weight forward. The hooks lift, not push: hook up under the thigh while the underhook rotates the shoulder, forcing a hand-post — and the post is the sweep. The underhook decides direction; when it's lost, arm-drag to the back. The central no-gi sweep hub and an entry to X-guard / SLX.

Half guard (bottom)retention · sweep

One of the passer's legs trapped between the thighs — one side already conceded, so every connection carries reduced margin. Decided by the underhook battle on the trapped-leg side: win it and you control the near hip, which gates the underhook sweep, back take, and wrestle-up. First priority is always getting off flat and onto your side to keep hip mobility.

Z-guard / knee shieldretention · frame

A half-guard variant with the trapped-side knee elevated and the shin angled across the passer's hip or chest — a diagonal frame that prevents flattening and buys distance. The frame must deflect (elevated, angled), never oppose as a straight-leg wall. A moment to move from, not a position to hold: with the underhook won it exits to a back take, butterfly, or wrestle-up.

Guard retention & re-guardingretention

Not a position but the framework for keeping and recovering guard. Guards pass in three stages (clear the feet → advance the knee line → break all connections), and retention intervenes as early as possible because early is cheapest: keep the feet on the line, stay square and re-face, preserve at least one connection (one is recoverable, zero is not), and drive everything from hip mobility. The instinct to fight is retreating — the correct direction is toward the passer or their legs.

Shin-on-shinentry · the Leg-river gate

The guard↔leg gateway: cross one shin over the inside face of the passer's lead shin, between seated guard and a committed entanglement. A two-point system (shin contact + a hand frame) that claims the first connection and inside space, and reads how the passer is weighting the lead leg. A decision point — forward pressure opens single-leg-X, a lateral step opens the direct ashi entry. The primary way into SLX and outside ashi.

De la Riva (DLR)entry · disruption

A gi guard kept for no-gi utility only: the outside leg wraps the passer's lead leg with a same-side shin grip. Without a collar it doesn't hold, so it's a disruption tool and entry platform, not a sustained control — hook plus grip bias the lead-leg hip enough to start. No-gi payoffs: the tripod sweep against a standing passer and inversion into ashi. Best entered from shin-on-shin, timed to the passer's step.

Reverse De la Riva (RDLR)entry · disruption

The mirror of DLR — the outside leg threads to the inside of the lead leg, blocking inside advances (knee cut, inside step). A transitional junction, not a hold, needing a shin/ankle grip as the second anchor. Its defining no-gi use is the K-guard entry; it also gives the reverse tripod sweep and re-threads back to DLR.

Note — the K-guard route from RDLR leads to inside-position leg attacks (cross-ashi / inside heel hook), which sit behind the individuation gate: the deferral belongs on that destination, not on the RDLR entry itself.
Turtleescape · recovery

A defensive position on all fours (head tucked, hips low, arms tucked) that shields the neck and arms — but transient, safe for a second or two before the top player consolidates the back or front headlock. Escape is active: work a priority hierarchy on arrival — stand up first, then re-shoot a single, then granby to guard, then situational rolls that turn their grip into a reversal. Never travel toward flat. Once the seatbelt with hooks locks, the back-defence system takes over.

Wrestle-up / technical stand-upget-up · escape-into-attack

The proactive return to a standing base from the bottom — standing up with protection, not just rising. Four steps: post the near foot, drive the hips backward into the top player (the destabilisation), fight the inside arm for an underhook or wrist on the way up, and arrive standing with inside position. Rising vertically or leaving the head exposed hands them the back or a front headlock; the hip drive and inside-arm fight are a race to connect first. It's escape-into-attack — the underhook on arrival opens an immediate single leg or back take, with seated guard as the planned fallback if it stalls.

Passing — top
Passing is pinning — the same task. A pass is done only when their connections break AND they're pinned.

Seated-vs-standing is the first decision (shared with guard), then three families — inside (through the guard), outside (around it), connected (locked to the body) — plus the connective drags. All of it feeds the Isolation river (pass → pin → isolate) and the Back river (the staircase up).

Inside passing — through the guard
Stack passinside

Stand in closed guard and drive the hips up over their shoulders, folding them in — the legs travel above the head and every hook, frame, and submission angle dies at once. A window, not a destination: circle to side control and load the chest before they unfold.

Knee cutinside · the universal pass

The knee slides across the inner thigh — the exact path a foot would hook — arriving first and cutting to side control, driven by the back-leg post; the far shoulder drops in the same beat to kill the near frame. The most universal no-gi pass; the chest pin sets before the knee stops.

Headquarters (HQ)inside · hub

The kneeling hub — knees split the feet outside the knee line without grips. A reading position: apply pressure and take the exit the reaction opens (fold to side control, sit-back to ashi, body lock, knee cut). Every exit fuses advance and pin; sitting and waiting is not passing.

Smash passinside · pressure

A pressure pass that goes through the knee shield, not around it — shoulder (not hands) under the knee, stack the legs flat. Near-arm control first, or they take the underhook and it's a scramble. Arrives in side control with the chest already loaded — pass and pin are one downward drive.

