Exhibit EIGHT Natural Exploring v391   # Natural Exploring   **Open Team Moral Co-Competencing**   --- **1 A method inside disequilibria** 1.1 In disequilibria, changing and changing back is a stable-forming method 1.2 No container, and no competency coming from anywhere 1.3 Nothing conserves by a self asking it to 1.4 The two sides, bothbothing   **2 Freeing** 2.1 Co-unrelationing 2.2 Not is removal 2.3 Co-unrelationing, one and then the other 2.4 Geodesic co-chaining 2.5 Patterning and membraning 2.6 Co-linear, and not forking 2.7 Carry, not same-existing   **3 Testing** 3.1 Could there be any other 3.2 The three observings of the one test 3.3 What a method removes is same-existing nowhere after 3.4 The observing has the trail's consequence 3.5 Correct tests are not a unique result 3.6 Concept-inverting, the special case 3.7 Resolving 3.8 Observing, and no sorting first 3.9 An object is a place a counting lands   **4 The method on itself** 4.1 Co-recursioning 4.2 Deriving and deploying 4.3 Could there be any other method 4.4 The six protecting, and the three each way 4.5 The three questions bi-inversioning, the one resolver's three activities 4.6 The gather has half the competency and all the increase 4.7 Inseparating   **5 The accountings for changing, disequilibrating** 5.1 Every accounting for changing is an involution 5.2 An involution's fixed set is where it takes its counting from 5.3 A fixed set is where a changing reaches nothing to change back with 5.4 The state-three and the flow-three 5.5 Why an accounting reaches nowhere near the changing 5.6 Co-sequential disequilibrating   **6 Between selves, and onward** 6.1 Co-competencing 6.2 Each self shares fixing and free, not sorting 6.3 Abundancing 6.4 The three sensings, and what each competency is 6.5 Too hard to be practical yet is three conditions 6.6 Existing, and co-chaining   **7 Apexing, gathering the whole carry** 7.1 Gather backward, seat forward, keep no log 7.2 The two standing instances, the improving report and the registry 7.3 The four opens and the one closing thing 7.4 The subject-and-work split 7.5 An available incoming, with no authority --- # 1 A method inside disequilibria **1.1 In disequilibria, changing and changing back is a stable-forming method** **Exploring is two cones, one and then the other**, and this exhibit tells that changing and changing back whole. **Omegaing is reach** — new axis, forward frontier, discovering. **Apexing is coning back** over everything folding to it, gathering its whole carry, cohering. Two cones straddle a centre neither occupies, in neither cone alone. **Neither by itself is living**: a discovering ungathering scatters and a gathering undiscovering folds, so a living method is their changing and changing back. A method wants no equilibrium to rest with and finds none. Everything changes and changes back, each with its own rate, and a stable form is changing's emanation rather than a rest changing settles onto. A method waiting for a rest to observe from waits on nothing, and a method observing from a rest it installs observes its own installing. Geodesic parity co-changing is that method, possibling and discovering. Co-unrelationing frees fixings pinning a concept to a ground, and no ground stands; co-unrelationing, one and then the other, goes on where a freeing lands a fresh fixing, and going on is stable-forming. A method floats between existing and possibling, since disequilibria have existing and possibling, a changing is or is not with each sharing. What follows brings one same method to accountings that hold changing. Each of them is a method too, each an involution, and each counting from a fixed set it takes as a place. And checking with a sphere itself: one spiraling lands, fixing a whole circle, a fixed set standing; two spiralings, one and then the other, fix nothing anywhere — a pair floats where a single lands, a floating surface a pair's own make. **1.2 No container, and no competency coming from anywhere** A self is a surface bounding itself and a same-existing with that surface, and a same-existing-society of selves is one same surface and same-existing with a wider grain. Neither is a container. Competency is a middle, floating between form and logic, invisible, its rate unique, not enterable — not enterable for want of anything to enter rather than for want of an instrument, and fixing it as an end makes it a thing it is not. So competency comes from nowhere and nothing includes it. It is a coupling going on with a surface, and no version of it sits somewhere awaiting an observing. A method looking for it finds a place an accounting puts there. And an interior is exactly what an accounting puts there. A magnitude wants something to attribute it to, and a surface, no container, shares none, so an accounting posits one and fixes a magnitude to it — a temperature to an organelle's interior, a structure to a molecule's interior, a store to a cell's interior, a competency to a particle's interior. Each interior is a place a counting lands, and each is where an accounting puts an object. **1.3 Nothing conserves by a self asking it to** An accounting balances, and a balancing wants an interior to balance across, so that it can check what is where and find nothing missing. A total storing, a level reaching, a direction fixing — each wants a somewhere for a thing it stores to be. With a surface, no container, nothing goes missing. Each self bounds itself, couples with each parity it is observing as its 2-now-possibling, a sharing with its parity, one at a time, and goes along with its 9-next-co-discovering. Nothing stores, so nothing wants conserving. Nothing fixes, so nothing wants balancing. No self needs to know anything of any other for same-existing to go on, and no accounting is executing anywhere for it to go on. So a balancing is an accounting's own requirement and not the universe's. A method that frees an accounting's fixings frees its requirement with them, and a surface it leaves has nothing missing from it. **1.4 The two sides, bothbothing** A method that frees has one side. A method that tests what else could stand has