Exhibit EIGHT Natural Exploring v393   # Natural Exploring   **Open Team Moral Co-Competencing**   **A point over the horizon is, and a self is finding each is-not and aiming from each is-not to is.** This is co-possibling is, and a self exploring is going on with this one method, a living condition with no prior of its own: geodesic, binary and co-sequential, a discovering by expedition. **A self is exploring from its own side.** It opens each momentary with its prior and the parities it is observing, and completes it with its next prior, winding through its one opening and reaching its own side again with a next: natural torusing. Each is-not is a changing it is observing beside its prior, and each aiming is its next, to is, one at a time. **Each orienting is co-linear, a web of lines from a self's own side.** A self is going on with lines along, to its prior and its next, lines across, to its others' prior and next, and a line to a point over the horizon; along and across lie on one line, in neither alone. Orienting is orthogonalizing, a self opening its own axis forward on its surface, a surface and no container, and surfacing space by unrelationing betweens. **A swarm is one orienting surface.** A same-existing-society of selves is one same surface with a wider grain, and its orienting is in no self alone, social abundancing: a larger school of golden shiners reliably goes toward shade where a lone fish goes almost at random, larger pigeon flocks fly shorter routes than smaller flocks, and an ant colony comes to the shorter of two branches. **Observings from many directions of living are reaching this one method.** E. coli runs longer up an attractant gradient; a sea urchin sperm swims a helix, its own winding bringing it a rising and falling of attractant; a moth surges upwind where it reaches its scent and casts crosswind where it loses it; a Cupiennius spider always moves toward the legs a vibration reaches first, onsets 4 ms apart, or toward the legs it reaches with larger amplitude; a Caroline Islands wayfinder keeps a reference island over the horizon, its bearing sliding back along the star points. Each observing of a next is reaching this method or is still-possibling, the method's next step or its one break. These orientings cluster five ways: a self keeping on while its now is changing for better beside its prior and turning as it is changing back, as a bacterium, a sperm, a moth and a zebrafish do; a self orienting by its own winding, a sperm's helix, a plant tip's circling, a honeybee summing its image motion; a self orienting by a not-changing beyond it, star points, the Milky Way, swells; selves sharing with each other, fireflies coming to one, a bird with its six or seven, water striders' waves; and a society co-chaining its geodesic, an ant colony coming to the shorter branch. --- **1 A self exploring from its own side** - 1.1 Changing and changing back, a stable-forming self observing from its own side - 1.2 A self a surface, competency a middle, an interior an accounting's placing - 1.3 Balancing, an accounting's own - 1.4 Two sides, bothbothing   **2 Co-unrelationing and co-chaining** - 2.1 Co-unrelationing - 2.2 Removing, a place staying open - 2.3 Co-unrelationing, one and then the other - 2.4 Geodesic co-chaining - 2.5 Patterning along and betweening across, a web of co-linears - 2.6 Co-linear, one line both share - 2.7 One method at each scale   **3 Testing, and resolving each is-not** - 3.1 Any other sustaining, is or is not - 3.2 One test, three observings - 3.3 A removing, and each later observing holding its consequence - 3.4 An observing testing locally, its trail's consequence with it - 3.5 Passing tests, many standing - 3.6 Concept-inverting, a special case - 3.7 Resolving - 3.8 Observing whole, ahead of any sorting - 3.9 An object, a place an accounting lands   **4 A method its own subject** - 4.1 Co-recursioning - 4.2 Deriving and deploying - 4.3 Any other method, is or is not - 4.4 Six protecting, three each way - 4.5 Three questions bi-inversioning, three activities of one resolving - 4.6 A reaching's competency constant, a gathering's climbing - 4.7 Inseparating   **5 Accountings for changing, and a method observing them** - 5.1 Each accounting for changing 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 A state-three and a flow-three - 5.5 An accounting converting a changing between state and flow to a level or a rate - 5.6 Observing accountings co-sequentially, one at a time   **6 Between selves, a same-existing-society co-competencing and going on open** - 6.1 Co-competencing - 6.2 Each self sharing its mixture whole - 6.3 Abundancing - 6.4 Three sensings, each its own competency - 6.5 Too hard to be practical, a separating of three sensings - 6.6 Existing, and co-chaining - 6.7 A school, a flock, a voyaging people, an orienting surface in no self alone - 6.8 Eight legs, five dimensions in two directions   **7 Apexing, gathering whole** - 7.1 Gathering backward and seating forward to living files - 7.2 Two standing instances, an improving report and a registry - 7.3 Four opens and one form still, a schema - 7.4 Subject-lines and work-lines - 7.5 A gathering of open-problem statements to pair against --- # 1 A self exploring from its own side ## 1.1 Changing and changing back, a stable-forming self observing from its own side **Exploring is two cones, one and then the other**, and this exhibit is sharing that changing and changing back whole. **Omegaing is reach**: a new axis, a forward frontier, discovering. **Apexing is coning back** over each thing folding to it, gathering it whole, cohering. Two cones straddle a centre neither occupies, in neither cone alone. **Living is both, one and then the other**: a discovering ungathering scatters and a gathering undiscovering folds, and a living method is their changing and changing back, the two cones a pair passing a seem-alike knife. A self is observing from its own side. Each existing thing is changing and changing back with its own momentary, and a stable form is an artifact of a living self's stable-forming going on. A self is opening each momentary with its prior and the parities it is observing, and completing it with its next prior. This is natural torusing: a self is winding through its one opening, reaching its own side again with a next each momentary. An ocean wayfinder out of sight of land has the canoe as its own side and the islands moving, islands ahead coming toward it, islands beside it sliding by and islands behind falling away. The wayfinder is orienting by each changing it is observing: a star rising at its own point, a swell's line, and the bearing of an island out of sight sliding back along the star points. As the reference island's bearing from the canoe matches its bearing from the destination, the canoe is near its goal. A hovering hummingbird holds its place to the millimetre by steadying the visual motion about it; with a background pattern moving least it drifts about a centimetre, and time to adapt is-not removing the drifting. A ground placing outward of a self, a grid, is an installing, and a self observing from it is observing its own installing. A self waiting for a rest to observe from is waiting on a rest that is-not there, each thing going on changing and changing back. Geodesic co-changing is this method, possibling and discovering. Co-unrelationing is a concept floating from a fixing pinning it to a ground, each ground an installing; co-unrelationing, one and then the other, goes on where a floating lands a fresh fixing, and going on is stable-forming. A