Outside passing — around the guard
Toreandooutside · standing

The primary standing pass: grip both shins mid-calf, palms down, and redirect the legs offline like a matador — push then step, one motion. Clearing the feet is only the first connection broken; close to the head, kill the frames, drop to the pin, all continuous. Speed beats the hip escape.

Tripod passoutside · standing

A standing pass on a three-point base — standing leg, shin grip, and one foot posted on the hip bone. A simultaneous push-pull folds the frame (the foot pushes the hip one way, the grip pulls the shin the other); step around the collapsed legs to side control. The toreando's complement — tripod when the legs extend toward you.

Leg weaveoutside · arm-thread control

Thread one arm between the legs from outside to inside and grip the near hip, turning the near leg from a retention tool into a captured limb — inside control applied from the top, blocking the hip escape. Step the far leg around to side control, the arm holding the leg until chest pressure secures the pin. The answer to knee-shield / Z-guard.

Connected passing — locked to the body
Body-lock passconnected

Level-drop and wrap both legs together above the knees with a Gable grip — locked as one unit they can't spread or steer, so the lock itself clears the feet. Chest drives continuously to the chosen side; a movement tool, not a hold. The mechanical parent of the over-under pass, and the same body lock you use standing.

Leg ride (folkstyle)connected · to the back

A folkstyle ride, not a pin — thread the inside leg over the near thigh, heel-hook the calf, chest down, pinning one hip to keep them belly-down and deny base. Its job is to deliver the back; the calf-slicer is only a backup. The value is in transitioning, not holding.

Framework & connective
Seated-guard engagementthe seated-vs-standing decision

The first beat against a seated guard: not yet a pass but the action that turns a live seated guard into a passable one — pre-emptive foot-clearing through inside wrist control and hook denial. Clear their hands and a seated player with no posts is about to lie down; the flatten drive (near shoulder to sternum) tips them supine.

Leg dragdrag to angle · back threat

Control a leg at the knee (never the ankle — an ankle gives them a pivot) and drag it across the centreline onto your hip, building hip-to-hip control at an angle. Step around the free leg and drop the far hip. An angular pass, not a pressure pass; at higher levels the same entry becomes a back-take threat.

Rau dragthe arm-drag applied to passing

The arm-drag repurposed as the answer to the knee shield. A frame is beaten by removing it: catch the framing arm and drag it across the line it's already framing, turning them onto their side and exposing the back → seatbelt, or a kimura trap on the dragged arm if the back is defended. Wins the inside line the shield existed to deny.

① The Back River
Every road to the back ends the same way — face-down, then the strangle.

The most decisive river in the game: the back is the one position where you attack a defender who cannot see you and cannot easily use their arms to fight. Its true objective is not "on the back" but face-down — if your own back is on the mat, you are the one being pinned. Everything here converges on the seatbelt and the blood choke.

The invariants this river trains
INV-11The underhook controls the hip

An underhook doesn't just grip an arm — it owns the hip on that side, and whoever owns the hips owns where the body can go. Depth decides everything: a shallow underhook suggests control, a deep one (elbow past the torso's midline) delivers it. The seatbelt is a double-underhook expression, which is exactly why back control steers the whole torso.

Why it matters here → it is what makes the arm drag and the seatbelt control, not just touch.
INV-S01A strangle needs both sides of the neck at once

A true strangle is a blood choke, not an air choke: the two carotid arteries feed the brain, and both must close simultaneously. One side is discomfort a tough opponent can gut through; both sides interrupt blood flow in seconds. Every finish in this river is a way to achieve bilateral compression — and the fix for a choke that won't finish is symmetry, never more force.

both carotids — blood choke one side — discomfort only
Top-down through the neck: windpipe front, a carotid each side, spine behind. Close both carotids at once (left) and blood to the brain is interrupted — fast, low on pain. Close one side (right) and the other keeps flowing: discomfort, not a choke.
Guyton & Hall, Textbook of Medical Physiology — cerebral blood flow. Mechanism, not a stopwatch: a blood choke arrives with little warning, so tap early and release on the tap, always.
INV-S03Control the secondary anchor

Every strangle has a primary target — the neck — and an anchor the defender hides behind, usually a hand fighting in or the chin tucked down. Control or strip the anchor and the closure lands; attack the neck while the anchor is free and you stall. The hand-fight is the finish.

Why it matters here → the whole back battle is a fight over the chin and the hands.
INV-PIN03Flattening removes frame capacity

A frame only works with a bend to push through; flatten the opponent and you take away the angles their frames need. Face-down back control is this principle applied to the back — prone, they have no frame to turn back into you.

Why it matters here → it is the mechanical reason "face-down" beats "seated behind."
INV-ST03Hands to the mat = advantage; hips to the mat = takedown

The standing read that feeds this river. Drive the opponent's hands down and you've earned a way behind; drive their hips down and you've scored the takedown. The arm drag and the snap-down are how you cash that read into back exposure.

Why it matters here → it connects the standing game to the back without a separate "takedown" system.
Downstream — offence (entry → control → finish)
Arm dragentry

Yank the opponent's arm across their centreline and the body must follow, exposing the back. The same drive lands your underhook — converting arm control into hip control — so step behind before they can turn. Works standing and from seated guard, which is why it's a through-line, not one move.

