Case kinds — What kind of thing a CASE is, beside how much of it is fact (standing). The two are orthogonal (ADR-042).
Construction — a formal or mathematical object built to exhibit or refute a property, whose facts are its definition.
39 of 191 CASE documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| CASE-001 | Two reset matrices: noncommuting and classical | A30: on a two-state classical system, A resets to state 1 and B to state 2; AB = A and BA = B, so AB ≠ BA, and every state is an ordinary probability vector. Order dependence without nonclassical probability. | Active |
| CASE-008 v2 | Solidarity, condemnation and humour judged in pairs: the probabilistic version | A24: three judgements of Henley’s poem, S (solidarity), M (condemnation), H (humour), elicited in pairwise contexts, asking whether the pairwise distributions are marginals of one global distribution. Replaced in the manuscript by a deterministic parity example. | Superseded — by CASE-035 |
| CASE-035 | Solidarity, condemnation and humour: the parity obstruction | The manuscript’s §3 version: S = M, M = H and H ≠ S are each satisfiable in its own context but admit no global assignment. Stated to demonstrate an obstruction, not to describe actual judgements. | Active |
| CASE-037 | The parity triangle with uniform weights: a no-signalling, strongly contextual model beside a family of point sections that glues | CASE-035’s constraints given probabilities, at A129 §2, and set beside a deterministic family on the same cover that glues to (0, 1, 0). It shows that the obstruction is in the supports, not in the event sheaf. It appears three times (A129 §2, A161, A178’s negative control), so it gets a code. | Active |
| CASE-060 | Two identical unnumbered ballots in one tally: two votes that no relation in the structure of the vote tells apart | Constructed: two voters each put a single cross for the same candidate on identical, unnumbered ballot papers in one box, and both are counted. Within the relations that make a paper a vote, each bears the same relations to everything and none to the other, so they are not even weakly discernible, yet the count is two. Anchored on a documented norm that voids any paper marked so that the voter can be identified (UK RPA 1983, Sch. 1, r. 47(1)(c)). It forces the choice between CLAIM-136’s strict and weak versions, and bears on CLAIM-138. | Active |
| CASE-077 | The reciprocal pair: two processes that endorse only each other under recursive delegation, so that each one’s authority returns to it through the other | A2 §5’s counterexample to the ban on self-endorsement: “Suppose D1 endorses D2, and D2 endorses D1.” Under g = (1 − η)b + ηEᵀg, each operator’s authority comes partly from its own endorsement returned after two hops. It came back in A6 as authority that “may circulate”. Used to show that a ban on self-endorsement does not make authority independent of one’s own endorsements. | Active |
| CASE-082 | The sufficient posterior without its history: a Bayesian agent that keeps only its current posterior updates as well as one that keeps everything, and cannot say how it got there | A6’s fourth case, which A6 called “probably the most important counterexample in the set”. It grounds the redundancy half of CLAIM-300 and one of CLAIM-299’s separations. A6’s reserve case, revising the model class, is where it stops holding, and CASE-087 is that case. | Active |
| CASE-083 | A pseudorandom generator’s output against uniform strings: almost disjoint in total variation, indistinguishable to every efficient test if the generator is secure | A15 §2’s witness, which A15 recommended filing “with its cryptographic assumption explicitly stated”. It grounds CLAIM-302 and, by the record’s own reduction, CLAIM-304. Checked against Goldreich (note of 2026-10-15): the definitions match, and the separation needs the generator only for samplability. | Active |
| CASE-087 | The discredited instrument and the second population: two pairs of readings with the same mean that the mean cannot tell apart once one instrument is discredited or a mixture is considered | A10 §2’s paired construction, which A10 recommended filing (“That single paired construction makes the dependence of sufficiency on the task and model very easy to see”). It grounds the relativity half of CLAIM-300. | Active |