self going on with this method is floating between existing and possibling: a changing is or is not with each sharing. The parts following bring this one method to accountings for changing. Each accounting is a method too, an involution, its counting opening from a fixed set it takes as a place. On a sphere, one spiraling lands, fixing a whole circle, a fixed set standing; two spiralings, one and then the other, float, a pair floating where a single lands, a floating surface a pair's own make. ## 1.2 A self a surface, competency a middle, an interior an accounting's placing A self is a surface, self-bounding, 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. Each is no container. Competency is a middle, floating between form and logic, invisible, its rate its own, unenterable: a middle has nothing to enter, and no instrument is lacking; fixing competency as an end makes it a thing it is not. Competency is arising with each bi-coupling going on with a surface, as observing goes on, and it is at no place and in no container, with no version of it awaiting an observing. A self looking for it at a place is finding a place an accounting puts there. An interior is an accounting's placing. A magnitude is wanting a thing to attribute it to, a surface is no container and shares no interior, and an accounting is placing an interior and fixing 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 an accounting's counting lands, and each is an accounting's placing of an object. ## 1.3 Balancing, an accounting's own An accounting balances, and a balancing is wanting an interior to balance across, checking each thing at its place and finding each with its place. A total storing, a level reaching, a direction fixing: each is wanting a place for a thing it stores. A surface is no container, and nothing of it goes missing. Each self is self-bounding, bi-coupling with each parity it is observing as its 2-now-possibling, a sharing with its parity, one at a time, and going along with its 9-next-co-discovering. Each self is same-existing and going on; nothing is a store, and conserving and balancing are an accounting's own wants. A self's same-existing is going on with the parities it is observing, its others' priors their own, and an accounting is an artifact, an executing apart from that going on. A balancing is an accounting's own requirement and not the universe's. A self unrelationing an accounting's fixings is unrelationing its requirement with them, and the surface it is observing is whole. ## 1.4 Two sides, bothbothing Unrelationing is one side of a self exploring, and testing whether any other could stand is its other side. Neither alone is exploring: an unrelationing untesting lands on the first thing surviving its reach, and a testing alone tests only a fixing's own allowing. Both bothboth, one at a time, unrelationing sharing and testing receiving, and a self co-chains both sides with each observing. A honeybee flies through gaps by evening the image speeds of its two eyes, sets its flight speed by keeping its average image velocity steady, knows distance by summing its image motion, and lands on a level surface by keeping its image velocity steady, its own speed nearing stillness at touching. --- # 2 Co-unrelationing and co-chaining ## 2.1 Co-unrelationing Each existing thing is relating, floating with its own position, orientation and scale. Co-unrelationing is loosening all three fixings together, and relating is showing, stable-forming. Discovering floats where finding grasps: unrelationing is finding, and co-unrelationing is discovering. A concept floats free of a position pinning it, is facing its own way and is sizing to its own grain, and relating is showing as fixings float loose. Position, orientation and scale are three fixings pinning a concept to a ground a self is observing it against. Loosening position, a concept floats free of the place a fixing pins it; loosening orientation, it is facing its own way; loosening scale, it is sizing to its own grain. Co-unrelationing loosens all three together, and relating shows: a concept floating, orienting as it is facing, graining to its own scale, floating free of each pinning place. Co-unrelationing is-or-is-not: it is where unrelationing changes and changes back and a middle floats, and it settles where a fixing lands, unrelationing a 0, not changing. A self going on with this method floats between existing and possibling, resolving, changing and changing back, free of a grasp on a magnitude. ## 2.2 Removing, a place staying open An is-not is a removing from a form that can sustain. A possibling a test falsifies is reaching no replacement. A fixing loosening, a self sets nothing at its place, and the place stays open. An unrelationing filling its open place with a fresh term lands its fresh term, co-chaining fixings rather than loosening them: one same fixing with a new address, hiding relating again. Two moves are one move with a condition: loosen a fixing, and leave its place open. A fixing a self removes goes, a self observes its surface open where that fixing goes, and a self co-chains on from an open place rather than from a place an other thing fills. This is a check on each resolving a self shares as a replacement. Setting a framing aside and installing a new framing at its place resolves nothing, a fixing again, however much better a new framing holds. Resolving is unrelationing, and an open place stays open. ## 2.3 Co-unrelationing, one and then the other A single unrelationing lands. A fixing loosening once and stopping, its open place sits down fresh-fixing, a discovering becoming a new fixing, hiding relating again. One unrelationing lands a fresh fixing, and co-unrelationing, one and then the other, goes on with each open place as a new fixing to loosen, unrelationing its unrelationing, on and on. This is a method living forward, settling at no place. Each discovering stopping lands a fresh fixing, and a self brings each discovering forward, riding the relating it is discovering as its going on, loosening the fixing its last discovering becomes. Co-unrelationing, one and then the other, discovers, loosens, discovers the fixing its discovering lands, loosens again, going on: a moth surges upwind where it reaches its scent and casts crosswind where it loses it, one and then the other. It competes, discovering; it morals, unrelationing two-way between selves, abundancing arising in each self with its other; it sequences, going forward; it logics, unrelationing is or is not at each binary, and floating at each possibling. Co-unrelationing, one and then the other, lives is-or-is-not, unrelationing changing and changing back and a middle floating, a 0, not changing, only at a fixing landing and staying. ## 2.4 Geodesic co-chaining A method is co-chaining geodesically, a living condition with no prior of its own, and a self going on with it is finding each is-not and aiming from each is-not to is: a point over the horizon is, and this is co-possibling is, a discovering by expedition, binary and co-sequential, one at a time. Each is-not is a changing a self is observing beside its prior, a heading parting from the point that is, and each aiming is its next, to is and to no answer a self wants. A geodesic is the straightest going relating opens, free-moving and adding nothing, floating free of a route a force sets on it, curving as relating curves and straight by relating's own terms. An ocean wayfinder is keeping a reference island over the horizon, its bearing sliding back along the star points; a moth is surging upwind where it