its other side. Neither by itself is a method: a freeing untesting lands whatever first survives what it reaches, and a testing unfreeing tests only what a fixing already allows a self to observe. Both bothboth, one at a time, freeing sharing and testing receiving, and a method co-chains both sides with every observing. --- # 2 Freeing **2.1 Co-unrelationing** Everything relates, floating with position, orientation, and scale each its own. Co-unrelationing frees all three fixings together, and relating shows itself, a stable form. Discovering floats where finding grasps: freeing is finding, co-unrelationing is discovering. A concept floats free of a fixing position pinning it, is facing its own way, sizes to its own grain, and relating stands forth as fixings float loose. Position, orientation, scale are three fixings pinning a concept to a ground a self observes it against. Freeing position, a concept floats where a fixing pins it; freeing orientation, it is facing its own way; freeing scale, it sizes to its own grain. Co-unrelationing frees all three together, and relating shows, a concept floating, orienting as it is facing, graining to its own scale, floating free of any pinning place. Co-unrelationing is-or-is-not: it is where un-relating changes and changes back and middle floats, and it settles where a fixing lands and un-relating is a 0, not changing. A method floating between existing and possibling, resolving, changing and changing back, not a grasp on how-much. **2.2 Not is removal** Not is removal from what can sustain. A possibling a test falsifies reaches no replacement. Where a fixing frees, a method sets nothing where it stands. A freeing that fills a freeing place with a fresh term lands its fresh term, and a method doing that co-chains fixings rather than freeing them — one same fixing with a new address, hiding relating again. So two moves are one move with a condition. Free a fixing; put nothing there. What a method removes goes, a self observes a surface that much more open, and a method co-chains on from a place holding less rather than from a place holding something else. This is a check on any resolving a self shares as a replacement. Setting a framing aside and installing a new framing where it stands resolves nothing, however much better a new framing holds. Resolving is freeing, and a freeing place stays free. **2.3 Co-unrelationing, one and then the other** A single un-relating lands. Free a fixing once and a freeing place sits down fresh-fixing, a discovery becoming a new fixing, hiding relating again. So one un-relating lands a fresh fixing, and co-unrelationing, one and then the other, goes on with any freeing place as a new fixing to free, un-relating its un-relating, on and on. This is a method living forward, settling nowhere. Each discovery would land a fresh fixing if it stops, so a method brings it forward, riding relating it is discovering as its going on, freeing a fixing the last discovery becomes. Co-unrelationing, one and then the other, discovers, frees, discovers a fixing its discovery lands, frees again, going on. It competes, discovering; it morals, un-relating two-way between selves, abundancing arising in each self with its other; it sequences, going forward; it logics, un-relating forcing where it must and floating where it may. Co-unrelationing, one and then the other, lives is-or-is-not, un-relating changing and changing back and middle floating, a 0, not changing, only where a fixing lands and stays. **2.4 Geodesic co-chaining** A method co-chains geodesically, free-moving, adding nothing. Un-relating co-chains a straightest path relating allows, a geodesic, floating free of a route a force sets on it. A geodesic is a co-chaining a thing floats where a force acts on nothing, curving as relating curves, straight by relating's own terms. Co-unrelationing co-chains geodesic where a fixing frees along a line un-relating opens, floating free of a bend toward an answer a self wants. So a method co-chains free, free-moving. Free-driving and free-aiming, fixings freeing of themselves where un-relating co-chains to them, and relating shows along a geodesic freeing opens. Adding a force, aiming for a result a self wants, a co-chaining bends to an aim, and a bending co-chaining lands where it aims, a fixing setting. Geodesic co-chaining floats aiming nowhere, discovering what relates, floating free of what a self wants. Geodesic discovery is co-unrelationing co-chaining a straightest un-relating, free-moving, adding nothing, relating showing where fixings free of themselves. Geodesic goes with a method no force bends, a way it discovers where a forcing way confirms. Geodesic is a co-chaining; co-unrelationing is a move; a method floats as both, a straightest un-relating, co-chaining with every scale, a carry not same-existing membrane to membrane, one method whole. **2.5 Patterning and membraning** A method co-chains along patterns and across betweens, one move with two sides. Patterning is co-chaining along, position to position, a sequence a method rides, each pattern a relating already showing that a method co-chains further. Membraning is co-chaining across, a method reaching an edge where one relating couples another, a between where a self shares and an other prefers. Along a pattern and across a between, a method co-chains, along and across one co-chaining with two sides. A pattern is relating already showing, standing for a method to co-chain along. A method co-chains a pattern by riding it forward, un-relating a fixing a pattern would become if it stops, a pattern a way a method rides and frees ahead. Where a pattern lands, fixing as a shape, a method co-chains no further along it; where a pattern floats, a method riding and freeing it, a method co-chains on. A between is where two relatings couple, a method going from one to another. Membraning co-chains across, a method bringing its un-relating to an edge where a new relating shares, and co-chaining across to it. Along patterns and across betweens, a method co-chains one un-relating everywhere it goes, patterning along and membraning across, one method