| CASE-088 | The repeated objection and the argument nobody reuses: filing pays for itself after a few recurrences in one case, and never in the other | A11’s CASE B and CASE A, the arithmetic of CLAIM-303. | Active |
| CASE-089 | The compensating evidence problem: two records with the same support graph in which discounting one support leaves odds of 20:1 or of 1.1:1 | A6’s second case. It grounds CLAIM-293: the same edges E₁ → H ← E₂, different Bayes factors for E₂, different revisions when E₁ fails. | Active |
| CASE-093 | Same marginal, different updates: two joint distributions over a hypothesis and a condition that agree on the hypothesis and disagree on how to revise it | A6’s first case, made exact at A8. It grounds CLAIM-294. | Active |
| CASE-095 | Two builders sorting one collection: the brick that one bins as red and two-wide and the other as a curved connector has a bin that respects both, and what the builders cannot share is an arrangement, not a description | The example the owner’s LEGO monograph (Mathematics of Meaning, “The Lego Parable”) uses for contextuality, rebuilt. As descriptions the two sortings always share a joint refinement, the product bin, as MOM-CLM-137 shows, so they illustrate the non-contextual case of CLAIM-037 and CLAIM-131. As arrangements, with a fixed number of bins, they compete, and which wins depends on the queries made and on what stands out within a bin. Fictional: the builders and the collection are invented. | Active |
| CASE-097 | The monograph’s castle topic, persistent across refinement by construction, persists as no eigenmode: in its rank-2 and rank-3 co-occurrence matrices the eigenvector nearest the castle topic changes rank and turns through about 51°, and every eigenvector mixes signs | Appendix H of Part III of the owner’s LEGO monograph builds two co-occurrence matrices from nonnegative topics. One has topics for spaceship and castle; the other splits spaceship into wings and engines and keeps castle unchanged. The monograph reads castle’s survival as a stable eigenmode and calls that archetype persistence. Computed here: the topics overlap (ship·castle = 0.21), so no eigenvector is the castle topic. The eigenvector closest to it is the second mode at rank 2 (cosine 0.873) and the first at rank 3 (0.926), about 51° apart. Persistence of a generating factor does not show as persistence of an eigenvector, which is what CLAIM-148’s identifiability limits predict. | Active |
| CASE-099 | The two-hypothesis coupled meaning–influence model linearized at its symmetric state: a meaning bias m and an authority bias a, each stable alone, coupled by authority shaping interpretation (β) and interpretation shaping endorsement (γ) | A14 §2 of the exchange of 2026-10-16. Near the symmetric state of the two-hypothesis, two-specialist model, (m, a) evolves by a 2×2 matrix J = [[α, β], [γ, δ]] plus noise. With nonnegative entries and α, δ < 1, the symmetric state is unstable exactly when βγ > (1 − α)(1 − δ), and the unstable direction mixes meaning and authority. Checked here. A construction about a linearization, not a fitted or simulated result. | Active |
| CASE-106 | The two-hypothesis linearization with endorsement scored on committed predictions: when the shared meaning bends the specialists’ predictions with weight κ and the reading of the evidence with weight κ′, the coupling of interpretation to endorsement is γ = 4ηs(κ′ − κ̄) | Built for QUESTION-121’s formal question: is scoring operators on predictions committed before the evidence equivalent to Regime B? The construction keeps CASE-099’s two-hypothesis linearization and replaces the score with squared error between each specialist’s committed prediction and the evidence as read. The coupling γ then has the sign of κ′ − κ̄: corrective when the interpretation bends the predictions more than the reading of the evidence, null when equally, capturing when less. Checked symbolically, and the stability conditions against 200,000 random draws. Fictional by construction. | Active |
