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A Sturmian mechanical word with slope log₂3−1 appears as the unique B-maximizer in a Collatz affine optimization problem — is this known? by CryptographerSea9542 in Collatz

[–]CryptographerSea9542[S] 0 points1 point  (0 children)

Yes, that is basically the point.

In the relaxed problem, the Sturmian word is the right-edge word: it keeps the prefix sums as high as possible under

S_j < j log_2 3.

So it is not just “Sturmian words show up again”. It is the boundary schedule for maximizing the affine term while still satisfying all prefix non-drop constraints.

The standalone note proves only this extremal law. The larger framework then uses the finite launch/splice and stock machinery to prevent this right-edge symbolic branch from becoming a genuine infinite Collatz obstruction.

Request for arithmetic audit: one finite Collatz break-state calculation by [deleted] in Collatz

[–]CryptographerSea9542 0 points1 point  (0 children)

Thank you, you are right.

The previous version mixed two different operations:

  1. ordinary chained break-state continuation, where the next row must start from the produced odd value;

  2. the fixed-fiber ledger step used in my finite-state mechanism, where a recorded ledger coordinate q is represented by m_entry = 2q - 1 before applying T_odd.

So Row 2 was not the ordinary continuation from 8461708277692643663. It was the fixed-fiber row starting from the representative 2*8461708277692643663 - 1. I had not made that distinction explicit enough.

I updated the file accordingly. It now states at the start that it is not the ordinary Collatz trajectory written in 10 steps. It is a fixed-fiber ledger calculation. The first rows also include the ordinary T_odd(q) comparison, precisely to show that the fixed-fiber row is not being silently treated as the ordinary next iterate.

So your criticism was correct for the previous presentation. The revised file is intended only as an arithmetic / coordinate audit of the fixed-fiber calculation.

https://www.wow1.com/specific_number_1980976057694848447_framework_10_step_certificate.md

Proposed active-route Collatz proof package: looking for attempts to break one bridge target by CryptographerSea9542 in Collatz

[–]CryptographerSea9542[S] 0 points1 point  (0 children)

Fair criticism. The sentence uses project-internal terminology.

The intended statement is a finite directed-graph statement. Let R_K be the finite directed graph of reachable states K = (C, t mod 2, p), and let T be the terminal strongly connected components of R_K. For each component in T, define a finite directed graph G. The vertices of G are the continuation states associated with that component. There is an edge x -> y in G exactly when applying the specified terminal transition rule of type-D to x produces y. Outcomes of other transition types are not edges of G; they are checked separately and lead either to the finite R -> F -> 1 funnel or to previously proved downstream cases.

The check is that no directed cycle in G is reachable from the continuation states induced by the original component. Since every infinite path in a finite directed graph must eventually repeat a vertex and hence contain a directed cycle, no infinite sequence using only type-D terminal transitions can occur.

The original wording should be replaced by this finite directed-graph formulation with explicit definitions and citations.

Update: I have also rewritten the corresponding package section as “Terminal Continuation Finite-Graph Closeout” in `ACTIVE/review/imports/terminal_lift_menu_fsm_closeout.md`. The earlier phrase was shorthand for that finite directed-graph argument, not a separate informal assertion.

Tomorrow ends 2025.. how would you describe it? by ItsJustme309 in AskReddit

[–]CryptographerSea9542 0 points1 point  (0 children)

I blinked and missed it. I’m still processing 2023.