Seatbeltcontrol

The over-under grip that is back control: strangle hand over the shoulder, control hand under the armpit, hooks inside the thighs, hip wedged between the hip bones (not on top). The strangle-hand / control-hand distinction is the whole game — confuse them and every finish breaks. Depth of the strangle hand (elbow to the ear) beats grip strength, because it places the load past what the defender's arm can peel.

Face-down (belly-down) backcontrol · the true objective

When they roll to escape, don't chase back to seated — ride them face-down. This is the objective of back control, not a detour: flattened to the mat they have no frame to turn back into you (INV-PIN03), the chest-to-back connection is total, and the strangle is more available than from seated, not less. Keep the seatbelt and your hooks through the roll and finish from on top of them.

Rear naked chokefinish · primary

The blood choke: forearm across one carotid, bicep against the other, second hand gripping your own bicep (not the wrist) so the squeeze closes both sides at once. Beat the chin with knuckle pressure on the jaw — never retreat the arm — and confirm the elbow is past the throat's midline before you squeeze. It's a depth problem, not a strength problem.

Safety — seconds to unconsciousness, with little warning. Tap early; release instantly on the tap.
Garrote (short choke) & rear trianglefinish · when the RNC is denied

When the hands fight high and the choking arm can't find full depth, the strangle moves to the legs (rear triangle) or shortens its lever (garrote). Same principle — bilateral carotid compression — reached by a different geometry.

Armbar (from the back)finish · when the neck is defended

The hands that fight high to defend the strangle expose the very arm they're defending with — isolate it and attack the elbow. Trap the arm, bring a leg over the head, and extend against the joint: the elbow is the axis, the wrist the far end, your hips the force. It pairs with the choke as a dilemma — defend the neck and the arm is there, protect the arm and the neck opens. Isolation and position come first; the finish is leverage, not strength.

Safety — once the arm is isolated the elbow hyperextends fast; control the speed of the extension and release on the tap.
Upstream — escape (survive → space → back to a river-mouth)
Chin tuck + the staged seatbelt escapeescape · primary

The escape is a race against the strangle, run with the chin glued down the whole time — the chin denies the carotid (INV-S01), so every step you buy depends on it. Priority order: don't get seated at all; if the seatbelt is on without hooks, hip-turn out; if hooks are in, run the three-step — strip the bottom hook, hip to the mat, rotate to face. Skipping the hook-strip is the classic failure.

Two-on-one hand-fightescape · buys time

Trap the strangle wrist with both hands to buy the seconds the rotation needs — but it costs you both hands, so it's a timer, not a solution. Fight the hand to escape, not instead of escaping.

Truck (crab ride) → the backcrossover · from the legs

The truck bridges the Leg river and the back: from the crab-ride you take the back (or attack the twister). Catalogued in full under the Leg river (deferred) — noted here because the back is one of its two destinations.

Lands at → a finished back escape isn't "safe" — it's back on top in the pin staircase, or into guard. Upstream deposits you at another river's mouth. That is escape-into-attack.
② The Front-headlock river
Snap-down or sprawl → the front headlock → the guillotine family. The other side of the snap-down branch.

The other side of the snap-down branch. A stuffed head — off a snap-down or a sprawl — gives the front headlock, a real control position, not just a finishing spot. From it you finish (the guillotine family), take the back (go-behind), or break the opponent down through four-point into face-down back control. The read that picks the finish is what they do with the near arm: post it inside → the arm-in family (D'Arce, anaconda, arm-in guillotine); keep it out → the guillotine and ninja; tuck the chin → the high-elbow to the side of the neck.

The position & its exits
The front headlockcontrol · the hub

Head-and-arm control (chin-strap) over a bent-over, turtled, or downed opponent, reached from a stuffed snap-down or a sprawl. It works by driving chest weight into the back of the neck — control the head and the body must follow; the grip alone is only a hold until pressure loads it. A hub, not a destination: it leads to the guillotine family and the arm-in chokes as finishes, the go-behind / back-take (the highest-value exit), or the breakdown to four-point on the way to the back.

Four-point / turtle-topcontrol · transition to the back

Top control of a turtled or four-point opponent, attacked from the side or side-rear rather than flat, with near-hip and near-arm contact. The engine is destabilise-then-break-down: a spiral breakdown reduces the turtle's contact points, the wrist ride strips a posted hand, a hip pull rotates them down. The hierarchy is back-take first, then crucifix, then flatten, then submission — never abandon the back-take to rush a lower-value finish.

Go-behindtransition → the back

The front-to-back transition (slide-by): from the front headlock or a front/side position, step or spin past the near leg and wrap the waist to emerge at chest-to-back rear control. It destabilises by changing your facing rather than their posture — emerging at the back invalidates a front-calibrated defence. The highest-value exit from the front headlock: take the back rather than finish from the front.

Crossover → breaking a turtled opponent down from four-point flattens them into face-down back control and the strangle — this is where the Front-headlock river and the Back river meet.
The finishes — the guillotine family
Guillotine (arm-out)finish · primary

The choking arm seats deep under the chin (forearm at the throat, not the jaw) with a cupped-fist grip, and finishes by driving the elbow up while the fist drives down — a scissor that loads both carotids, not the airway. Falling to closed guard, hips forward, is the most reliable finish.