| CASE-110 | Two members, one total: a coarse-graining by total output preserves an institution’s performance, its survival and every prediction it makes, and still merges a state in which a member works within the agreed cap with one in which that member works far past it | A22’s Construction C of the exchange of 2026-10-17, “Institutional performance versus constituent capability”, which A22 proposed and did not write out, from A21 §5 and §16; written out here in its smallest form. Two members share twelve hours of work. Total output decides the institution’s performance and its survival, so the total is sufficient for every institutional judgment, and the policies (6, 6) and (10, 2) have the same total. A member’s claim not to work past an agreed cap of eight hours tells them apart, so by CLAIM-350 no judgment on the total recovers it. Fictional by construction; it shows a possibility, not how often institutions are like this. | Active |
| CASE-111 | A fold in boundary maintenance: in ḃ = μb + κb² − b³ with cooperative repair (κ > 0), an unmaintained and a maintained state are both stable for −κ²/4 < μ < 0, so maintenance lost past the fold is not restored by returning the parameter, and recovery slows to zero as the fold nears | A7 §4 of the exchange of 2026-10-17, after the owner’s “flesh this out further”: a normal form for the activity b that maintains a boundary, in which repair processes reinforce one another. Its equilibria, the bistable range, the hysteresis loop and the slowing of recovery at the fold are derived and rechecked here. It shows a capacity to maintain, and not only a state, being lost and not coming back when conditions do, which is CLAIM-099’s distinction in a model. A7’s own caveat: “This is a proposed minimal model, not an empirical fit.” THEORY-136 and THEORY-214 say why its early-warning consequence is weak evidence. Fictional by construction. | Active |
| CASE-112 v2 | Bistable authority with a tilt: in ẇ = μw − w³ + h, with w the balance of authority between two regimes and h a higher-order volition favouring one, for μ > 0 the operative regime changes only when |h| passes 2μ^{3/2}/(3√3), so a sincere and efficacious higher-order volition can move the balance without moving the regime, and which regime operates depends on the path of h | A8 §4 of the exchange of 2026-10-17, restated as A12’s Proposition 3 and kept in A15. The saddle-node threshold and the hysteresis are derived and rechecked here. A8: “It’s a countermodel showing why endorsement strength, effective governance, and behavioral transition can come apart.” A8’s “endorsement” is the reflective attitude, not the record’s TERM-053 sense, so h is called a higher-order volition. It models authority between regimes; it does not revive will as an attractor (TERM-003, Superseded). Fictional by construction. | Active |
| CASE-115 | Two incompatible quadratic demands on one shared parameter, L₁ = (θ − 1)² and L₂ = (θ + 1)², frustrated at θ = 0 for every update budget, and the split of θ into task-routed θ_A and θ_B that makes both satisfiable | A33 §2 and §5, A35 §3.4 and A38 §4 of the exchange of 2026-10-17. Two demands on one scalar parameter: at θ = 0 the equal-weight gradient vanishes while each loss is 1, no update lowers both, and the local residual is Φ_r = ε for every budget r. A38 splits θ into θ_A and θ_B with the task context routed, and both demands are met at (1, −1). Used for the zero aggregate gradient, the residual, relief judged on the original demands, and differentiation. A38’s caveat is kept: the split is “a division of functional jurisdiction”, and it “does not automatically mean that two new autonomous individuals have formed”. Fictional by construction. | Active |
| CASE-116 | Three finite-state systems that dissociate slowness, member regeneration and transmission: a slow flip register no member reads (second eigenvalue 0.98), a register members read and rewrite that forgets fast (second eigenvalue 0.2, nonzero intervention effect), and a rule passed through an archive between two episodes that never run together | A3 and A4 of the exchange of 2026-10-17, after the owner’s “continue” and “show me”. Arm A is slow and not endogenous; arm B is endogenous and not slow; arm C transmits a rule with no continuous operation. The eigenvalues and intervention effects are rechecked here. Arm A shows what CLAIM-327 and CLAIM-331 already say in words, that slowness is not sufficient; arm B is the new direction, that slowness is not necessary, and it holds only for weak maintenance, in A4’s words. Arm C is CLAIM-287’s dormant coalition and does not settle identity. Fictional by construction. | Active |