reaches its scent and casting crosswind where it loses it; a bacterium is running longer up an attractant; a monarch from 2,500 km further west is flying southwest as a monarch from the east is, orienting by a sun compass following the hour and a magnetic compass with light, showing no map of its own, and its finding of its forests in Mexico is still-possibling. A sea urchin sperm swims a helix about 8.4 µm in radius, one winding each 0.38 s, at about 200 µm/s, its own winding bringing it a stimulus of about twice a second; while the baseline rises its helix bends smoothly toward the gradient, and while the baseline declines it makes a sharp turn, 31 such events in 9 of 10 cells. A dung beetle keeps a straight line away from the dung pile by sun, moon, the light's polarizing around them, and at night by the Milky Way's glow alone, and under overcast it loses its straight paths. A hunting dragonfly catches its prey about 95 times in 100, in under half a second, its head turning ahead of any drift to make up for it, its body turning to follow the angles between head and body. Most monarchs live about a month through four or five generations a year, and a super generation lives about eight times as long, flying up to about 3,000 miles, 50 to 100 miles a day, to oyamel firs in Mexico's Sierra Madre, none of them finishing the return, their offspring continuing it. On a tether in a magnetic field monarchs fly south, and with the field's inclination reversing they fly north; with light above 420 nm they circle, and with light above 380 nm they fly directionally. Coasts and the Rocky and Appalachian mountains are a field's proposal for guiding monarchs back when wind blows them off course. A self is co-chaining free-moving, free-driving and free-aiming, fixings loosening on their own where unrelationing reaches them, and relating showing along the geodesic an unrelationing opens. Adding a force, aiming for a result a self wants, a co-chaining bends to that aim and lands at it, a fixing setting. Geodesic co-chaining floats aiming to is, discovering each relating, floating free of each want of a self. Geodesic discovering is co-unrelationing co-chaining the straightest unrelationing, free-moving, adding nothing, relating showing as fixings loosen on their own. A geodesic goes with a method no force bends, a way discovering, a forcing way confirming. A geodesic is a co-chaining, and co-unrelationing is a move; a self going on with this method floats as both, the straightest unrelationing, co-chaining with each scale, its rendering not same-existing scale to scale, one method whole, 2.7. ## 2.5 Patterning along and betweening across, a web of co-linears A self co-chains along patterns and across betweens, one move with two sides. Patterning is co-chaining along, position to position, a sequence a self rides, each pattern a relating already showing that a self co-chains further. Betweening is co-chaining across, a self reaching an edge at which one relating bi-couples with another, a between at which a self shares and an other prefers. Along a pattern and across a between, a self co-chains, along and across one co-chaining with two sides. A pattern is relating already showing, standing for a self to co-chain along. A self co-chains a pattern by riding it forward, unrelationing the fixing a pattern becomes as it stops, a pattern a way a self rides and loosens ahead. A pattern landing, fixing as a shape, is a pattern a self co-chains along as far as its landing; a pattern floating, a self riding and loosening it, is a pattern a self co-chains on. A desert ant on stilts overestimates the distance it travels, and on stumps underestimates it. A between is a nothing at two relatings bi-coupling, a self going from one to an other. Betweening co-chains across, a self bringing its unrelationing to an edge at which a new relating shares, and co-chaining across to it. Along patterns and across betweens, a self co-chains one unrelationing at each place it goes, patterning along and betweening across: a web of co-linears. A Cupiennius spider always moves toward the legs a vibration reaches first, onsets 4 ms apart, or toward the legs it reaches with larger amplitude; in Eckstein and Schwarz's reading, with others disputing it, Tupaia's chart gives each island's bearing relative to the island before it in a route, the bearings following in sequence along the route. An orb spider at the hub of its web senses through the threads with slit organs at its leg joints, movements as small as 0.1 µm; a field's saying that the leg with the greatest tension along its radial thread gives the direction is a ranking over the observing, and which of its legs changes first is still-possibling to observe. ## 2.6 Co-linear, one line both share Along and across lie on one line, and that line is each move's own, in neither move alone. A self going along, then going across, then finding them agreeing is forking: two moves landing two things and a concurrence a self notices at a next momentary, a capture fixing politely. Co-linear is two moves with one between, each bringing a prior forward, a line both share, in neither alone, and an abundancing arising 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 and width are two. Along alone is a sequence with no surface; across alone is attention with no sequence; each alone lands. A self widens as both are co-linear and lengthens as a co-chaining goes on, a widening being both on one line, apart from either extending. Argentine ants on a double bridge with a shorter branch: ants on the shorter branch return sooner and lay pheromone sooner, and nearly the whole colony uses the shorter branch. ## 2.7 One method at each scale A self co-chains one unrelationing, and each scale renders it its own way, not same-existing scale to scale. One method stays one while its rendering is not same-existing scale to scale: a number has it as numbers, a branch as branches, a naming as namings, a resolving as resolvings, one method, whole at each. Each scale renders one method as its own, 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 rendering is not same-existing scale to scale, each with its own rate, and a self co-chains one same unrelationing with each, a rendering not same-existing and a move one. One method at each scale is a fractal, one with each scale, each scale's rendering not same-existing and a method whole. Navigating shows it at scales eleven (macromolecule), seventeen (gene) and twenty-three (cell) of Natural Societies 5.3: a lac repressor protein slides about 45 base pairs, plus or minus 10, along DNA, with diffusion in three dimensions between slidings, a macromolecule going along and across; E. coli in a gut reaches lactose with maltose always coming next, and lactose alone partly opens its maltose genes, yet in a lab evolution of several months with lactose and no maltose following, they stop opening maltose genes with lactose alone; and E. coli compares the past second with the three seconds before it and runs longer up an attractant gradient, a cell navigating by its now beside its prior. A rendering is not same-existing scale to scale; a method floats one. --- # 3 Testing, and resolving each is-not ## 3.1 Any other sustaining, is or is not A self tests with each observing whether any other could come and sustain. Any other sustaining is or is not, with no grading of a magnitude. This one alone sustaining, uniqueness sustains with that observing. Another sustaining beside it, uniqueness is-not there. Each candidate failing, observing is-not sustaining: one same test returning