Safety — vascular choke; seconds to unconsciousness once bilateral compression closes. Tap before it locks; release on the tap.
Ninja chokefinish

An arm-out carotid choke finished with an RNC-style figure-four — one hand hooks under the chin, the other grips that arm's bicep behind the head so the bicep closes the far carotid directly. Finished with a pull-and-squeeze (elbows together, head to chest). Primary context is a single-leg counter.

Safety — a closed figure-four is very hard to strip and works in 4–8s; both partners must recognise the lock and tap early.
Arm-in guillotinefinish

A guillotine with the near arm trapped inside the choke, filling the near-side space so it compresses tighter and faster than arm-out. The trapped arm must be squeezed tight against your own ribs so the finish stays vascular, and the high-elbow vertical drive is kept — a forward-and-down pull turns it into a crank. The conversion when they post the near arm inside a standard attempt.

Safety — elevated: compounds fast vascular compression with lateral neck loading; loose mechanics make it a crank. Tap on the compression; drill only after a clean arm-out guillotine.
High-elbow guillotinefinish · beats the chin

Defined by the choking elbow pointing straight up alongside the head, cutting the forearm blade diagonally into the carotid triangle on the side of the neck — the target a tucked chin doesn't protect. Finished from seated guard. Demands precise placement: an elbow angled out or a forearm on the jaw becomes a crank.

Safety — elevated: faster than a standard guillotine and a cervical crank if the elbow isn't vertical. Verify placement; drill light with a clear tap point.
D'Arcefinish · arm-in

An arm-in triangle from the front headlock, available when they post the near arm inside: the choking arm threads under that arm and over the neck, so their own shoulder forms one wall and your bicep the other — bilateral compression using their arm against them. Thread deep and clear behind the neck before squeezing; finish with a bike-lock grip and a forward roll over the head. Reciprocal with the back take.

Safety — vascular; tap once the squeeze bites, release on the tap.
Anacondafinish · arm-in

The reverse-threaded partner to the D'Arce, from the same "near arm inside" read: thread under the near arm and under the near side of the neck to lock on the far side. Static compression is weak, so the finish is a forward roll over the opponent — the roll strips their base and tightens the grip in one motion. D'Arce and anaconda form a defensive dilemma.

Safety — tightens rapidly through the roll; tap as it tightens, not after it completes.
③ The Leg river
Shin-to-shin → single-leg-X → outside ashi ASAP → the footlock / heel-hook dilemma. The foot is the handle; the knee is the target.

The fundamental spine is an outside-position game, learned in order. Inside-position attacks (50-50, cross-ashi, inside sankaku) sit behind the individuation gate — reserved until the outside game is solid, and shown below only as the next branch. This is the highest-risk area in grappling: tap to rotation, not pain.

Fundamental — outside-position first
Shin-on-shinchain · rung 1

Rung 1 of the entanglement chain — the shin crosses the inside of the opponent's lead shin, the most direct stepping-stone in. Read the response: a forward press elevates to single-leg-X, a lateral step opens the direct ashi entry. A decision point, never a hold. (Also the guard↔leg gate — see Guard.)

Safety — positional here, but it feeds SLX/ashi where heel hooks live; know the downstream risk before drilling transitions at speed.
Single-leg-X (SLX)chain · rung 2

Rung 2 — the leg elevated and isolated (inside foot at the hip, outside leg across the shin, hip driven into the inside space). The hip drive is the mechanic; without it the leg is hooked but not lifted and they posture free. The outside heel is immediately exposed; steer toward outside ashi.

Safety — heel hooks are immediately accessible and load the knee with little warning. Hide the heel the instant the leg is up; tap to rotation. Learn the escape before drilling it offensively.
Outside ashi garamichain · rung 3 · "upgrade ASAP"

The "upgrade ASAP" target — the body sits to the far side of the leg, wrapping from outside, exposing the outside heel with no defensive leg between grip and heel, and opening the kneebar alongside. Held by the leg-triangle squeeze on the thigh plus chest contact. The belly-down escape (turn toward the entangled leg) is the dominant counter — drill it equally.

Safety — the outside heel hook loads the medial knee with very little rotation once the heel is gripped. Never bridge (it rotates the knee into the finish). Tap to rotation before pain.
Straight ankle lockfinish · dilemma horn 1

The correct first leg lock: compress the Achilles and load the ankle by driving the hip toward the heel with the foot dorsiflexed. The submission is the hip extension, not the arm squeeze — the angle is everything. Legal everywhere, so it's where hip-angle mechanics are learned; if the ankle lock isn't clean, the heel hooks won't be either.

Safety — force builds fast on a sharp angle; the defender plantarflexes and taps early as pressure escalates.
Outside heel hookfinish · dilemma horn 2

The primary finish from ashi and outside ashi — external rotation loading the medial knee (MCL, posterior capsule), the heel pulled down-and-away. The foot is the handle, the knee is the target: resistance should be felt at the knee, not movement at the foot. Learn it only after the ankle lock is clean; the hip-angle sensitivity transfers directly.