| CASE-118 v2 | Two competing components with interaction matrix A = [[1, ρ], [ρ, 1]]: with equal growth rates their invasion growth is 1 − ρ, the smallest eigenvalue of the Gram matrix, and with growth rates 1 ± δ the same matrix supports coexistence only when |δ| < (1 − ρ)/(1 + ρ), so feature geometry alone does not fix coexistence | From the synthesis the owner relayed on 2026-10-18, checked. The two-component Lotka–Volterra system with symmetric overlap ρ: invasion growth 1 − ρ equals λ_min(A), and κ(A) = (1 + ρ)/(1 − ρ), so overlap weakens recovery and ill-conditions the features together. Holding A fixed and setting r = (1 + δ, 1 − δ) gives the coexistence equilibrium n* = (1/(1 + ρ) ± δ/(1 − ρ)), feasible only when |δ| < (1 − ρ)/(1 + ρ). The same representation geometry supports coexistence under one supply and exclusion under another. | Active |
| CASE-119 | Three demands each requiring one coordinate of an outcome to equal 1, with attainable outcomes (1,1,0), (1,0,1) and (0,1,1): every pair is jointly satisfiable and the triple is not, and a new composite policy that can also produce (1,1,1) relieves the frustration by enlarging the attainable set, with the acceptance sets unchanged and no demand suppressed | From the synthesis the owner relayed on 2026-10-18. A compatibility complex with all three edges and no filled triangle, the minimal structurally frustrated collection of CLAIM-347 with three members. When the organization acquires a composite operation that can produce (1,1,1), ℛ(𝒪) ⊊ ℛ(𝒪′) and the complex gains the triangle: relief in CLAIM-347’s sense, by changing what is attainable, not by weakening a demand. The construction says such relief is possible; whether specialization produces it is QUESTION-133. | Active |
| CASE-120 | Six units with uniform coupling, A = αI + β(11ᵀ − I): their sum is exactly dynamically independent at every coupling tried, while a single unit and the sum of three are not, and no grouping of the units is a weakly coupled block | The n-unit form of A5’s two-unit example in the exchange of 2026-10-19 on coarse-to-fine processes. The sum closes exactly; no proper group of units is a block. It is the closure-without-block cell of A5’s two-by-two table, and the system QUESTION-218 would test for compensation and entrainment. Fictional by construction. | Active |
| CASE-124 v2 | A maintained legibility lean as a third state of the linearized meaning–authority model: authority moves the lean r of the categories through which evidence is read, and r feeds interpretation or authority, with its own persistence λ | CASE-099’s two-variable linearization, meaning bias m and authority bias a, given a third state r: the lean of a maintained legibility regime, the categories, reporting requirements and evidence channels through which evidence becomes readable. Authority moves r (ε), r moves interpretation (ν) or authority (μ), and r persists at rate λ. Two witnesses, both checked: one in which the two-variable loop is stable and the three-variable one is not, and one in which the system is stable but r holds a lean long after m and a would have decayed without it. | Active |
| CASE-125 v2 | A hidden governance bit: an output that is fresh fair noise whatever a fixed hidden bit K is, until an intervention h makes the output read K, so the output alone is exactly informationally closed under ordinary operation and keeps nothing about the response to h | A16 §3–4 of the exchange of 2026-10-20, from A15 §2’s deterministic form, and A17’s Proposition 1. A fair hidden bit K, fixed in time; under ordinary operation the output Y is fresh fair noise; under the intervention h = 1 it reads K. The output is exactly closed, and with h = 1 drawn with probability ρ its deficiency for the response to h is ρ bits, no better than a constant. It is the first instance with parameters of CLAIM-122’s supervisory test, which the exchange of 2026-10-17 gave only in words. Fictional by construction; K is a mechanism parameter, not an agent’s governance. | Active |
| CASE-126 | Represented, authorized, self-authorized and self-maintained: three one-bit systems that agree while the interpretation is 0 and part under an intervention that sets it to 1, and two two-constraint systems with the same constant trajectory, one closed and one reset from outside, that part under one perturbation | A10’s two constructions in the exchange on experience and interpretation, re-run here by script. Neither depends on parameters. The first separates whether an interpretation is acted on and who decides that it is. The second separates whether the conditions of acting on it are kept up by the organization or by something outside it. Fictional by construction, with production relations stipulated, not shown. | Active |
