Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Mathematics — mathematics read for itself — category theory, topoi and sheaves, spectral geometry, set and measure theory — including mathematical frameworks applied to other fields.
15 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-017 | E1: synthetic three-state stochastic computations (C2–C3) | Run at U23 (“run it”): hand-chosen row-stochastic matrices on three abstract states, seed 20261008, “not fitted to text, pretrained models, or human measurements”. Executed; results are exact properties of the chosen matrices. None reached a later draft. | Active |
| 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-039 | Who crosses the meeting point first? Two craft near light speed, and the relativity of simultaneity | The owner’s U47: two craft approach each other near light speed, and each frame is said to answer that it crosses the meeting point first, so the local interpretations cannot be glued. A164 corrected the physics. Read either way, the owner’s own scenario has an invariant answer; only spacelike-separated events change order between frames, and there the frames are reconciled by a Lorentz transformation. Standard special relativity; the scenario is the owner’s. | Active |
| CASE-057 | Swapping the two persons of a dyad: nonreciprocal T/V address is changed by the swap and reciprocal address is not, with a constructed French–English dyad and a three-person teasing round | Built on a documented distinction. In Brown and Gilman’s account of T/V address, power address is nonreciprocal (the superior says T and receives V) and solidarity address is reciprocal, so swapping the two persons changes the first act and leaves the second fixed. Two constructions extend it. A master-and-servant dyad in French and in modern English is changed by the swap in one realization and fixed by it in the other. A three-person teasing round gives a group whose automorphism can swap characters, so the anchoring of CLAIM-249 has work to do. | 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-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-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-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-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-179 v2 | A proposed study: one network of locally described units in which physical coupling, the correspondence maps that say which local states agree, and the apparatus that revises those maps are manipulated independently, to find which of compatibility, attraction, effective boundary constraint, persistent individuation and reliable revision come apart, and how much each costs to establish | The experiment the owner’s review of the pull request named as “the cleanest way to investigate the central claim that interacting processes can generate the conditions of their own further organization”, put together from A22 §10 and A23 §XIII of the exchange of 2026-10-27. It has three independent manipulations: the physical coupling, the correspondence maps, and whether and how an apparatus may revise those maps. Its readouts are global compatibility, attraction, effective boundary laws, robustness under intervention, the cost of recovering the structure, and whether revision improves prediction on interventions the apparatus did not choose. Not run. | 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 |