Safety — highest-risk submission in grappling: damage within a few degrees of rotation with essentially no pain warning. Requires established mat culture and experienced partners. Hide the heel; address the grip before torsion. Tap to rotation, not pain.
Aoki lockfinish · the trilemma's third horn

A medial-knee attack from a reverse-ashi configuration — the heel trapped under the armpit as the control point, then rotation/compression on the inside of the knee. It turns the footlock-vs-heel-hook dilemma into a trilemma (heel hook / toe hold / Aoki), where defending one opens another. Proficient-level; a partial configuration loads the ankle, not the knee.

Safety — reaches structural threshold faster than expected given its low recognition. Recognise the reverse configuration early; the medial knee gives limited warning — tap before pain.
⚠ Deferred / advanced — inside position (behind the individuation gate)

The next branch after the outside game is fully developed — not fundamentals. Shown for completeness; every position here carries the shortest tap windows in grappling.

50/50deferred · symmetric

The symmetric entanglement — both players mirror each other and both have heel access, so the position alone gives no advantage; the game is the inside-space and heel-management micro-battle, and the higher hip breaks the tie. It arises whether or not you intend it, so both offence and defence must be developed — you can be submitted while believing you're attacking.

Safety — both heel hooks live for both players. The gravest error is rolling in the direction of rotation — identify which way the heel turns before any movement. Tap to rotation.
Backside 50/50deferred · position

The asymmetric variant of 50/50 — one player rotates to face the opponent's back while keeping the entanglement, winning a directional slice of inside space and a positional "underhook" on the near hip the symmetric player can't match. That back-facing angle exposes the heel by geometry and cuts the other player's escape resources. Its primary finish is actually the outside heel hook (the inside heel only via a leg-config change), and it carries a back-take threat — but it lives in the same advanced, gated branch.

Safety — an elevated leg-lock position; the heel hook damages the knee within a few degrees once gripped. Hide the heel, never bridge into the rotation, tap early.
K-guarddeferred · entry to the inside game

A bottom guard whose stacked "K" leg configuration is built to expose the inside heel — the opposite of ashi/SLX. An outside-position entry (primarily from reverse de la Riva, also shin-on-shin) that yields the inside-position game via transition: its real job is the gateway to cross-ashi and the inside heel hook, so the deferral attaches to that destination, not the entry. Also a transitional hub — flows to outside ashi, 50/50, or back exposure when defended.

Safety — designed to produce an inside heel hook that loads the ACL fast; don't drill offensively before the inside-heel-hook defence, and tap before the knee loads once a heel grip and rotation begin.
Cross-ashi (saddle / honey hole)deferred · the inside heel hook

The inside-position entanglement — both of the attacker's legs cross to one side of the leg, giving bilateral hip control and exposing the inside heel with no leg barrier. The hardest entanglement to escape (it removes the secondary leg), and the inside heel hook from here has the shortest injury-to-tap timeline of any submission in grappling. Triangling the legs upgrades it to inside sankaku.

Safety — shortest tap window in grappling; rotation reaches damage within a few degrees, no pain signal at the point of contact. Begin the escape the moment it's identified, never when the finish is felt. Never bridge. Tap to rotation.
Inside sankaku (triangled saddle)deferred · sealed control

The triangled upgrade of cross-ashi — the crossed legs close into a figure-four, sealing the hip line bilaterally and removing the small rotations a defender escapes a looser saddle with. The most locked-down inside heel hook control in grappling; presupposes fluency in the saddle and its escape first.

Safety — the escape window is shorter still than the saddle. Requires saddle + escape fluency before any finish pressure. If rotation begins, tap before pain.
Inside heel hookdeferred · finish

The finish from cross-ashi (the saddle), where the bilateral leg wrap eliminates the escape tools that work against ashi. It attacks the ACL and medial knee by internal rotation across the body toward your opposite hip — the foot is the handle, body rotation is the force, the knee is the target. The single most dangerous submission in no-gi by both severity and speed: the tap window between rotation and damage is effectively zero.

Safety — the highest-risk submission in the system: damage occurs before pain, and stillness does not mean safe. Tap early to the rotation (a verbal tap is appropriate); the attacker releases on any signal, including stillness. Not for drilling at pace without an experienced heel-hook mat culture.
Woj lockdeferred · finish (variant)

An advanced heel-hook variant from cross-ashi (and inside-access 50/50) where the hooking elbow drives compressed toward your centreline and the finish comes from a shoulder drop plus hip extension rather than pure arm rotation. The changed angle reaches the knee from a direction the standard inside heel hook doesn't, so a defender safe against the conventional grip may have no answer to this one. Same injury mechanism, a warning curve if anything narrower. A variant, not a starting point.

Safety — the same highest-risk profile as the inside heel hook, and it can finish faster than intended against a resisting defender. Tap to the rotation, not pain; both partners must know the mechanics before any resistance.
Kneebar · Calf slicer · Toe holddeferred · finish

The rest of the deferred lower-body catalogue: the kneebar (hyperextending the knee), the toe hold (a rotational ankle-and-knee lock), and the calf slicer (compression of the calf against the shin). Behind the gate with the inside game — learned after the outside footlock and heel-hook mechanics are clean.