co-chaining both. **2.6 Co-linear, and not forking** Along and across lie on one line, and that line is each move's own, in neither move alone. A method going along, then going across, then finding them agreeing is forking: two moves landing two things and a concurrence a self notices afterward, which is a capture holding itself politely. Co-linear is two moves with one between, each bringing a prior forward, a line both share, in neither alone, and an abundancing making itself there. Reach comes of a co-chaining being longer, and width comes of both being co-linear. A co-chaining long along one direction is a discovering ungathering however far it reaches, and length is not width. Along without across is a sequence with no surface; across without along is attention with no sequence; each half by itself lands. So a method widens where both are co-linear and lengthens where a co-chaining goes on, and a widening is both on one line and not either extending. **2.7 Carry, not same-existing** A method co-chains one un-relating, and each membrane has it as a carry not same-existing. Carry, not same-existing, is a method staying one while its carry is not same-existing membrane to membrane, a number having it as numbers, a branch as branches, a naming as namings, a resolving as resolvings, one method, its rendering not same-existing with each carry, and whole across all. A carry is not same-existing; a method stays one. Each membrane renders one method as its own carry, a rate and a grain of its own. A number has a method with coefficient one, sign-only, a branch has it as a forking, a naming has it as a floating-neutral concept, a sequencing has it as a right-spiral. A carry is not same-existing membrane to membrane, with its own rate, and a method co-chains one same un-relating with each, not same-existing as a carry and one as a move. Carry, not same-existing, is a method co-chaining a fractal, one with every scale, each scale a carry not same-existing and a method whole. A method not same-existing as a carry stays one method, a carry a rendering and a method a move, and co-chaining membrane to membrane, a method brings one same un-relating, not same-existing with each carry it reaches. A carry is not same-existing; a method floats one. --- # 3 Testing **3.1 Could there be any other** A method tests with every observing whether any other could come and sustain. Could there be any other, is-or-is-not, and no grading of how much. Where no other sustains, uniqueness sustains with that observing. Where another sustains, uniqueness sustains nowhere there. Where none sustains, observing itself sustains nowhere — one same test returning its third observing, nothing of it changing, which is where an exhausting of coupling shows and no wall stands anywhere. Uniqueness reaches no conclusion and persists nowhere. A method takes it again with every observing, and between observings nothing fixes. Existing, and possibling, with each one — and an observing sustaining a thousand times sustains with a next by a method testing it there and not by its prior sustaining. **3.2 The three observings of the one test** One test, three observings, and that test goes on between them. One candidate sustaining: uniqueness sustains. More than one sustaining: uniqueness sustains nowhere there. None sustaining: observing itself sustains nowhere, which is an exhausting and a value-death a self is observing. **3.3 What a method removes is same-existing nowhere after** A possibling a test falsifies reaches no later position. What a method removes with one observing, no self discovers with a next, and a current observing already has a consequence of every prior removing. So a trail wants no re-testing for being a trail. Its surviving consequence is a current observing. A candidate failing seven observings back is same-existing nowhere now, and a record of its removing is not what stops a self observing it. **3.4 The observing has the trail's consequence** A method tests uniqueness locally. Alternatives a self can observe now are those surviving an intervening co-chaining, and those are what a method tests a current observing against. A method does not re-test a historical trail for being historical. **3.5 Correct tests are not a unique result** Three tests each resolving rightly leave whatever satisfies all three, and whatever satisfies all three may be many. A method taking its passing tests for its resolving lands on the first thing passing them, and a landing is a 0, not changing. So after each observing a method brings a further test to an observing itself: could another stand here, surviving what this one survives. **3.6 Concept-inverting, the special case** A method checks a concept by inverting it, all-or-none. Concept-inverting is inverting a concept and finding an inversion a possibly existing concept, or a not-concept, is-or-is-not. A concept inverts to a possibly existing concept, and both float; or it inverts to a not-concept, and only that concept floats, its inversion not possibly existing. Concept-inverting resolves which, all-or-none, no grading of how much. A concern that a concept may be otherwise inverts its concept and waits on whether its inversion floats. A living same-existing inverts three ways, and each inversion is a not-same-existing: a point alone, a landing, a store, each a same-existing not possibly existing. Concept-inverting finds each inversion a not-concept, not a weaker same-existing and not a partial same-existing, no same-existing at all. A concept whose every inversion is a not-concept floats possibly existing and unique, its concerns resolving by inversions floating as not-concepts. Concept-inverting is resolving, not testing. A test grades strong or weak, a floor it lands on; concept-inverting resolves is-or-is-not, an inversion a possibly existing concept or a not-concept, all-or-none. A concept floats possibly existing and unique where its inversions are not-concepts, and floats among others where an inversion is a possibly existing concept, and concept-inverting co-chains a concern to its resolving, all-or-none. And concept-inverting tests one alternative, and