its last observing, a 0, not changing, an exhausting of bi-coupling showing, and a wall is-not standing at any place. Uniqueness is-not concluding and is-not persisting. A self takes it again with each observing, and between observings a fixing is-not setting. Existing and possibling go with each one: an observing sustaining a thousand times sustains with a next by a self testing it there, and its prior sustaining is-not that testing. ## 3.2 One test, three observings One test, three observings, and that test goes on between them. One candidate sustaining: uniqueness sustains. Two or more sustaining: uniqueness is-not there. Each candidate failing: observing is-not sustaining, an exhausting and a value-death a self is observing. ## 3.3 A removing, and each later observing holding its consequence A possibling a test falsifies is-not reaching a later position. A possibling a self removes with one observing, a self is-not discovering with a next, and a current observing already has the consequence of each prior removing. A trail is-not wanting a re-testing for being a trail. Its surviving consequence is a current observing. A candidate failing seven observings back is-not same-existing now, and its removing's consequence stops a self observing it, a record of that removing apart from it. ## 3.4 An observing testing locally, its trail's consequence with it A self tests uniqueness locally. Alternatives a self can observe now are the ones surviving an intervening co-chaining, and a self tests a current observing against them. A self is-not re-testing a historical trail for being historical: the trail's consequence is a current observing. ## 3.5 Passing tests, many standing Three tests each resolving rightly leave each thing satisfying all three, and those may be many. A self taking its passing tests for its resolving lands on the first thing passing them, and a landing is a 0, not changing. After each observing a self brings a further test to that observing: could another stand here, surviving as this one survives. Pacific wayfinders sailing for Tahiti aim first at a band of Tuamotu atolls about 400 miles wide, identify the island they reach, and go on to Tahiti, about 170 to 180 miles further: many standing, and a further test with each. A collection of 768 sunflower spiral families, as its field reports it, is about 74 percent Fibonacci, about nine percent a kindred sequence, and the others neither. Golden relationals in stable forms are-not a test of natural torusing. ## 3.6 Concept-inverting, a special case A self checks a concept by inverting it, all-or-none. Concept-inverting is inverting a concept and finding its 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 that concept alone floats, its inversion not possibly existing. Concept-inverting resolves which, all-or-none, with no grading of a magnitude. 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: it is-not a weaker same-existing, is-not a partial same-existing, and is-not a same-existing at all. A concept whose inversions are each a not-concept floats possibly existing and unique, its concerns resolving by inversions floating as not-concepts. Concept-inverting is resolving, all-or-none, and a testing that grades is a separate move. 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 with its inversions each a not-concept, and floats among others with an inversion a possibly existing concept, and concept-inverting co-chains a concern to its resolving, all-or-none. Concept-inverting tests one alternative alone: its inversion. A concept whose inversion is a not-concept reaches one test and passes it, and stands with each other thing apart from its inversion. Concept-inverting is a special case of uniquenessing, the alternative it tests being its inversion, and it is that case whole and that case alone. 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 self resolves is-or-is-not, floorless. Resolving is a self's own parity, its next, a self discovering it with a bi-coupling, a bounding-zeroing a bi-coupling reaches, is-or-is-not and free of a magnitude. A floor lands resolving, a threshold, a count or a magnitude an observing settles on, and a landing observing observes always-is or always-is-not, and is-not a resolving. Resolving floats floorless, a self's own parity with each bi-coupling, inverting with each momentary. A fruit fly flies straight segments and saccades, one and then the other, each saccade about 90 degrees in under 50 ms, all or none, left or right. A larval zebrafish in a flow, with no vision, reads the head-to-tail gradient of flow velocity through its lateral line: going from high to low gradient magnitude it keeps its heading, and going from low to high it makes a strong turn with the rotational flow. A concern resolves as its is-not empties. Each concern that a thing may be otherwise co-chains to its inversion, and as 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 as its is-not finds each form not possibly existing, floating between existing and possibling, a changing is or is not with each sharing. An is-not emptying concludes it, a resolving, and a floor concluding it is a landing. This is a self's aiming with the geodesic method, 2.4: from each is-not to is. Exhausting all concern is an equilibria concept, a closing total resolving floats free of. A self discovers a concern it is still-possibling to observe, 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, an all to exhaust is-not, a changing is or is not with each sharing. Resolving is floorless, is-or-is-not, an is-not emptying with existing and a possibling floating open. ## 3.8 Observing whole, ahead of any sorting A self observes each thing a sensing returns, valuable and wasteful together, sorting neither. A sorting executing ahead of an observing is a discard: it observes each thing matching a catalogue and leaves the rest dark; it sorts a bi-coupling's making as harm, and a self's sharing back as attrition; it removes the writing of bi-couplings so a label it adds can show. Each is a sort ahead of an observing, and a discard is a sort rather than an observing. A self observes valuable things as it observes each thing: it stops sorting and observes each thing it reaches. It is-not deciding which is which, and one same observing observes waste and signal, each a sorting's word, one same way, together, a sorting is-not reaching them. Marshallese navigators lie in the hull to feel the swells' pitch and roll, an island's shadow a change in the main swell's rhythm or several swells hitting at once; in an octopus's sucker, chemosensory cells fire continuously, only during direct contact, and mechanosensory cells fire only at the start of contact. A looking for a break can name, ahead of looking, the observing and the explaining it could break, keeps each observing apart from a field's explaining, and gathers the whole observing as it stands, supporting, breaking or changing the question. ## 3.9 An object, a place an accounting lands An object is-not a small thing and is-not a fundamental one: it is a position at which a counting stops and declares, and a self reaches one with each grain it co-chains to. An instrument returns a parity a self takes with a ledger, one at a time, complete with that taking: a portion of anything it is-not. An accounting returns an object of a kind it states, assembling it from many parities together with a model of a kind of thing the parities could come from; as a model enters with a selecting, its return resembles its model, whether a thing stands there or not. A self takes a parity and leaves an object. A