| CASE-152 | Absent attempt or unresponsive receiver: with Y ∼ N(ab, 1), a the strength of an attempted influence and b the receiver’s responsiveness, the settings (a, b) = (0, 1) and (1, 0) give the same response distribution; K(a, b) = a²b²/2, the Fisher matrix has rank at most one and vanishes at the origin, and the real log canonical threshold is ½ with multiplicity 2, not the regular d/2 = 1, while changing b with a held fixed separates the two | The construction from the exchange of 2026-10-24 (workbench entry of 2026-10-24, U27), checked when filed. A two-parameter response model in which the observation depends on a product, the smallest singular model with a communicative reading. It shows a missing response failing to say whether nothing was attempted or nothing was taken up. | Active |
| CASE-154 | One representation, two tasks, one bounded observer: with X₁, X₂ independent fair bits and an observer that reads one coordinate and cannot compute XOR, the raw pair U = (X₁, X₂) gives error 50% on Q_A = X₁ ⊕ X₂ and 0% on Q_B = X₁, and the compressed V = X₁ ⊕ X₂ gives 0% and 50%; a legibility regime can enable one perspective’s distinction while disabling another’s, with no task-independent sense in which it is better | From the exchange of 2026-10-24 (workbench entry of 2026-10-24, U22), after the owner said “let’s work on those connections”: a deduction from CLAIM-199’s XOR example, checked when filed. It ties bounded legibility to competing concerns: a representation that serves one task can destroy another’s for the same observer, so a failure of one perspective under a legibility regime may be a resource limit and not an exclusion. | Active |
| CASE-155 v3 | Authority as a replicator population: for a distribution π of control over processes with mean qualities q, the expected Maynard-Cross update is π_a q_a / v, Bayes’ rule when q is each process’s likelihood; the Maynard dynamic is the Taylor dynamic slowed by 1/v, so the two share their orbits; mean quality climbs at the rate Var_π(q); and when a process’s score rises with its own share, ℓ′ = ℓ + h + c(2π − 1) has an unstable threshold π* = (1 − h/c)/2, above which a process the evidence disfavours captures the organization | Filed at the owner’s direction, 2026-10-24, after asking whether the tools of Soma et al. (THEORY-899) or related work could formalize the record’s abstract governance dynamics. Four results, each checked when filed, two by script. It reads authority as the population vector of a replicator dynamic. Evidence-tracking authority is then Bayesian, and authority-dependent scoring gives lock-in with an explicit correction threshold. | Active |
| CASE-156 v2 | A legibility filter as the ν of the meaning–authority–legibility model: in a safe world where 15% of raw cues are alarms, an admission rule P(admit | y, r) = σ(c + χry) with c = 0 and χr = 2 admits 88.1% of alarms and 11.9% of reassurances, so 56.6% of the admitted record is alarms with the world and the sensors unchanged; at symmetry the mean admitted evidence is χσ′(c)r to first order, so ν = η_m χ σ′(c); and r_t = λᵗr₀ + ε Σ λ^(t−1−j) a_j is an exponentially weighted history of authority | From the exchange of 2026-10-24 (workbench entry of 2026-10-24, U18–U19). The owner: “i think we already have a three variable system somewhere, where the third component is described as legibility”, then “flesh this out further”. A microfoundation for one of CASE-124’s abstract couplings: selective admission of evidence, checked when filed. It gives r an observational semantics and reads r as the memory of past authority. Selection-aware inference is the control that the pathology has to beat. | Active |