Safety — fast-loading joint locks; the toe hold and kneebar reach the joint quickly. Apply progressively, tap early.
Truck (crab ride)deferred · leg ↔ back bridge

The crab-ride / truck — an inside leg-entanglement that also delivers the back and the twister side. Reached from the berimbolo, the shoulder crunch, or a leg-entanglement scramble. Advanced: it bridges the Leg river and the Back river, which is why it lives here and is referenced from the back.

Deferred — inside-position control; the heel and twister attacks from here carry the same fast-loading risk as the rest of the inside game. Tap early.
④ Pins & the Isolation river
Top control that is control, not finish — the staircase climbs toward mount and the back — and the finishes it feeds: isolate a limb, then finish.

Establish chest-to-chest or chest-to-back, flatten, wedge, and reinforce with weight. Side control is control, not a finishing position; the staircase climbs to mount → S-mount / technical mount → the back. From these pins the Isolation river runs: isolate a limb or segment the body, then armbar · kimura · triangle · head-and-arm.

Pins / top control
Side controlcontrol · the hub

Cross-body chest-to-chest pin, perpendicular, loading weight diagonally (near shoulder to far hip) to cover the hips and flatten. The central top hub — control, not a finish — the staircase climbs to mount, north-south, knee-on-belly, or the back; the near arm feeds the isolation finishes.

Kesa & reverse kesacontrol

Scarf hold — sit hip-on-mat facing the head, one arm around the head, the other trapping the near arm; in no-gi it controls through the low seated hip and friction, and doubles as an americana/keylock platform. Reverse kesa rotates 180° to face the feet, adding a two-direction threat and feeding the kimura and near-side armbar.

Knee-on-bellytransitional

Upright point-pressure — one knee in the ribs, the other foot posted wide — a destabiliser, not a true pin. Read the reaction and match it (push → armbar, reach → triangle, bridge → back). Mobile and mid-value; the single-foot base is both its pressure and its sweep risk.

Mountadvance · highest pin

Straddle the torso chest-to-chest with the legs neutralised, removing their primary escape engine. Low-mount (stable) to high-mount (max submission access); double underhooks the highest control state. The highest-percentage finishing platform and top of the staircase — upgrades to S-mount, technical mount, or the back.

S-mountadvance · arm-attack platform

A mount where one leg steps over the far arm, trapping it — the arm is pre-isolated before any attack, so isolation is guaranteed by geometry, not the opponent's error. A three-way reactive system: arm straight → armbar, bends → kimura, shoulder rises → mounted triangle.

Technical mounttransitional · to the back

A mount with one leg stepped out flat beside the hip, entered by riding their escape turn. Transitional, not stable — the stepped-out leg already points at the back, so continuing their turn takes it; the angle also loads the near arm into the neck for the arm-triangle.

North-southcontrol · upgrade to side control

An inverted chest-to-chest pin facing the feet, hips driving through the sternum so the bridge can't lever it. Both arms fall accessible at once — the highest submission density of any top pin (N-S choke, kimura, far armbar). A strong upgrade from side control when mount is unavailable.

Top half guardtransitional · passing

One leg trapped between theirs — the last foot connection to clear before the pass completes. A fixed three-step: win the underhook (or concede the back), flatten them, extract the leg to side control. Passing and pinning are one action; the failure is pausing after extraction, and the kimura punishes when you win the underhook.

The isolation finishes
Armbar (top & bottom)finish · the hub

The foundational elbow lock — the isolated arm laid across the hip (elbow the fulcrum, thumb up, knees pinched), hip extension driving the elbow past straight. The entry angle wedges a leg between arm and torso, breaking every reconnection. A hub finish — chains with the triangle and kimura; the arm must be perpendicular for full leverage.

Safety — the elbow hyperextends with no warning zone past straight; apply with controlled hip extension, never explosive. The tap window is near-zero at speed.
Kimura (top & bottom)finish · & control system

A figure-four shoulder lock in internal rotation — the bent arm's wrist driven toward the far shoulder blade. Isolates by breaking the self-grip, blocks the roll with body position; the same grip doubles as a control and back-take system, so their roll becomes your back. Body rotation, not arm pull, is the lever.

Safety — 5–10° from discomfort to labrum damage; speed is the primary risk. Set the grip slowly, finish controlled.
Americanafinish

The external-rotation counterpart to the kimura, same figure-four but the forearm arcs toward the mat. Its condition is mount on a flat back — the mat removes the torso-rotation escape, concentrating force on the joint (from side control it's far more forgiving). The finish is the rotational arc, not straight-down pressure.

Safety — AC joint, narrow warning band (a flat back removes the escape valve); apply slowly, arc not push.
Triangle (front)finish

A bilateral carotid choke from guard — the legs wrap neck and one arm, your thigh on one carotid and their own trapped arm on the other. The finish is geometry (hips to shoulder height, head down, hip-twist), not a leg squeeze. The trapped arm sits in armbar range — triangle → armbar is the defining dilemma of the system.

Safety — bilateral blood choke; unconsciousness in 3–5s of full compression. Release instantly on the tap.
Side trianglefinish

A triangle applied laterally from the top — entered from side control or north-south, perpendicular. Same bilateral compression, but the finishing vector is a lateral hip drive away from the head and top weight assists. High-percentage once locked; the triangle → armbar dilemma carries over, and a miss resets to side control.

