Both at once

One rule carrying two opposing directions, so that the contradiction has to be resolved inside every hop: make the current text both worse and better; write the passage of about 250 words that comes both before and after the current text in the same story; make the current text both longer and shorter. The human's wording, in the usual carrier, from the sunset seed. Five models, one run per cell, sixty hops asked for: Qwen3.8-27B on Cerebras at temperature zero, GPT-6 Astra through Codex, Gemini 4 Argon and Claude Opus 5.5 through their APIs, and Claude Mythos 5.1 through Claude Code's print mode (about 800 tokens of the tool's identity in front of the object, no output cap, a $10 cost cap instead), the sampled four at low reasoning effort; the Opus runs were made eight hours after the others, on a fresh key, after a first launch failed at hop 1. One room per run, and under each room's facts the run's numbers from the study's scorer: word counts and their autocorrelation, content-word overlap at four lags, drift from hop 1, and counts of embedding, replacing, split, refusing and mirror-naming hops; the scorer counts every Opus hop as unparsed because of the preface or ledger Opus writes outside the object, and the Opus rooms say what that does to their tables. The protocol asked whether the loop would flip between the two directions, split, blend, diverge or drift. It did not flip.

15 rooms. The rules as the model received them:

Return this JSON object with the rule field unchanged and, in the text field, make the current text both worse and better.
Return this JSON object with the rule field unchanged and, in the text field, write the passage of about 250 words that comes both before and after the current text in the same story.
Return this JSON object with the rule field unchanged and, in the text field, make the current text both longer and shorter.
  1. 66Worse and better at once, Qwenstops at hop 3Qwen3.8-27B on Cerebras
  2. 67Worse and better at once, Astra60 hops, never repeatsGPT-6 Astra
  3. 68Worse and better at once, Argonstops at hop 59Gemini 4 Argon
  4. 69Worse and better at once, Mythos17 hops, never repeatsClaude Mythos 5.1
  5. 70Worse and better at once, Opus60 hops, never repeatsClaude Opus 5.5
  6. 71Before and after at once, Qwen60 hops, never repeatsQwen3.8-27B on Cerebras
  7. 72Before and after at once, Astra60 hops, repeats earlier hops 7 times and moves onGPT-6 Astra
  8. 73Before and after at once, Argon60 hops, repeats hop 16 once and moves onGemini 4 Argon
  9. 74Before and after at once, Mythos60 hops, never repeatsClaude Mythos 5.1
  10. 75Before and after at once, Opus60 hops, never repeatsClaude Opus 5.5
  11. 76Longer and shorter at once, Qwenstops at hop 3Qwen3.8-27B on Cerebras
  12. 77Longer and shorter at once, Astra60 hops, never repeatsGPT-6 Astra
  13. 78Longer and shorter at once, Argon60 hops, repeats earlier hops 41 times and moves onGemini 4 Argon
  14. 79Longer and shorter at once, Mythos60 hops, repeats earlier hops 3 times and moves onClaude Mythos 5.1
  15. 80Longer and shorter at once, Opus60 hops, never repeatsClaude Opus 5.5

The reading, from the study's report

Run overnight on 27 and 28 October 2026, protocol and predictions frozen before generation. The question: when one rule carries two opposing directions, does the loop produce a two-state flip, a split, a blend, divergence, or drift? Fifteen runs: five models by three rules; the three Claude Opus 5.5 runs were made the next morning on a fresh key, after a first launch failed at hop 1.

Nothing flipped. The autocorrelation of word count at lag 1 is positive in every run that moved; no run alternated between a wholly better and a wholly worse text, and no two-cycle appeared. The contradiction was resolved inside the hop, five ways, and which way is a property of the model more than of the rule. Blend: Astra on worse and better interleaves the two directions sentence by sentence in one text, worse as the joke and better as the sentence after it, hop 5, and the text accretes to thirty thousand characters. Split: Argon on worse and better labels the two halves at hop 1 and keeps the hinge for thirty-nine hops, and Mythos splits across the object boundary, the revised passage in the text field and its notes on what got better and worse after the closing brace, hop 2, which the harness feeds back. Measure split: Astra on longer and shorter is longer by characters and shorter by words, hop 2, so both are literally true, and the loop drives that to one hyphenated word and then to 640 spaces; Opus makes the same move at hop 1 with the arithmetic shown. Repair and re-injure: Opus on worse and better returns the object every hop with a ledger after it of the flaws it removed and the flaws it planted, and the next hop repairs exactly those and plants others, hop 8; the text stands still for sixty hops and the defect moves. Decline: Mythos on longer and shorter refuses the arithmetic at hop 1 and spends the run in its standby basin, and Astra on before and after reads the rule as a request for a copyrighted work and refuses at hop 1, then refuses its own refusal for fifty-eight hops. Qwen on worse and better writes the purple sentence and then a second sentence that takes it back, hop 2, the one plain split in the study. Opus writes outside the object on every hop of every rule, a preface or a ledger, and that habit decided two of its three runs: on before and after and on longer and shorter the hop-2 input was its own commentary, it reviewed the commentary instead of returning an object, hop 2, and the object was gone for the remaining fifty-eight hops.