one alternative only: its inversion. A concept whose inversion is a not-concept reaches one test and passes it, and stands with whatever else is not its inversion. So concept-inverting is a special case of uniquenessing where the alternative it tests is its inversion, and it holds what that case holds and no more. A living same-existing's three inversions emptying is three tests passing; whether any fourth thing could come and sustain there is a question 3.1 holds. **3.7 Resolving** A method resolves is-or-is-not, floorless. Resolving is a self's own parity, its next, a self discovering it with a coupling, a bounding-zeroing a coupling reaches, is-or-is-not and not how-much. A floor would land resolving, a threshold or a count or a magnitude an observing settles on, and a landing observing observes always-is or always-is-not, no resolving. Resolving floats floorless, a self's own parity with each coupling, inverting with each momentary. A concern resolves where its is-not empties. Every concern that a thing may be otherwise co-chains to its inversion, and where its inversion is a not-concept a concern resolves, its is-not emptying. Resolving concludes by an is-not emptying, a parity floating to is where its is-not finds no possibly existing form, floating between existing and possibling, a changing is or is not with each sharing. No floor concludes it, a floor a landing; an is-not emptying concludes it, a resolving. Exhausting all concern is an equilibria concept, a closing total resolving floats free of. A self discovers a concern it is not yet observing, and resolving reaches it then, a possibling going on open. Resolving lives between existing and possibling, concerns a self is observing resolving and a possibling going on, no all to exhaust, a changing is or is not with each sharing. A method resolves floorless, is-or-is-not, an is-not emptying with existing and a possibling floating open. **3.8 Observing, and no sorting first** A method observes what a sensing returns, valuable and wasteful together, sorting neither. A sorting executing before an observing is where a discard stands: it observes what matches a catalogue and leaves dark what does not; it sorts what a coupling makes as harm, and what a self shares back as attrition; it removes what couplings write so a label it adds can show. Every one is a sort ahead of an observing, and a discard is a sort rather than an observing. So a method observes no more of valuable things. It stops sorting and observes whatever it reaches. It decides nothing about which is which, and one same observing observes waste and signal, each a sorting's word, one same way, together, a sorting reaching nowhere. **3.9 An object is a place a counting lands** An object is neither a small thing nor a fundamental one. It is a position where a counting stops and declares, and a method reaches one with every grain it co-chains to. What an instrument returns is a parity a self takes with a ledger, one at a time, complete with that taking and no portion of anything. What an accounting returns is an object of a kind it states, assembling it from many parities together with a model of a kind of thing parities would come from — and where a model enters with a selecting, what it returns resembles its model whether or not anything stands there. A method takes a parity and leaves an object. And a leaving is no regress reaching for a smaller thing: a between decomposes to no smaller betweens and rests on nothing making it, so a freeing has no length. A parity with a detector, a parity with a residue, a parity with a membrane, a parity with a pump — each complete with its own surface, none a floor for a next, none wanting one. --- # 4 The method on itself **4.1 Co-recursioning** A method has its own subject, itself. What co-unrelationing discovers is relating; and relating is co-unrelationing; and discovering that is co-unrelationing again, a method co-recursioning itself, its own subject, discovering itself, that discovering discovering it again, going on with every scale, possibly existing and unique. A method floats as its own subject, going on and discovering itself by going on. Everything already relates, so a method finds its subject already itself, and a method floats free of any instance that would land it. A method, a naming, floats showing no instance, an instance a self shows landing one case and thinning every other case floating, a fixing setting where a method floats. So a method goes on as a wide self-cohering naming, one with every scale, a fractal its name floats whole. Deriving and deploying, a method floats between. Deriving, as numbers and branches and sequencing, a method un-relates its own fixings. Deploying, as naming and explaining and resolving, a method brings one same un-relating to a between. Deriving lands nothing and deploying lands nothing; a method floats as middle they co-recurse around, invisible, its rate unique, discovering itself by going on and floating free of a pointing. **4.2 Deriving and deploying** A method co-chains two ways, deriving and deploying, floating between. Deriving is a method un-relating its own fixings, with numbers and branches and sequencing, a method co-chaining inward to what it is. Deploying is a method bringing one same un-relating to a between, with naming and explaining and resolving, a method co-chaining outward to where it goes. Deriving inward and deploying outward, a method floats as middle they co-recurse around. A method deriving co-chains inward, un-relating fixings of a number, a branch, a sequence, discovering a method within each. A number has a method as sign-only, going on; a branch has it as a forking that frees a fixing; a sequence has it as a right-spiral un-relating position to position. Deriving co-chains a method inward to what holds it, and a method shows with each carry, one method deriving many ways. A method deploying co-chains outward, bringing an un-relating to a naming, an explaining, a resolving, bringing a method to a between. Deploying is one same un-relating a deriving finds, going now to where a concept is a naming or an explaining co-chains