Safety — bilateral blood choke; the lateral approach doesn't slow it. Release on the tap.
Head-and-arm (kata gatame)finish · mounted arm-triangle

A head-and-arm arm-triangle that is pin and choke at once — the chest drives their own near arm into their neck while your over-arm closes the far carotid, so the pin is the choke and every escape tightens it. Taught primarily from the mount (also available from side control); the finish walks the hips ~45° toward north-south. Distinct from the arm-in guillotine — this is an arm-triangle, not a guillotine.

Safety — an arm-in blood choke; tap before the 45° finishing angle, compression completes rapidly.
Omoplatafinish · shoulder lock

A shoulder lock from guard that isolates the arm with the legs and rotates the shoulder past its range — also a potent sweep and back-take threat when the finish is defended. Chains with the triangle and armbar off the same arm isolation.

Choi barfinish · armbar hybrid

An armbar / omoplata hybrid — a leg traps the shoulder while the arm is extended, attacking the elbow from an angle a standard armbar defence doesn't cover. Fits the isolation river's logic exactly: isolate the limb, then load the joint.

Baratoplata · Tarikoplatafinish · deferred

Advanced omoplata-family shoulder locks (the baratoplata's short-arm shoulder lock; the tarikoplata's kimura-grip variant). Reserved for after the fundamental isolation finishes are solid — individuation, not first principles.

Deferred — the fundamental isolation finishes come first; these are the next branch.
Berimbolotechnique · to the back

The inversion from reverse de la Riva (or DLR) that spins underneath to take the back — the no-gi version rides the shin/ankle grip and the crab-ride / truck rather than a lapel. A high-level back-entry that has earned its place in the modern fundamental toolbox off the RDLR game.

Escapes & defence
The upstream of every river — what a beginner does most. Escape into attack, not passive re-guard.

You're pinned and caught far more than you attack in the first year, so this is trained heaviest and comes online first. The movements are the ABCs; the pin escapes and submission defence are the survival core.

Fundamental movements & breakfallsfoundation · day one

Breakfalls first — front, back, and side — spreading impact across the forearm, slapping the mat open-handed, chin tucked, so being swept or thrown is safe before any live sparring. Then the solo vocabulary every escape is built from: the bridge (hip extension to lift weight), the shrimp / hip escape (the primary space-maker), the granby roll (invert away from pressure), the sit-out (turn to face from turtle), and the technical stand-up (posted-hand tripod to the feet). No escape uses just one — they combine — and all drill solo, across the mat and back, until they're mechanical.

Mount escapeescape

The exits from bottom mount, the highest-submission-density pin, worked by stage. The two foundations: the trap-and-roll / upa (trap a posted wrist and same-side ankle, bridge over the trapped side to reverse to top) and the elbow-knee / shrimp escape (frame the forearm on the knee, shrimp a sharp gap, thread the knee back to guard). Every option turns to a side to free the hips and destabilises before moving — bridging without trapping just gives the top player a base. Frame the knees to deny high mount, and where you can, escape into attack: the upa lands straight on top.

Side-control escapeescape

Recovering guard or standing from under chest-to-chest side control. The core is the two-frame system — near forearm to the hip, far forearm to the collarbone — which breaks the chest connection so a shrimp can travel into the gap and the knee shields back to guard. Read the opponent for the secondary tools: ghost escape when they're chest-heavy (turn belly-down, slide out toward their legs), underhook and come up when they post an arm. Frame first, never push the shoulders, and shrimp toward their legs, not their head.

Knee-on-belly & north-south escapeescape

Two transitional top pins escaped through their specific weaknesses. Knee-on-belly has a narrow base: grip the posted ankle so the knee can't follow, then shrimp the knee off the body (plus the early knee-shield before it weights). North-south loads the head and leaves the hips light, so it's beaten by rotation not force — frame both forearms on the hips, shrimp, and circle out toward their legs to re-face and recover guard. In both, push at hip level laterally — never against the loaded chest — and keep the arms tucked when a choke or kimura threatens.

Submission defence — upper bodydefence

The shared rule for the armbar, triangle, kimura, guillotine, and RNC is one thing: defend early — posture, hide or connect the limb, and hand-fight the grip, because a finished version of each is very hard to escape and the honest late answer is to tap. The one key early answer for each: armbar — elbow welded to the ribs so the arm can't isolate; triangle — head up, never one-arm-in/one-arm-out; kimura — elbow in, grip your own thigh to deny the figure-four; guillotine — chin to chest, head to their body, side-step to the free side; RNC — chin tucked from the moment the back is exposed and two-hand the choking arm so the figure-four never locks. Prevention costs far less than any escape.

Submission defence — the heel hookdefence · safety-critical

Four principles: hide the heel (point the toes, dorsiflex, turn the knee — no heel, no hook), push the hip with the free leg to open the extraction lane, clear the knee line, and manage the rotation, not the pain. The mechanics differ by entanglement — ashi (secondary-leg push + knee-to-chest extraction), outside ashi (turn belly-down toward the trapped leg), cross-ashi/saddle (the most dangerous — tap early if untrained). Learn the four principles and the ashi escapes first, and never bridge in a leg entanglement — bridging drives the exact rotation the hook finishes with.