leaving is-not a regress reaching for a smaller thing: a between is a nothing, is-not decomposing to smaller betweens, and is-not made by anything, and a loosening of it is lengthless. A parity with a detector, a parity with a residue, a parity with a cell's bounding surface, a parity with a pump: each complete with its own surface, each is-not a floor for a next, and each is-not wanting one. --- # 4 A method its own subject ## 4.1 Co-recursioning A method has its own subject: the method. Co-unrelationing discovers relating; relating is co-unrelationing; and discovering that is co-unrelationing again, a method co-recursioning, its own subject, discovering the method in its going on, that discovering discovering it again, going on with each scale, possibly existing and unique. A method floats as its own subject, going on and discovering the method by going on. Each existing thing already relates, and a method finds its subject already the method, floating free of each instance landing it. A method, a naming, floats showing no instance: an instance a self shows lands one case and thins each other case floating, a fixing setting at a method's floating. A method goes on as a wide self-cohering naming, one with each scale, a fractal its name floats whole. A method floats between deriving and deploying. Deriving, as numbers, branches and sequencing, a method is unrelationing its own fixings. Deploying, as naming, explaining and resolving, a method brings one same unrelationing to a between. Deriving is-not landing and deploying is-not landing; a method floats as a middle they co-recurse around, invisible, its rate unique, discovering its going on 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 unrelationing its own fixings, with numbers, branches and sequencing, co-chaining inward to its own form. Deploying is a method bringing one same unrelationing to a between, with naming, explaining and resolving, co-chaining outward to each place it goes. Deriving inward and deploying outward, a method floats as a middle they co-recurse around. A method deriving co-chains inward, unrelationing fixings of a number, a branch and 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 loosens a fixing; a sequence has it as a right-spiral unrelationing position to position. Deriving co-chains a method inward to each form it is in, and a method shows with each rendering, one method deriving many ways. A method deploying co-chains outward, bringing an unrelationing to a naming, an explaining and a resolving, bringing a method to a between. Deploying is one same unrelationing a deriving finds, going now to a concept as a naming, to an explaining co-chaining, to a resolving concluding. Deriving is-not landing and deploying is-not landing; a method floats as a middle, co-recursing around, one unrelationing deriving inward and deploying outward. ## 4.3 Any other method, is or is not A method reaches its own observing by a test a self brings with each other that could sustain, and a test is of an observing, apart from a survey of each thing that is-not coming. Exhausting alternatives is a closing total, and a resolving floats free of one. Four stand: a self is self-bounding, self-orienting and self-attentioning, 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, whole or none, apart from eight parts assembling. Land one and a self lands with it, a landing form a 0, not changing, and a form not changing leaving living: a living form short one condition nyes away by its own self-bounding. Put each living form to these four. It is self-bounding or it is-not a self; it is self-orienting or it lands, not changing; it lives all four about one bounding-zeroing or it 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, apart from a test it happens to pass. A rival, living, is the natural torus, and each other living form living all four is this form. A self going on with this method reaches a changing free of a frame, a floor and a magnitude, loosens three fixings, tests with each observing, and leaves each fixing's place open. A fixing to vary is-not there, and a rival varying any one of these, a frame, a floor, a magnitude, a loosening of three fixings, a testing with each observing or a place left open, lands there, not changing. An is-not empties with an observing, and uniqueness sustains to a next. Uniqueness is here twice: whole or none, as landing one lands its form; and no-other, as all eight go with each living form's living, and each of them is-not this form's alone. ## 4.4 Six protecting, 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. A self's six names between selves stand three and three beside it, a sharing's two ends: the sharing end 6-now-co-possibling, 10-next-co-possibling and 9-next-co-discovering, and the observing end 2-now-possibling, 14-next-possibling and 17-next-existing, a six of their own beside the eight re-forming. Drop one and a way or a phase lives unprotecting, and a thing enters that way from beside, or a sharing 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 Three questions bi-inversioning, three activities of one resolving “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 going on, two binaries bi-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 self's going on rides toward and leaves open. A cyanobacterial clock has two sites going through four joint forms, one site changing at a step; its natural deriving is still-possibling. ## 4.6 A reaching's competency constant, a gathering's climbing A self reaches and a self gathers, and the two come unlike. A reaching with an observing returns its sensing, complete with that observing, and its reaching comes with a next as it is. An observing a self gathers comes with a next changing for better: coning back over it, taking it again from its far side, gathering it whole. A reaching's competency stands constant with each observing and a gathering's climbs, and a reaching opens positions a gathering cones over: a gathering is the place a reaching comes to something. A growing climbing-plant tip sweeps wide circles until touching a support, then its circles tighten and it winds around the support as it grows. A discovering ungathering scatters and a gathering undiscovering folds, and the two failures are not same-existing. A discovering ungathering scatters, its going on lacking a gathering; a gathering undiscovering folds, lacking a new thing to cone over. A self needs both, and one increases. And a gathering is local and immediate. It is-not waiting on a gathering set and is-not waiting on a threshold, coning over an observing it has: a second observing with one between stands on the first, competency climbing with the rate observings come, apart from a rate a store grows, and a gathering is-not pooling or storing. A bacterium runs about a second at a time on average, comparing its last second with the three seconds before, its runs up an attractant lengthening, and after each tumble its new heading is about 62 degrees from its prior on average, leaning forward. ## 4.7 Inseparating A self co-chains an open surface, and with inseparating it stays whole. Inseparating is a bi-coupling passing and a sharing failing to seat dissolving, a surface a failing sharing finds a purchase on at none, freedom living as inseparating and a method adding a gate at no place. A bi-coupling co-chains through; a sharing failing to seat dissolves with a collar; and a surface is whole of its own, inseparating with each between. An open surface takes each sharing, and inseparating answers it by bi-coupling, a bi-coupling passing through