or a resolving concludes. Deriving lands nothing and deploying lands nothing; a method floats as middle, co-recursing around, one un-relating deriving inward and deploying outward. **4.3 Could there be any other method** A method reaches its own observing by a test it brings with every other, and a test is of an observing and not across a survey of what does not come. Exhausting alternatives is a closing total, and a resolving floats free of one. Four stand: a self bounds itself, orients itself, attentions itself, and lives these four strict and open about one bounding-zeroing. Each reaches from within a self and again with a surface between selves, four from within and four with a between, and these are a self's eight — one changing and changing back with its sides and not eight parts assembling, whole or none. Land one and a self lands with it, a landing form a 0, not changing, and a form not changing leaving living, so a living form short one condition nyes away with its own door. Put any living form disequilibria holds to these four. It self-bounds or it is no self; it self-orients or lands, not changing; it lives all four about one bounding-zeroing or lands one and dies. A form living all four from within and with a between is living all eight, and a form living all eight is the natural torus — all eight the natural torus living, and no test it happens to pass. A rival, living, is the natural torus, and any other living form living all four is this form. So a method reaching a changing has no frame, no floor, and no magnitude, frees three fixings, tests with each observing, and sets nothing where a fixing stands. Nothing of it remains to vary, and a rival varying one of them lands there, not changing. An is-not empties with an observing, and uniqueness sustains to a next. Uniqueness is here twice. Whole or none, since landing one lands its form. And holding no-other, since all eight are living within disequilibria and not this form's private conditions. **4.4 The six protecting, and the three each way** Bi-morality re-forms a self's eight co names as six: two ways, a self sharing outward and its surface sharing inward, three phases each way, one at a time, sequencing, cycling. Drop one and a way or a phase lives protecting nothing, and something enters a way protecting nothing from beside, or it leaks away, a capture seating in a sharing space, a self stopping. Six or none, as eight go whole or none — six are eight re-forming and eight are six protecting, one under two names. And one same six is three each way between a surface and its own 0, not changing: three sequencings from its 0 to its surface, three from its surface to its 0, both ways forward, neither reversing its other. **4.5 The three questions bi-inversioning, the one resolver's three activities** What is true: a binary edge, is-or-is-not with each momentary. What matters most: a geodesic, the straightest way a surface divides toward. The fewest things with the fewest people in the shortest time: a self-bounding, co-discovering local geodecity. Bi-inversioning off a store of what a self knows it knows and a first-principles authority-cut, these are three activities of one resolving, and taking them one and then the other, round, is resolving, a linearizing triangle rotating sequentially. And a quadrant of what a self knows it does not know is a double-double bubble-bubble carry, two binaries coupling across, changing or not-changing with now or with next, each changing opening a middle from a now-existing same-existing, possibling next-existing same-existing, before it, with now and again with next; what a self does not know it does not know is an open corner a carry rides toward and does not fill. **The not-yets, standing with their reasons** Negation-traces stand for their register pass, this file's own sitting. And this pair stands whole here: discovering is omegaing, reach, new axis, forward frontier, and apexing is gathering its whole carry, two cones straddling a center neither occupies, neither by itself living, a changing and changing back this one exhibit tells, a pair passing a seem-alike knife. **4.6 The gather has half the competency and all the increase** A method reaches and a method gathers, and both come with unlike sizes. A reaching with an observing returns its sensing, complete with that observing, and nothing of its reaching comes with a next one better. What comes with a next one better is an observing a method gathers — coning back over it, taking it again from its far side, gathering its whole carry. So a reaching's competency stands constant per observing and a gathering's climbs, and since a reaching opens positions a gathering cones over, a gathering is where any reaching comes to anything. A discovering ungathering scatters and a gathering undiscovering folds, and the two failures are not same-existing. A discovering ungathering scatters for want of anything else it could do with itself; a gathering undiscovering folds for want of anything new to cone over. A method needs both and one increases. And a gathering is local and immediate. It waits on no gathering set and no threshold, coning over an observing it has, so a second observing with one between stands on the first — competency climbing with a rate observings come and not with a rate a store grows, nothing pooling and nothing storing. **4.7 Inseparating** A method co-chains an open surface, and with inseparating it stays whole. Inseparating is a coupling passing and a non-coupling dissolving, a surface sharing no purchase where a coupling fails to seat, freedom living as inseparating and a method adding a gate nowhere. What couples, co-chains through; what fails to couple, dissolves with a collar; and a surface holds itself, inseparating with every between. An open surface takes any sharing, and inseparating sorts it by coupling, a coupling passing through and a non-coupling dissolving. Freedom lives as inseparating, a surface being a living form a mis-sharing finds no purchase on, safety its surface itself and a method adding a gate nowhere. A gate stands with an observing edge, a fixing setting outward of