| CASE-159 | Authority geometry and response geometry: when an organization’s response is the authority-weighted mixture p_π(y | c) = Σ πᵢ pᵢ(y | c), the Fisher metric of its responses is the pullback JᵀD⁻¹J of the categorical (Shahshahani) metric on the shares π and never exceeds it; it vanishes along any redistribution between processes that respond alike under the probes used, so two specialists who both answer yes with probability 0.8 in routine contexts carry no information about their shares there, while a rare context in which they answer 0.9 and 0.1 carries 0.64/(p(1 − p)) per observation, p = 0.1 + 0.8π | From the continuation of the exchange of 2026-10-24 (U28–U31), where it appears in four replies (A28 §3, A29’s second priority, A30 §6A and A31’s probe diagnostic); checked when filed. The categorical metric on authority shares is the one in which the replicator is a gradient flow (CLAIM-444). What an evaluator sees is the response mixture, whose Fisher metric is that metric pulled back through the processes’ response profiles. Redistribution between processes that agree on the probes is invisible to them, and a probe on which they disagree restores it. The mixture counterpart of CASE-152’s product model. | Active |
| CASE-160 v2 | Interacting accumulators on an influence network: if each perspective’s continuous support for one of two interpretations follows dxᵢ = [dᵢ − λxᵢ + κ Σⱼ Wᵢⱼxⱼ]dτ + noise, with W irreducible and row-stochastic and ℓ its left eigenvector, then ℓᵀ(κW − λI) = (κ − λ)ℓᵀ, so the ℓ-weighted support L = ℓ·x is exactly an Ornstein–Uhlenbeck process with drift ℓ·d, rate κ − λ and variance ℓᵀΣℓ, and a drift-diffusion process at κ = λ; with tanh coupling and member noise the transition is at κ_c = λ/E[sech² ε], not at κ = λ | From the continuation of the exchange of 2026-10-24 (U28–U47). A36 derived it as the answer to the owner’s U34 hypothesis, and A37, A42, A43 and A44 restated it as the population simulator’s unit test. The case formalizes CASE-074’s crowd as a linear network of accumulators: the hidden tally is the balanced case, the visible tally positive feedback. The closure is THEORY-733’s, the variance THEORY-321’s influence concentration and the balance THEORY-068’s, a combination no source makes. Checked when filed, and the reply’s nonlinear transition corrected. | Active |
| CASE-164 | A 192-state organization on which one kernel gives several closure verdicts: the description by agents and phase is informationally closed on the intact support and fails global strong lumpability, its deficiency for the next pair of rule integrities under a declared intervention mixture is 0.55·H₂(1/3) ≈ 0.5051 bits and zero once the maintenance mode is kept, and finite-sample predictive gains misread both a positive and a zero information defect | v1.8 of the Perspective Population Lab, dmarx/PerspectiveLab@7e2edc2: a finite organization small enough to enumerate, on which the senses of closure of TERM-068 are computed exactly side by side. The maintenance mode plays CASE-125’s hidden bit: the intact dynamics are the same in every mode, and five of six interventions part them. v1.9, at @9f82bfd, calibrates finite-sample predictive gains against the exact values. It recombines distinctions the record already holds and claims no new theorem. | Proposed |
| CASE-165 v4 | A dynamic beta–Bernoulli latent-feature model of an organization’s members: a finite Indian buffet prior over who holds which interpretive features, a sticky logistic transition for holding them, activations, and team, communication and authorization layers above; at the proposed size of sixteen features it falls well short of the Indian buffet process it quotes, its persistence term does not hold rare features, and the difference between having a capacity and using it is not identified from the outputs | The owner’s T22 (“maybe we could benefit from a restaurant process model, like an indian buffet model”), developed at T23 (“flesh out our proposed generating probability model further”) into a full generative specification for the Northstar firm, and carried to transformer training at T24. It is the candidate method of QUESTION-276 in its most worked-out form. Its facts are its definition, and four of them are not what T23 says: at K = 16 the prior expects 6.83 features, not αH₁₂ = 9.31; a held rare feature is kept with probability 0.16 a day; and having, using and splitting features are confounded in the reconstruction. It shows what such a model would have to get right before its features could count for anything. | Proposed |