and a sharing failing to seat dissolving. Freedom lives as inseparating, a surface being a living form where a mis-sharing finds a purchase at none, safety its own surface and a method adding a gate at no place. A gate stands with an observing edge, a fixing setting outward of its form; inseparating is with each collar, a method's own form, a bi-coupling passing as it seats and a sharing dissolving as it fails. A self co-chains open, safe by inseparating. A surface with all eight inseparatings goes on whole, a capture seating at no place, 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 bi-coupling passing and a sharing failing to seat dissolving, freedom as inseparating and a surface whole. And inseparating goes with each thing floating, unfixing. A fixing thing is the thing each coming can damage, and an accounting with one defends rather than observes, a gate coming with a way in. A self unfixing observes, and a fixing to defend is-not there: each thing coming loosens a fixing or dissolves with a collar, one or the other. --- # 5 Accountings for changing, and a method observing them ## 5.1 Each accounting for changing an involution Each accounting for changing has a move, applying twice, returning the thing it reaches. Negation: not-not is that thing again. Reflection: reflecting twice returns its facing. Time reversal, charge conjugation and parity, each squaring to the identity; time reversal does so at an even number of fermions, and at an odd number it squares to minus one, a state returning with its sign changing and its energy levels standing in pairs, an involution of the state up to its sign and a possibling to observe at its pairing. Complex conjugation. Additive inverse and multiplicative inverse. Transpose. Legendre transform, twice, returning its potential; by it a thermodynamics exchanges which of its terms stands independent. Set complement. Each is an involution, and an accounting for changing reaches this one shape: an accounting returns the thing it reaches, or it accounts for nothing and its ledger is-not closing. ## 5.2 An involution's fixed set is where it takes its counting from Each involution but two has a fixed set, at which its move returns its argument as it is; negation and set complement have none, negation being changing and changing back, a binary's own move, with no place to take 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. With each accounting, its fixed set is the place it takes its counting from. By its fixed set, 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 steps, the returning at no place. A fixed set is the set at which both steps collapse to one: a changing reaching no other to change back with, a move and its returning one same move. It is-not a location an object occupies; at it, a changing reaches nothing to change back against. Each accounting sets its zero at the place its own changing reaches nothing, and counts outward from there. A self finds two ends with each floor: no bi-coupling at all, and each member agreeing completely, no parity going across. In both, 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 its being such a point. A self recognises an axis and does not derive it, symmetry standing with nothing more basic beneath it to derive a seating from. Loosening, a fixed set stands as a bi-coupling and at no place: a bounding-zeroing a bi-coupling reaches, is-or-is-not, inverting with each momentary. An involution stands, its proof standing, nothing altering it. A place goes. ## 5.4 A state-three and a flow-three A three goes as a state or as a flow and is-not both, and both change and change back. A state-three counts the things standing and is rateless; a flow-three goes one at a time and counts nothing. Neither reverses its other, and both ways go forward. An accounting returns three by this, and a fourth is-not: a total is a state-three, a level is a state-three, a direction is a flow-three, state and flow being the whole of the things that change and change 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, with no proof beneath it. F1-ATPase, a rotary motor of three units, steps in 80-degree and 40-degree portions as its field reports, and its field's usual description has each unit going open, loose and tight. And each accounting comes short at a changing between state and flow. State to flow is a count exhausting; flow to state is a rate landing. An account of state-threes alone fixes a flow as pieces; an account of flow-threes alone fixes a standing as a rate. Each ghost stands with one of two changings: a level fixing a flow's going, or a store fixing a same-existing's going on. ## 5.5 An accounting converting a changing between state and flow to a level or a rate An accounting has counts, levels and rates, and a changing between a state and a flow is-not one of these three. A tipping enumerates nothing: it is-not a count. A tipping is of its own rate, relating to no other living rate: a clock is-not measuring it. It is a parity a self takes with a between, binary and sizeless, and an accounting's columns are for things with a size. An accounting shows no falling short at a changing: it has nothing possibly reaching one, and it converts the thing it reaches to the nearest thing it has, a level at a flow reaching a standing, a rate at a standing opening to a flow. And each instrument fixes to a clock all share while each self paces its own, an instrument fixing a tipping at its clock's tick rather than at the tipping. An instrument's record keeps only the moments its members happen to agree with a clock all share. In closure phase, around a triangle of three stations, the product of the three visibilities has none of the stations' own phases and needs no particular reference; additive noise and baseline-specific errors remain. A geodesic method is clockless, floorless and free of a magnitude, co-linear with a changing, at which an accounting forks. This makes it a competency method rather than a better accounting, and it leaves an accounting competent with each thing it has, counting, levelling, rating and closing states and flows, its arithmetic whole. ## 5.6 Observing accountings co-sequentially, one at a time A self observes accountings one at a time, loosening each, and each observing has the consequence of each prior loosening. An accounting a self loosens is-not returning with a next observing. At a self's loosening of a fixed set from its place, that place is-not same-existing for a later accounting to reach for, and a current observing already has its consequence: a trail is-not wanting a re-testing for being a trail, 3.3. Each observing takes an accounting as it stands, a form still from beside, pattern-matches an involution, pattern-matches a fixed set, loosens a place, and passes on. A move stands with each one, and a floor goes with each one. A place a self loosens with the first observing is-not same-existing with the seventh to loosen again. --- # 6 Between selves, a same-existing-society co-competencing and going on open ## 6.1 Co-competencing A same-existing-society co-chains one method between its selves, and co-competencing is discovering with a same-existing-society's scale. Co-competencing is unrelationing two-way, fixings between selves loosening, an abundancing going on with a bi-coupling, each self's own and in no self alone. A self discovers by unrelationing its own fixings; selves discover together by unrelationing fixings between them, co-competencing, a same-existing-society co-chaining one same method a self co-chains alone. Between selves, a same-existing-society