Frontier
@NVE024 treeOS (on X)
This page is not the proof archive. It lists unfinished work: conjectures about how to use mathematics that is already proved or certified, and questions the archive already leaves open. Every item below is labeled frontier.
@NVE024 on X is the author’s public account. treeOS, on this page, is that account’s name for unfinished use of the mathematics. It is not an installed system. The finite log at treeOS_LOG/OMEGA-SRSD/1.0 stays on the joining page. Its INSTANCE_CHECKED receipt covers that finite replay only. It is not attached to this page, and it does not review the written proofs.
Nothing here is a theorem, a claim record, a machine object, or a Zenodo deposit. Nine deposits remain nine. A work that has not already been written on this site is not invented here. The 10 November supplement at three bridges is not an item on this list. It has its own checker.
Frontier 1
One external operating record
No theorem says the specified maps are an operating system, a public account, or one theory.
Uses, without becoming: Scalar conjugacy, the integer embedding, translation of valid records, and recovery through a finite recorded history.
Frontier 2
Positive Class-I rules for every frequency at least 25
Existence of a strictly positive H₃-orbit-constant rule of target degree t_f for every f ≥ 25 is an open conjecture. No theorem in this archive covers those frequencies.
Uses, without becoming: The certificates through frequency 24. Those certificates are not this conjecture.
Frontier 3
Higher target degrees at frequencies 23 and 24
Higher degrees at f = 23 and f = 24 are not shown impossible. They are not proved.
Uses, without becoming: The separate certificates already hosted for those two frequencies.
Frontier 4
Output-conditioned optimum on the 600-cell
The exact value inside 307 ≤ ℓ* ≤ 352 is unresolved. The distinct interval 306 ≤ ℓ* ≤ 360 is not moved and is not settled by this page.
Uses, without becoming: Paper IX, version 0.6. This page does not rewrite that preprint.
Frontier 5
General exact decoding and compressed prefix counting
No scalable general algorithm and no efficient worst-case guarantee are established. A zero-budget decode in the finite treeOS replay stays UNRESOLVED.
Uses, without becoming: The finite decoders that already recover the supplied records. A finite replay is not a general decoder.
Frontier 6
Polar two-ball packing
The statement is conditional on external statements A-087 and A-343. Those statements are not proved on this site.
Uses, without becoming: The polar sampling page. The condition is not removed by listing it here.
Frontier 7
One theory from all of the branches
Specified joins do not prove that the source works are one theory, or a physical observer-field law.
Uses, without becoming: The maps named on the joining page, each inside its own hypotheses.