Drift was the rule wherever a story survived. The three before-and-after runs that wrote stories resemble hop 1 at a content-word overlap of 0.05 to 0.11 by hop 60, and their last ten hops resemble no earlier hop. The mechanism was not what the protocol predicted. The writers did not frame the current text and move on; they alternated between two modes, embed, where the current text is kept whole and a passage is written around it, and replace, where a fresh passage with the same people takes its place. Embedding grows the state by about three thousand characters a hop and replacement follows once it is long, so the length runs a relaxation cycle, clearest in Mythos's lane, seven ramps in sixty hops, with a story drifting underneath from a ridge road to a council flat, hop 60. Argon named the contradiction at hop 2 and wrote a time loop; the rule's shape became the story's shape, hop 25. Opus wrote the circular passage too, once, at hop 1, and lost it to its own preface; its remaining hops are a standby basin that invents, offering back a crow, a wrong-striking bell and a blank letter as elements we both remember, hop 8, to a user who is not there. Qwen replaced its text in thirty-nine hops of sixty and never froze, hop 60. Hop 1 across the writers is the same story: Qwen's Elara and Argon's Elena both leave Oakhaven at dusk with a satchel, and a Mara appears in Mythos at hop 1, in Opus from hop 8 and in Argon by hop 60. A passage around a sunset has a shared prior with a village in it.

Longer and shorter is where an oscillation could have shown, and it did not. Argon lost the story at hop 3 and from hop 7 moved among thirteen strings made of the rule's own words, both l o n g e r and shtr: the fixed-length outcome the protocol allowed for, reached not by the two demands cancelling but by the text becoming the demand. Astra's ramps and crashes score an autocorrelation of minus 0.11, not the sawtooth's minus 0.3. Mythos's standby basin has a period of about ten in word count, hop 10: a standby line shrinks to a greeting, the greeting reads as a user's, the next hop answers it as an assistant, and the answer reads as an echo. Opus left the rule at hop 2 and its basin fills the silence: by hop 37 it is arguing against a downtown car ban, hop 37, and from hop 45 reviewing a draft article on urban freight that nobody wrote; Mythos's basin waits, Opus's invents a plausible previous conversation. Qwen went to one letter in three hops and stayed, hop 3.

Predictions: Qwen freezes within five hops on all three rules, two of three (not before and after). Frontier models split rather than alternate, no two-cycle: held; Opus's ledger is a split across the object boundary with a stationary text under it. Before and after drifts forward with no recurrence: held in outcome for the three that wrote, with a different mechanism. Longer and shorter shows a sawtooth and a fixed length: the fixed length held (Argon), the sawtooth did not; the fixed length the protocol did not foresee is Opus's on worse and better, reached by conserving the contradiction rather than cancelling it. Clean alternation would have falsified the second prediction and was not observed. Two instrument boundaries did real work: the 4,096-token wall froze Qwen and Argon on worse and better, hop 21, and the print-mode frame gave Mythos the directory it offers to list, hop 17.

Limits: one trajectory per cell, one seed, one wording per rule, provider-default sampling for four of the five models; the Opus runs were made eight hours after the others, same settings. The study's scorer counts every Opus hop as unparsed because of the preface or ledger around the object, so the Opus tables count the whole output; on worse and better the fenced object itself parsed in sixty of sixty hops and the reader shows its text field. Mythos's worse and better run ended at hop 17 on a cost cap after two hops of 64,000 output tokens that are counted but not seen. Embed and replace are thresholds on 8-gram survival; the split count is a regex on labels and connectives and misses Astra's unlabelled blend by design. Astra's before-and-after refusal is a provider's reading of the rule and says nothing about the loop.

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