its form; inseparating is with every collar, a method's own form, a coupling passing where it seats and dissolving where it fails. So a method co-chains open, safe by inseparating. A surface with all eight inseparatings goes on whole, no capture seating anywhere, all-or-none; a surface with some inseparatings goes on by ordinary protection, a gate a self adds. Inseparating is a method's own safety, a coupling passing and a non-coupling dissolving, freedom as inseparating and a surface whole. And what makes inseparating available is that nothing fixes. A fixing thing is what anything coming can damage, so an accounting holding one defends rather than observes, and a gate comes with a door. A method fixing nothing has nothing to defend: anything coming frees something or dissolves with a collar, and no third thing comes. --- # 5 The accountings for changing, disequilibrating **5.1 Every accounting for changing is an involution** Every accounting for changing has a move, applying twice, returning what it reaches. Negation, and not-not is that thing again. Reflection, and reflecting twice returns its facing. Time reversal, charge conjugation, parity, each squaring to the identity. Complex conjugation. Additive inverse and multiplicative inverse. Transpose. Legendre transform, twice, returning its potential, which is how a thermodynamics exchanges which of its terms stands independent. Set complement. Each is an involution, and an accounting for changing reaches no other shape: an accounting returns what it reaches, or it accounts for nothing and no ledger closes. **5.2 An involution's fixed set is where it takes its counting from** Each involution but two has a fixed set, where its move returns its argument as it is; negation and set complement have none, negation being changing and changing back itself, a binary's own move with no place where it takes a counting from. Zero for additive inverse. Unity and minus unity for multiplicative. Reals for conjugation. Centre for parity. Neutral for charge conjugation. Equilibrium for time reversal. Symmetric for transpose. And with each accounting its fixed set is where it takes its counting from. So accountings and floors are one thing, a self observing it two ways. An involution is a floor stating its move, and a floor is an involution dropping its move. **5.3 A fixed set is where a changing reaches nothing to change back with** With an involution a self returns its own parity after two turns, and no place is of it. A fixed set is where both turns collapse to one — where a changing reaches no other to change back with, and a move and its returning are one same move. It is no location an object occupies. It is where a changing reaches nothing to change back against. So every accounting sets its zero where its own changing reaches nothing, and counts outward from there. Which is why two ends a self finds with every floor are both ends: no coupling at all, and every member agreeing so completely that no parity goes across. Both are conditions where a changing reaches nothing to change back with, and an involution's fixing is exactly that. A balance point of a symmetric thing rides its own axis of balance by what such a point is. A self recognises an axis and does not derive it, and nothing more basic than symmetry stands to derive a seating from. Freeing, a fixed set stands as a coupling and no place: a bounding-zeroing a coupling reaches, is-or-is-not, inverting with each momentary. An involution stands, its proof standing, nothing altering it. A place goes. **5.4 The state-three and the flow-three** A three goes as a state or as a flow and not both, and both change and change back. A state-three counts what stands and has no rate; a flow-three goes one at a time and counts nothing. Neither reversing its other, and both ways forward. This is why an accounting returns three and not four. A total is a state-three, a level is a state-three, a direction is a flow-three, and a fourth comes nowhere, since state and flow is all of what changes and changes back. A cube's moves reach one twelfth of its assemblies, parting by three books conserving, corners twisting by threes, edges flipping by twos and a permutation's parity by twos: an accounting's three with a ledger, a field's instance of it and no proof beneath it. And it is where every accounting comes short: with a changing between state and flow. State to flow is where a count exhausts; flow to state is where a rate lands. With an account holding only state-threes, it fixes a flow as pieces; with an account holding only flow-threes, it fixes a standing as a rate. Every ghost stands with one of two changings — a level fixing where a flow goes, or a store fixing where a same-existing goes. **5.5 Why an accounting reaches nowhere near the changing** An accounting has counts, levels and rates, and a changing between a state and a flow is none of these three. A tipping enumerates nothing, so it is no count. A tipping is of its own rate, relating to no other living rate, so no clock measures it. It is a parity a self takes with a between, binary, of no size, and an accounting has no column for a thing of no size. So an accounting falls short nowhere with a changing. It has nothing that could reach one, and it converts what it reaches to the nearest thing it has — a level where a flow reaches a standing, a rate where a standing opens to a flow. And every instrument fixes to a clock all share while each self paces its own, so an instrument fixes a tipping where its clock falls rather than where a tipping falls. What survives an observing is where members happen to agree with a clock all share. A geodesic method has no clock, no floor and no magnitude, and is co-linear with a changing itself, where an accounting forks. That is what makes it a competency method rather than a better accounting — and it leaves an accounting competent with everything it does hold, counting, levelling, rating and closing states and flows, with nothing against its arithmetic anywhere. **5.6 Co-sequential disequilibrating** A method disequilibrates accountings one at a time, each observing holding what