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Claim. Theorem 1 of the five-page note A partial result on distinct consecutive values of Euler's function asserts that if $L=L(x)$ is positive, integer-valued and satisfies $L\log(2L)=o((\log x)^2)$, then for all but $o(x)$ integers $n\le x$ the values $\phi(n+1),\ldots,\phi(n+L)$ are pairwise distinct. Its Corollary 1 answers Problem 1004 affirmatively for every fixed $c<2$, and its Corollary 2 gives the explicit range $L\le(\log x)^2/(\log\log x)^{1+\delta}$ for each fixed $\delta>0$. The route is a union bound over the shifts $h<L$ of a block, fed with the uniform shifted-collision bounds of Pollack, Pomerance and Treviño, Theorem 3.1 for the unstructured collisions and Theorem 3.3 for the structured even-shift family, together with an average estimate $\sum_{k\le L}c(k)\ll\log L$ for the coefficient of Theorem 3.3 that the note asserts on its own. The note prints no author, venue or date. It was linked from a post in the site's discussion thread by the account aditya on 29 April 2026, which opens by attributing the result to "Gpt 5.5 pro"; the claimant recorded here is the submitting account, with the system named as the post names it. The note and its displayed claims are recorded in the research lead Unverified native note on distinct consecutive totient values.

Covers. Every fixed exponent $c<2$, in the almost-all form: for all sufficiently large $x$, all but $o(x)$ of the $n\le x$ have $\phi(n+k)$ pairwise distinct for $1\le k\le(\log x)^c$, which gives the asked $n\le x$. It says nothing about any $c\ge2$, so the question for every fixed $c>0$ stays open.

Depends on. No page of this wiki. The two published theorems the note uses are library cards, and its average estimate is its own.

Standing. An anonymous, unpublished note with no stable bibliographic identity, no refereeing and no formalization; its argument has not been reviewed. On 2026-10-05 the site labeled the problem OPEN (page last edited 12 April 2026) with no proof claim, and the thread carries a reader's remark that the statement is implicit in the source paper; the community's AI-contributions wiki lists the note as a partial result implicit in the literature of Pollack, Pomerance and Treviño. The partial statement is public since 29 April 2026 but accepted by nobody.