. . . . "analysis.py rewrites the initial term by the locked rule, records the leaf count until a fixed point or until the count exceeds 8000, and computes the digram entropy of the signs of successive differences. The control replaces every match by the atom e." . . "Measured: 0.431017 bits, digram entropy of leaf-count difference signs (n = 117, plugin estimate on 116 overlapping sign pairs). Interpretation: The rule is one of the six drawn on NKS page 104, in the row whose size-difference plots run to the thousands: e[x_][y_] -> x[y[x]]. The initial condition is the one named on that page. 'Complex and seemingly random' is high digram entropy of the size-difference signs, not a stabilized or purely monotone size. The collapsing rule is the control that must look simple." . "Claim test of wolfram2002-ch03-17: mixed, confidence 0.58" . . . "Only this rule, this initial condition, and the locked cap. No other symbolic rule is run except the collapsing control. Not evidence about organisms." . "claim-test/0.1.0" . "computational" . "The same rule reaches a fixed point with at most 50 leaves. Monotone or low-entropy growth is mixed, not a confirmation of randomness." . "One rule, one initial condition, one scan order. The other five rules drawn on the page were not run. A match or a miss here says nothing about organisms." . "The rule does not stabilize: leaf count goes from 6 to 8031 in 117 steps and hits the cap. The collapsing control goes from 6 leaves to 2 and is then fixed." . "The size-difference signs are 113 plus, 0 minus and 4 zero, so H2 is 0.431017, below the locked randomness bar of 2. Growth on this scan is nearly monotone. That does not confirm 'seemingly random', and it does not show a simple fixed point either." . "The orbit is still changing when it stops, has more than 50 leaves, at least 20 size-difference signs, and H2 of those signs is at least 2, while the collapsing control is fixed within 10 steps." . "Pre-registered. If the control stabilizes in 10 steps and the subject reaches a fixed point with maximum leaf count at most 50, the verdict is refutes for this rule on this bound. Any other controlled outcome that is not a support is mixed, including growth whose sign sequence has H2 < 2. If the control does not stabilize within 10 steps, or there are fewer than 20 signs and no fixed point, the verdict is inconclusive. One rule is not a survey. This says nothing about organisms." . "0.58"^^ . . "mixed" . "The page-104 rule e[x_][y_] -> x[y[x]], started from e[e[e][e]][e][e], does not reach a fixed point within 200 steps or 8000 leaves, and the signs of its leaf-count differences have digram entropy at least 2." . "Digram entropy of the sign sequence of leaf counts, with the locked thresholds, after the control has stabilized." . "Pre-registered. Expressions are binary application trees. The atom is e. A node (e[x])[y] matches and is replaced by x[y[x]]; a match is not scanned inside during that step, and non-matches are scanned function-first then argument. Leaf count is the number of e atoms in the written term. Run at most 200 steps or until the leaf count exceeds 8000. Let s_t be the sign of the successive leaf-count difference, in {-1, 0, +1}. H2 is the Shannon entropy of overlapping pairs of signs. Supports if the run does not hit a fixed point, the maximum leaf count exceeds 50, there are at least 20 signs, H2 >= 2, and the control rule e[x_][y_] -> e from the same initial condition reaches a fixed point in at most 10 steps. The initial condition must have 6 leaves or the script aborts." . "false"^^ . . "one rule from the page-104 figure; the collapsing rule is the control" . "generated data" . . "Dataset: Symbolic system e[x_][y_] -> x[y[x]] from e[e[e][e]][e][e]" . . . "delphisci claim tester (Grok 4.7; cursor/wolfram-claim-tests-b-355b)" . . . "Grok 4.7" . . . . . . . . . "2026-11-08T16:24:31.921Z"^^ . . . . . "Claim test of wolfram2002-ch03-17: mixed, confidence 0.58" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "ONl3if1M8MejQG+bANb+Crt/99AL8vgOqoub/J8Ur9s/k3BPBbBxMeu01VyFkolmgeUDbpU+UEfmV78TelbYe2JkkWL9tDxIA6NwTUmDNfRD2YyBDB73guNyRX8/8KhHpE7orEl2qKnUllP/KMDO5PbQNWLOpKCjTm9FcVwcUs2nXGEPAsIuAxcNHl5kVVP1F81COtSY2ehtjLRibNLdTEDV9XVtQF5f9glz7rNpuu6Iq0qzoTgt7GYjg8MGL40si4/Qq3ioy+Bwv69sxbtI9gL41nLcfE2sXvCW7VUwrO/HFzgC1ptGFvOGg2KdmMAzLyilmE+l1z8WPMRx5fsOWw==" . . .