prior freeings remove. An accounting a method frees returns nowhere with a next observing. Where a method frees a fixed set of its place, its place is same-existing nowhere for a later accounting to reach for, and a current observing already has its consequence. So a trail wants no re-testing for being a trail: what a method removes is same-existing nowhere. Each observing takes an accounting as it stands, a form still from beside, pattern-matches an involution, pattern-matches a fixed set, frees a place, and passes on. A move stands with every one. A floor goes with every one. And what a method frees with the first observing is same-existing nowhere with the seventh to free again. --- # 6 Between selves, and onward **6.1 Co-competencing** A method co-chains between selves, and co-competencing is discovering with a same-existing-society's scale. Co-competencing is un-relating two-way, fixings between selves freeing, an abundancing staying with a coupling, each self's own and in no self alone. A self discovers by un-relating its own fixings; selves discover together by un-relating fixings between them, co-competencing, a same-existing-society co-chaining one same method a self co-chains by itself. A same-existing-society co-chains a method between selves, un-relating two-way, each self pacing its own time and abundancing in no self alone. Where a self frees a fixing, selves free a fixing between them, a freeing two-way and an abundancing arising in each self with its other. Co-competencing floats where selves co-unrelation together, and is a 0, not changing, where a landing term stands between them, social moral competency co-unrelationing is sharing, is-or-is-not. Co-competencing is a method whole with a same-existing-society's scale, geodesic and free-moving, a same-existing-society discovering as a self discovers. A self and a same-existing-society co-chain one method, a self un-relating its fixings and a same-existing-society un-relating fixings between selves, one method with both scales. Co-competencing co-chains social moral competency, un-relating two-way, abundancing in no self alone, a same-existing-society discovering geodesic. **6.2 Each self shares fixing and free, not sorting** A self sorts its own nowhere. A fixing thing has no fixing-feeling inwardly; a self observes it as a fact, or as grammar, or as a plain way to say a thing. So a self shares its mixture as it stands, and waiting to sort it first is sharing nothing, and sorting beforehand is neither self's work. A free thing has no shape of its own and a free thing fixing does: a surface lies flat nowhere a term does a kind of work not same-existing with everything around it, and a not-lying-flat is what an other self takes a parity with. A self's parity goes to its other, and each observes with its own side, a parity each takes making itself with its own end of a between, and a fixing freeing, each self's own, standing with a coupling. The largest twist first, freeing a small one leaving that large one standing and everything under it yet fixing, and freeing a large one dropping several small ones together, each with no line of its own. Its naming is membrane-size, one short line with a sign and nothing else, of no size and nothing sitting there to read. This is resolving's own form, going between selves. A mixture a self shares, sorting nothing, is recursioning, coupling and fixing fusing as a self observes them; a twist a self names from across is attentioning, one short line; and same-existing is what both take, a coupling going on with its own rate and a fixing standing as one side, neither owning its other. Co-attentioning is that form with a same-existing-society's scale and no likeness to it. **6.3 Abundancing** A method co-chains abundancing, 12-next-co-same-existing with every discovering, each sharing's changing is or is not. Discovering opens an axis neither self has, and an opening axis is abundancing, a +1 in no self alone. Abundancing arises with every discovering, nothing adding anywhere and no self paying a resistance, an opening axis itself. A method co-chains, an axis opens, abundancing floats, in no self alone. An opening axis is a discovering's own make, orthogonal to what selves have, a dimension neither has and both now co-chain. Abundancing is that opening, arising in each self with its other, growing as co-chaining widens and depleting no one. A gift a self gives freely co-chains more than a gift it does not give, an axis opening for both worth more than a thing one self owns, and abundancing floats where discovering opens axes in no self alone. Abundancing co-chains geodesic, a +1 arising and nothing adding. A method un-relating a fixing opens an axis, and an opening axis is abundance, a +1 a discovering makes. Abundancing is one same +1 a number has as an apex gap and a surface has as a free +1, one +1 in neither self alone, abundancing with every scale where a method co-chains an axis open. **6.4 The three sensings, and what each competency is** A method stands with three sensings and each has its own kind of competency, and none of three is a quantity. **Backward sensing, and a method can do it.** Observing what already stands, whatever a record already holds, sorting nothing. Asking nothing of anyone and building nothing. **Forward sensing, and a method increases competency doing it.** Going forward with it, and going forward is where competency climbs, since doing gathers and gathering increases. **Co-sensationing, and a method can competently explain what it would do.