Safety — the heel hook injures ligaments before pain registers: the shortest injury window in grappling. Escape windows exist only before rotation begins; once the knee starts to rotate, tap immediately — fighting it then accelerates the injury. Never bridge.
The effectiveness test

Invariant coverage — 50 / 50

A curriculum that claims completeness has to prove it. The paper-validity of this fundamental set is its invariant coverage: does learning these techniques, in these phases, train every one of the fifty principles? It does.

17/17
Universal
6/6
Standing
5/5
Guard
4/4
Passing
4/4
Pinning
4/4
Scramble
5/5
Leg
5/5
Submission

Robust, not sampled once. The seventeen universals — the physics — are each trained from several directions: inv-11 (underhook → hip) in the body lock, the seatbelt, and the crossface; inv-12 (rotation) in the kimura, the heel hook, and the armbar; inv-14 (isolation) in the armbar, the kimura, and the arm-in strangles. Every tag on every technique card above links to the principle it trains — that is the map made literal.

What coverage proves, and what it doesn't. It proves the map is whole — no invariant is orphaned. It does not prove skill: paper completeness is not competence. The ~400 quality mat-hours in the environment below are what convert the map into a grappler.

What to expect of yourself

Day one → the standard

Time is the wrong unit — the real currency is quality mat-hours × transfer × retention. At 3×/week you bank roughly 200 quality hours a year. Assuming honest, resisted training in the environment below, and an ordinary but motivated adult:

Headline band
~18–30 months · ~2yr median
to genuine two-way competence across all four rivers.
In mat-hours
~350–450 quality hrs
hours, not the calendar, is the real gate.
Individual swing
±6–12 months
the biggest accelerator is tolerance for hard rounds + competition.

Competence is not uniform — the order it comes online is the point. This emerges in each student from the resistance ladder (beginners are forced into losing positions, so defence develops first); it is not a room-wide schedule.

Dimension0–3mo3–9mo9–18mo18–30mo
Escape & retention (most live time)buildingreliablereliablefluent
Guard bottom (retain / sweep)seedbuildingreliablefluent
Leg river (shin → SLX → ashi)not yetbuildingreliablefluent
Back river (→ face-down → strangle)seedbuildingreliablefluent
Top: passing & pinsnot yetseedbuildingreliable
Finishing vocabulary (all four)not yetseedbuildingreliable
Milestones: SurviveNot-a-beginnerTwo-way gameThe Standard (two-way fluency under live resistance).

Cadence: this assumes 3×/week. At 2× stretch to ~3–4 years; at 4–5× compress to ~14–20 months, recovery-limited. Why the core-focus is faster: fewer things → more reps each (faster automaticity); invariant anchoring → transfer (learn inside position once, it pays off in passing, legs, and pinning at once); through-lines → one skill spans phases; live-heavy → trained under the only conditions that count.

The environment & approach

Conjugate, live-heavy, coach-scaled

Not a technique-of-the-day school — a machine for building competence under resistance, and the tolerance that accelerates it, safely. Five operating principles:

1 · Constraints, not commands. The game makes the right solution the available one; intensity is controlled by design, not by asking people to go easy. 2 · The model is the language. Every cue is a river or an invariant, so feedback transfers. 3 · Primarily live, at moderate load. ~70 of a 90-minute class is resisted play against navigable opposition. 4 · Escape-first. Early rounds start in the bad spot — triage for where beginners drown. 5 · Standardise the frame, individualise the finish. Shared trunk; personal finishes; the individuation gate holds.

The conjugate program — not blocked

All four rivers, both directions, stay in continuous rotation all year. One all-levels room can't park three-quarters of the game for months without dropping below the frequency and breadth that keep practice ecologically close to the real match — which never serves one river at a time. Emphasis rotates for variation; nothing is ever parked. The only differentiation is the coach scaling per student, per round, live (resistance · partner handicap · start position · win condition) — never a syllabus pre-sorted by level.

The resistance ladder

  1. 1Cooperative flow — learn the shape (brief)
  2. 2Positional start, progressive resistance
  3. 3Positional start, full resistance, win conditions
  4. 4Rounds vs less experienced partners, full effort — where offence is actually executed and iteratedthe engine
  5. 5Rounds vs peers / equals
  6. 6Rounds vs more experienced partners — the growth / tolerance zoneaccelerator
  7. 7Competition — the biggest single compressoraccelerator

The bulk of live volume sits at the engine (rungs 4–5, ~65%), with the accelerator (6–7) a smaller, potent dose. A beginner has almost nobody less experienced than them, so their volume is forced onto rungs 6–7 — which is why defence develops first. The coach's early job is to manufacture rung-4 reps by handicapping the more experienced partner, so offence isn't starved while the student climbs. The room then feeds itself: today's beneficiary becomes tomorrow's rung-4 provider for the next beginner.

The promise
Train this fundamental set diligently, against resistance, in a conjugate, live-heavy room — and in roughly two years of honest 3×/week work you will express all fifty invariants: a genuinely competent submission grappler, offence and escape, standing to the finish. Not a paper standard — a mat standard. Everything beyond this trunk is yours to grow: your style, your specialisations, the inside-leg game, and the finishes that suit your body. The canon is the floor, not the ceiling — and it is a floor you can hold your coaching to.