. . . . "analysis.py runs the even-to-5n/2 and odd-to-(n+1)/2 map from each seed 1..32, stops at the first repeated state or at 8000 steps, and scores bit-length range, strict direction changes, and size periods through 30. A second run matched derived/measured.json byte for byte." . . "Measured: 17 seeds in 1..32 whose size fluctuates with no repeated state and no size period <= 30 inside 8000 steps (n = 32, exact on this finite horizon). Interpretation: The parenthetical rule in the claim is the map used here, with no extra factors. 'Overall sizes' are bit lengths. 'Fluctuate in a complex, apparently random way' is the range and the turn count. 'No sign of repetition' is the absence of a repeated integer state and the absence of a size period of 30 or less, inside a horizon of 8000. The claim says the rule can produce such a sequence, so one seed is enough to support it, and only a repeat on every seed in 1..32 refutes it inside this test. A cycle past step 8000 is invisible. The computation says nothing about organisms." . "Claim test of wolfram2002-ch04-05: supports, confidence 0.76" . . . "Orbits generated by the checksummed script from seeds 1..32 under the stated rule, horizon 8000. No external table and no organism record." . "claim-test/0.1.0" . "computational" . "Every seed from 1 to 32 repeats a state at or before step 8000." . "Seventeen seeds meet the bar inside 8000 steps, and fifteen seeds fall into a cycle by step 9. The claim is that the rule can produce a fluctuating non-repeating size, which these seventeen do on this horizon." . "Size is bit length, not the integer itself. Direction changes count turns of that length, not a randomness test of the digits." . "The longest orbits end near bit length 1200 and were still growing in envelope. A cycle after step 8000 is not ruled out. A longer run could change a seed from fluctuating to eventually periodic." . "This is a computation about one arithmetic rule. It says nothing about organisms." . "At least one integer from 1 to 32 has an 8000-step orbit with no repeated state, bit-length range at least 20, at least 100 strict direction changes, and no bit-length period of 30 or less." . "Pre-registered. Refutes if every seed in 1..32 repeats a state within 8000 steps. Mixed if at least one seed avoids a repeated state but none meets the range, turn, and size-period conditions together." . "0.76"^^ . . "supports" . "The whole-number rule that sends an even n to 5n/2 and an odd n to (n+1)/2 produces, for at least one start in 1..32, a size sequence that swings by at least 20 bits with at least 100 turns and neither a repeated state nor a short size-period inside 8000 steps." . "Count seeds that meet every fluctuation clause, and count seeds that repeat a state. One full success supports. Universal repetition refutes. An escape from repetition that misses the range or the turn count is mixed." . "Pre-registered. Rule: even n goes to 5n/2, odd n goes to (n+1)/2. Seeds 1 through 32. Horizon 8000 steps, stopping a seed at the first repeated state. Size is the bit length of the state. A direction change is an interior index where the two adjacent first differences of size are nonzero and have opposite signs. A seed counts as fluctuating without a short repeat only if no state repeats within 8000 steps, the size range is at least 20, there are at least 100 direction changes, and the size sequence has no period p with 1 <= p <= 30. Supports if at least one seed counts." . "false"^^ . . "the whole-number orbits whose sizes are the test" . "" . . "Dataset: Orbits of the even-to-5n/2 and odd-to-(n+1)/2 rule" . "sha256:a86249d921c1eee0947cc4621cb1c95b1c8e05967a64a58d2a7fc28be6d8373f" . . "delphisci claim tester (Grok 4.7; cursor/claim-tests-wolfram-programs-b8d9)" . . . "Grok 4.7" . . . . . . . . . "2026-11-08T16:24:31.922Z"^^ . . . . . "Claim test of wolfram2002-ch04-05: supports, confidence 0.76" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "gofjtwdwZSZVFinBuA75ynlIZzSYkJCF9HWB5vXpWrwYhjw0G4HbDXGaHof7f/rKKoEGmzrn4mWDhLmZrlTPhqO2FcaASB9F1gF0iu2d/gfhTHr6/vWdxMP3WUp8WPu7tPBJGH0zlOgu77H86VYby7nCW5YOQaaI/rE8iOmyc8FsYYymnlT6PmSLuh71wmlJFN54dKlktSG+g9HTuTbURIRTVQLSzG/lbPN6gHwAg2D4LFeqL5qq1ec6Yc1/8YCnLdxQmuvkblBnwoBsN5hEiy++QvzJCfd3NU158W5NTVvEgZok8rA2E1LO1qiiIViEUWuzDY7udMhrtJPKO869MA==" . . .