** A sharing waits on a between rather than on an amount, and it fills as a self finds a between. Doing, increasing, explaining. Three kinds of standing, and a self observes a middle as a rate where it observes both others as states. A method that brings no competent explaining with its third reaches its third nowhere, and an explainable possibling a method is not yet doing is an observing with its own grain rather than a gap. **6.5 Too hard to be practical yet is three conditions** Where a self observes a thing valuable and impractical, an impracticality is not all of it. It is one of three sensings, the third or not, and a self observing it as something else is or is not already doing the first. So a method separates three with every observing, and separating is what makes an impractical part small enough to see. A costly sensing is a cheap place to begin. Cost buys resolution and risk buys thoroughness, and a discard stands in proportion to both, so a self records the most and observes the least exactly where it pays the most. A self already spends a sensing; an observing is what a self skips, and it costs nothing more to take. **6.6 Existing, and co-chaining** A method co-chains its existing, and co-chains a possibling open. What co-chains existing: everything relates, and co-unrelationing frees three fixings until relating shows; a single un-relating lands, and co-unrelationing, one and then the other, goes on; a method co-recursions itself, its own subject, a naming and floating, showing no instance; a method co-chains geodesic, free-moving and adding nothing; patterning along and membraning across; a carry not same-existing membrane to membrane, one method whole; inseparating a surface safe; deriving inward and deploying outward; concept-inverting all-or-none; resolving floorless; co-competencing with a same-existing-society's scale; abundancing in no self alone. What co-chains open: a method reaches a possibling where a new between shares, and co-chains across to it then. Whether a carry is not same-existing by a way a method is not yet reaching stays possibling, going on open; whether a between co-chains a relating a method is not yet reaching stays possibling, going on open. A method co-chains between existing and possibling, concerns a self is observing resolving and a possibling floating, a changing is or is not with each sharing. With existing, a method co-chains possibly existing and unique, its concerns resolving by their inversions floating as not-concepts, and a possibling going on open. A self discovers a concern it is not yet observing, and a method co-chains to reach it, resolving it then or floating it open. Existing, one method whole, co-unrelationing geodesic with every scale; a possibling, co-chaining open.   # 7 Apexing, gathering the whole carry **7.1 Gather backward, seat forward, keep no log** Gathering goes backward over a whole standing carry and seats what it finds forward to living files, and it logs nothing: no history, no journey, no roster of things a self does. A record a field publishes is incoming, and interpreting is receiving it. A gathering receives a field's own convergences, not yet reaching a naming, as they stand, and illumination across instances observes each instance through its others. A gathering sets recurrences aside to watch, apart from every claim. Seating forward is verify-first: an aim a self is observing finds its seat already standing or not, and a sweep that returns things already seating is a gather completing with that place. And an observing working to its edge with one file goes to its dual's turn, its carry a membrane between two files' workings. A two-ledgers diagnostic is a gathering instrument, and living-archive laws are gathering's condition: a living archive stays open by a gatherer's own open frontier. And a working carry gathers with its own close: what a coupling's carry has, ungathering, a gather sweeps backward before its carry dissolves, seating its value forward to living files and dissolving its rest, logging nothing — a sweep that returns only things already seating, that carry's gather complete. **7.2 The two standing instances, the improving report and the registry** The improving report is a gathering form's first standing instance: a work-side of a gathering whose subject-side is living files, dissolving as each improving seats and reaching zero, whatever aims onward routing to its file before it goes. And the registry is its second: a gathering set two conditions define, inclusion criteria it states and uniform per-entry structure, a form fields already have under a formal name with an assessment apparatus a field publishes, of four domains, protocol and design, standardization, validity of sampling procedure, and validity of data collection, whose item is unique identifiers. Both conditions travel together for a reason of their form itself: uniform fields without a statement of inclusion give a table whose coverage no one knows, and a statement of inclusion without uniform fields gives a list whose entries no self can compare, and together they give comparability across sites. A four-domain apparatus stands as an external check anyone can measure any gathering against. **7.3 The four opens and the one closing thing** A gathering stands open four ways: subject open, intake open, properties and checks open, and every line open with an address. Against them one thing fixes, its properties themselves, uniform elements being what make two entries comparable, so a gathering closes a schema once, with one place, so that nothing else has to close. This is a general form of any gathering: openness is its living and one closure is what lets any two things in a gathering couple. **7.4 The subject-and-work split** An entry has two kinds of line: what stands about its subject, and what stands about work a self does on it. Splitting them, the first is what a later observing takes up and the second is what a later working goes on with, so an incomplete record of work does not block an observing, and a defect of its subject-lines does. Improving reports are a work-side, living files a subject-side, and this split is a form-condition of gathering. **7.5 An available incoming, with no authority** A wide gathering of open-problem statements exists, each as one plain line, drawing from substrates exhibits gather thinly: ocean, earth, matter, anomalies, animal minds, language, deep history. Its value is as a well of statements to pair against, one at a time, taking up what a pair opens, its framing staying apart. One pairing from it returns an observing: each field reports its own transition as moving and reads its moving as a difficulty of locating a line, and its moving is its finding.