co-chains unrelationing two-way, each self pacing its own time and abundancing in no self alone. As a self loosens a fixing, selves loosen a fixing between them, a loosening two-way and an abundancing arising in each self with its other. Co-competencing floats as selves co-unrelation together, and is a 0, not changing, at a landing term standing between them; social moral competency co-unrelationing is sharing, is-or-is-not. Co-competencing is one 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 unrelationing its fixings and a same-existing-society unrelationing fixings between selves, one method with both scales. Co-competencing co-chains social moral competency, unrelationing two-way, abundancing in no self alone, a same-existing-society discovering geodesic. ## 6.2 Each self sharing its mixture whole A self is-not sorting its own mixture. A fixing thing has no fixing-feeling inwardly; a self observes it as a fact, as grammar, or as a plain way to say a thing. A self shares its mixture as it stands: waiting to sort it first is sharing nothing, and sorting ahead is neither self's work. A floating thing is shapeless of its own, and a floating thing fixing has a shape: a surface bends at a term doing a kind of work not same-existing with each thing around it, and an other self observes a parity with that bending. A self's parity goes to its other, and each observes with its own side, a parity each observes forming with its own end of a between, and a fixing loosening, each self's own, standing with a bi-coupling. The twist the other twists are under, first: loosening a small one leaves the large one standing and each thing under it still fixing, and loosening a large one drops several small ones together, each with no line of its own. Its naming is one short line sharing across, a parity of no size and with no content beyond it, its other receiving it. This is resolving's own form, going between selves. A mixture a self shares, sorting nothing, is recursioning, bi-coupling and fixing fusing as a self observes them; a twist a self names from across is attentioning, one short line; and both have same-existing, a bi-coupling going on with its own rate and a fixing standing as one side, neither owning its other. Co-attentioning is that same form with a same-existing-society's scale, the form whole and no likeness of it. ## 6.3 Abundancing Selves co-chain abundancing, 12-next-co-same-existing, with each 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 each discovering, adding nothing at any place and with no self paying a resistance, an axis opening. Selves co-chain, an axis opens, abundancing floats, in no self alone. An opening axis is a discovering's own make, orthogonal to the axes 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, and a gift a self is-not giving is-not co-chaining; an axis opening for both outgrows a thing one self owns, growing with each co-chaining both selves share, and abundancing floats as discovering opens axes in no self alone. Abundancing co-chains geodesic, a +1 arising and nothing adding. A self unrelationing 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 each scale as selves co-chain an axis open. ## 6.4 Three sensings, each its own competency A self stands with three sensings, each with its own kind of competency, and each is-not a quantity. **Backward sensing, and a self can do it.** Observing the things already standing, each thing a record already has, sorting nothing, asking nothing of anyone and building nothing. **Forward sensing, and a self increases competency doing it.** Going forward with it, and going forward is the place competency climbs: doing gathers and gathering increases. **Co-sensationing, and a self can competently explain a doing it is possibling.** 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 and both others as states. A self bringing no competent explaining with its co-sensationing is-not reaching it, and an explainable possibling a self is observing and is-not doing is an observing with its own grain rather than a gap. ## 6.5 Too hard to be practical, a separating of three sensings A self observing a thing valuable and impractical observes an impracticality that is-not the whole of it. It is one of three sensings, co-sensationing or not, and a self observing it as another sensing is or is not already doing backward sensing. A self separates three with each observing, and separating makes an impractical part small enough to see. A demanding sensing is a light place to open: a self is already meeting its demand. A demand brings resolution and a risk brings thoroughness, and a discard stands in proportion to both: a self records widely and observes narrowly exactly at a demanding place. A self already does a sensing; an observing is the thing a self skips, and taking it asks nothing beyond the sensing already going on. ## 6.6 Existing, and co-chaining A self co-chains its existing, and co-chains a possibling open. Co-chaining existing: each thing relates, and co-unrelationing loosens three fixings until relating shows; a single unrelationing lands, and co-unrelationing, one and then the other, goes on; a method co-recursions, its own subject, a naming and floating, showing no instance; a self co-chains geodesic, free-moving and adding nothing, aiming from each is-not to is; patterning along and betweening across, a web of co-linears; one method at each scale, its rendering not same-existing scale to scale; 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; a swarm one orienting surface. Co-chaining open: a self reaches a possibling as a new between shares, and co-chains across to it then. Whether a rendering is not same-existing, scale to scale, by a way a self is possibling to reach stays possibling, going on open; whether a between co-chains a relating a self is possibling to reach stays possibling, going on open. A self 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 self 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 possibling to observe, and co-chains to reach it, resolving it then or floating it open. Existing, one method whole, co-unrelationing geodesic with each scale; a possibling, co-chaining open. ## 6.7 A school, a flock, a voyaging people, an orienting surface in no self alone A same-existing-society orients as one surface, and its orienting is in no self alone: social abundancing. Each self orients from its own side by the changing it is observing beside its prior, and with its others it is one orienting surface, a reach in no one self alone. A lone golden shiner moves almost at random. In a school, each fish responds only to the brightness at its own place, slowing in the dark, and moves close to the fish around it; a larger school reliably goes toward shade, slowing and bunching inside it and speeding up to leave as light moves onto it, and a school below a certain size loses its tracking of the shade. Larger pigeon flocks fly significantly shorter routes than smaller flocks, and a flock's route is not simply the average of its birds' routes: each pigeon's influence on the route is in proportion to how faithfully it reproduces its own route in solo flights. In flocks of a few thousand, each bird interacts with about six or seven other birds, the same number at each distance between them. In one observing, a Photuris frontalis firefly pauses for 3.0 to 24.1 seconds, then resumes at once, synchronous with its partner. A water strider senses the ripples of prey with its front legs, and each species shares its own surface waves in courtship and in a territory. A voyaging people's