cot-quilt graph viewer — run 20261001T190939Z-4bb8f5f5

prompt: Design a minimal local algorithm that decides which cell of a cellular graph receives the next unit of computation budget, given per-cell potential and resistance values. The rule must use only a cell and its direct neig
seeds: 52840 / 25780 / 24417 mothquantum 16-bit × 3 3 CoT samples6 clusters4 divergent routes5 critique cells7 cluster edges (p=mean typesafe dependency)
6/10 v4-pro self-judged thoroughness
The graph captures the high-level components but omits the key aging, tie-breaking, and proof mechanisms, so it is only moderately thorough.
0.90 0.88 0.55 0.87 0.73 0.98 0.82 Taskdefinition Task definition: Design a local rule using only a cell and its direct neighbors to choose the next budget recipient and ensure fairness/no starvation. (load 2.91) Local urgencyscore Local urgency score: Combine potential and resistance into a local priority, typically potential/resistance, for comparing a cell with its neighbors. (load 2.56) Token holdermoves locally Token holder moves locally: Use a single token whose holder considers itself and neighbors and moves or serves based only on local values. (load 2.97) Servicelowers futurepriority Service lowers future priority: After service, reduce potential or raise resistance so the served cell's score drops and it stops monopolizing. (load 2.71) Local-maxstarvationrisk Local-max starvation risk: A deterministic local-max/greedy token can get stuck and starve lower-urgency cells, so a safeguard is needed. (load 2.59) No-starvationfairness No-starvation fairness claim: The chosen local mechanism ensures long-run fairness and no cell starves forever. (load 2.84) Global maximumimpos divergent route (samples [0]): A purely local rule cannot find the unique global maximum in one step, so it must use local maxima, token passing, or randomized propagation. Tie-breaking/backoff divergent route (samples [0]): If several strict local maxima or ties occur, break ties by ID or local backoff. Randomized tokenwal divergent route (samples [0, 1]): Randomize the token's next location in proportion to local weights, with a positive floor, yielding an irreducible walk that visits every cell infinitely often. Aging-baseddetermin divergent route (samples [2]): Add a local waiting/aging term so an unserved cell's effective urgency rises until the token leaves a local maximum and reaches it. g1 CHECK CHECK: Check that a one-step local rule cannot compute the unique global maximum, so a token or local propagation replaces global argmax. g2 DECISION DECISION: Add explicit aging λ_i to the score, resetting served cell age and incrementing others to force eventual selection. g3 CHECK CHECK: Check tie-breaking/backoff for equal local scores or multiple local maxima to avoid loops deterministically or randomly. g4 INFERENCE INFERENCE: Infer that positive-floor local probabilities can form an irreducible token walk visiting every cell infinitely often. g5 CHECK CHECK: Check formal no-starvation proof: aging dominates bounded p/r and crosses every cut, or irreducibility/recurrence holds.
● cluster (size=occurrence, hue=load) — edge (width=count, opacity=p) □ divergent route ◆ critique cell — hover for full text
cell signature — in: {prompt, n_seeds, lenses} · out: {graph_v1, graph_v2, judge, receipts} · clusters → value cells · edges → links with p as dial weight · judge.gaps → question-cells · critique nodes → next generation
repo: github.com/SuperInstance/cot-quilt · erised playground: erised-mirror.pages.dev