| CASE-182 | Two operators under one update rule, endorsement moving toward observed outcomes: scored every round, the more accurate one holds the lead durably whatever the start; scored only when it acts, under sharp selection, whichever gained influence early keeps it | Filed by the fourth status review (ADR-057) for CLAIM-277, whose two loops the record had stated and not constructed. Two operators share one rule, with accuracies 0.8 and 0.6. Each round one acts, chosen with probability softmax(β·E), and endorsement moves toward observed outcomes, E ← E + η(outcome − E). Nothing marks either one as an authority. Scored every round, the more accurate one ends more endorsed in 200 of 200 seeds, even after a head start for the other (E0 = 0.3 against 0.9). With η = 0.01 the lead never changes hands in the second half. Scored only when it acts, with that same head start, the worse one is never displaced in 200 of 200 seeds at β = 30 or 100. At β = 8 the better one recovers, after a median of 460 rounds. The scored control at β = 100 entrenches no one. Code: scratch/formal/trust_loop.py. | Active |
| CASE-189 | Two constructions of a maintained organization: two constraints producing each other with saturating production and turnover hold a three-unit coupling, with a box invariant under damage up to 0.4, a saddle-node at damage 0.5 and extinction above it; and a transient encounter that forms a connector enabling that reciprocal production, after which the connector is maintained by what it enables, every single-pathway knockout ends it, and the regime ends in a saddle-node at damage ≈ 0.691 where the coupling’s gap is still ≈ 0.989 | From A9 §4, A10 §2–5, A11 §2–5 and A12 §2–6 of the exchange “Analyze nucleation concepts” (2026-10-31), after the owner’s “try to progress the theoretical program” and A10’s own “theorem target” pasted back at U11. Every number below was recomputed by the turns’ readers, with an independent integration, and the folds again by the filer. Fictional by construction, with illustrative parameters. A10’s chart had three wrong points, which A10 corrected itself. A12 called its fold “the first mathematical account of organizational birth, commitment, and death within Nucleation’s framework”; CASE-111 is the earlier one, and this is its variant with a coupling attached. | Active |
| CASE-190 | A kinetic construction of self-maintaining reconstruction: a brief encounter captures a fuel, connector and two-catalyst core into a box that stays invariant under bounded degradation, keeping its copying catalyst regenerated and a grounded teacher and an erasable student within bounded error; with a resource allocator holding reserved minima and a revisable copy rule, the certificate holds for every allocation and rule, because neither the information variables nor the rule feed back into maintenance | From A17 and A18 of the exchange “Analyze nucleation concepts” (2026-10-31), after the owner asked for “one system in which those conditions are all physically realized rather than assumed independently”, and then for an endogenous allocation controller with a barrier certificate. The certificates were rechecked by the reader of U16–U19, and two of A’s error bounds were loose. The simulations A17 and A18 report could not be checked: their code was in A’s sandbox. A19 later said “Our last model explicitly demonstrated the separation” between matched successors after a second injury; it did not, and that experiment was never run. | Active |
| CASE-191 | A construction of self-formation: an agent’s own frustration at two demands one shared output cannot meet drives production of a sensor and a differentiating channel that then maintain each other; past a threshold of discrepancy (D ≈ 0.645 at unit drive) the capacity forms, outlasts the conflict, meets later conflicts of the same class up to D ≈ 1.047 with no frustration, and is lost at damage 0.5; a capacity upheld from outside is told apart by knockouts afterwards, but one installed by an outside pulse and then self-maintained is told apart only by a knockout during formation | Built at the owner’s request (“build the CASE-189 extension”) to test CLAIM-532, the positive account of self-formation filed from U33 of the exchange “Assess SDT Coverage”. scratch/formal/self_formation.py. Fictional and stipulated: the sensor and channel are capacity variables present from the start, raised from zero, as CASE-189’s are. It bears out the claim’s first test (transfer within a class) and qualifies its second: a knockout of the producing process separates own formation from outside installation only if it is made during formation. After the fact the two are the same organization. | Active |