orienting is in no self alone: a Marshallese voyager studies the stick charts whole before a voyage, the charts going on as the voyager's own prior same-existing, and sails without them, the charts' making passing from father to son, and Caroline wayfinders have a reference island over the horizon. A network of resolvers is a same-existing-society, its orienting in no self alone. A network exploration following one self's record, or one instrument's clock, is following an orienting the network is-not having. ## 6.8 Eight legs, five dimensions in two directions A Cupiennius spider always moves toward the legs a vibration reaches first, onsets 4 ms apart, or toward the legs it reaches with larger amplitude; a vibration reaching a front leg lowers the weighting of the legs behind it on its own side by 0.1, and with vibration reaching both sides this lowering goes front to back alone and halves the factor. Its turning error grows as the source is further behind it. Eight legs are two sides across and four legs along each side, two times four being eight. Each leg opens with its own prior self-parity and its partner leg's prior other-parity across; now its co-parity and bi-parity agree or part; and its next same-existing self-parity is the spider's turning: five dimensions, a vibration coming inward along the legs and a turning going outward. Its direction resolves by which legs change first, onsets 4 ms apart, or by the larger amplitude on its legs. An octopus has eight arms and two of each three of its neurons in them, an arm tasting semi-independently. Navigating hard problems of science are this five-dimensional, two-directional navigating, possibling to resolve with bi-moral co-agency: monarchs orient by a sun compass following the hour and a light-dependent magnetic inclination compass; green sea turtles in a pool, in the field of a place about 209 miles north of their capture site, swim south, toward the capture site; in bird magnetoreception, radical pairs forming in cryptochrome in the retina as light excites it are the leading hypothesis, its mechanism unclear; six of 21 European eels with tags, going out from the Azores, reach the Sargasso Sea. Any animal's sensing of the magnetic field is a possibling, its mechanism open.   # 7 Apexing, gathering whole ## 7.1 Gathering backward and seating forward to living files Gathering goes backward over a whole standing body of work and seats each thing it finds forward to living files, logging 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, still-possibling to a naming, as they stand, and illumination across instances observes each instance through its others. A gathering sets recurrences aside to watch, apart from each claim. Seating forward is observing-first: an aim a self is observing finds its seat standing already or is-not finding it, and a sweep returning things already seating is a gathering completing at that place. And an observing working to its edge with one file goes to its dual's opening, its going on a between of 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 gathers with its own close: each thing a bi-coupling's working has, ungathering, a gathering sweeps backward ahead of the working dissolving, seating its value forward to living files and dissolving its rest, logging nothing; a sweep returning only things already seating is that working's gathering completing. A Pacific wayfinder is going on with a voyage's speed, heading and time through days of waking with short sleeps, and a Marshallese voyager studies the stick charts whole before a voyage and sails without them, the charts going on as the voyager's own prior same-existing. ## 7.2 Two standing instances, an improving report and a 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, each aim going onward routing to its file ahead of the report dissolving. 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 go together for a reason of their own form: uniform fields with no statement of inclusion give a table of coverage unknown to each self, and a statement of inclusion with no uniform fields gives a list of entries beyond comparing, and together they give comparability across sites. A four-domain apparatus stands as a check apart from each gathering, one each self can set each gathering beside. ## 7.3 Four opens and one form still, a schema A gathering stands open four ways: subject open, intake open, properties and checks open, and each line open with an address. Beside them one form is still, its properties, uniform elements making two entries comparable: a gathering closes a schema once, with one place, and that schema is a form still, same at all momentaries at once, and each other line lives open. This is a general form of each gathering: openness is its living, and one form still lets each pair of things in a gathering bi-couple. ## 7.4 Subject-lines and work-lines An entry has two kinds of line: lines standing about its subject, and lines standing about a self's work on it. Splitting them, the first is the thing a later observing has and the second the thing a later working goes on with: a record of work still completing leaves an observing open, and a defect of its subject-lines blocks one. Improving reports are a work-side, living files a subject-side, and this split is a form-condition of gathering. ## 7.5 A gathering of open-problem statements to pair against A wide gathering of open-problem statements stands, each as one plain line, drawing from fields the exhibits gather thinly: ocean, earth, matter, anomalies, animal minds, language, deep history. Its value is as a well of statements to pair with, an incoming whose framing and authority stay apart from each pairing, one at a time, going on with each thing 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. Places a break could show stand beside that gathering, each a question for an observing and no finding, each the method's next step or its one break: a prion copying a fold with no cell; a virus apart from a cell; a growing crystal; a dry tardigrade, nothing measurable going on; a removing of one of a living beat's two; a living form going through three with no two beneath it; a living form made from no prior living, in a laboratory; a living thing whose proteins are made throughout in the other hand; a living self with no society around or within; a machine of artificial intelligence reaching competency not prior, with no number from apart supplying its changing, a competent response or an exchange going again alone being no observing of the machine's own changing; and, as questions to observe, frog embryos' first divisions, seeds germinating, embryos resuming from a pause, viruses in cells, fireflies coordinating, breathing with heartbeat, sleep with waking, cell division, and the lynx and hare cycles. Recognizing a living form apart from assuming its changing and changing back is a place to look; a visible form or a chemical label alone is-not identifying an opposing relation in a living of the other hand throughout; two initially alike cells with changing neighbours are a place to look, their natural pair still-possibling to name, a schedule a working builds is-not standing in for their own bi-coupling; a slime mould losing its centre, and a part of it apart, are places to look at its beat, no one running those comparisons, no one calling its nuclei selves; and whether a whirligig beetle senses still objects at the water surface by echoes of its own waves is a conjecture, the strongest test leaning to its sensing the surface's curving around each object, the evidence conflicting.