PRM-002 · Split Jordan carrier J3(O_s) (indefinite trace form)

Premise

Register corrected — R81 (D1, S327j). The PI ruled this correction to the register row (Trackers/RULING_R81_S327_PREMISE_REGISTER.md). Name now Split Jordan carrier J3(O_s) (indefinite trace form) (was Split Jordan carrier). The register row the drafting lane quotes below is the row as it was supplied to the lane, before R81; it is kept in the register's history (R29: nothing is overwritten).

Register kind: ADOPTED_PREMISE. Located suite statement:

The raw split algebra $J_3(\mathbb{O}_s)$ has signature $(15,12)$ (indefinite, not formally real), decomposing as $(3,0)_{\rm diag}\oplus 3\times(4,4)_{\rm off\text{-}diag}$.

Appendix L · Trace-form signature discriminator · PDF p.236 · appendix_l_born_bell_foundations.tex:117.

The registered excerpt and/or kind needs the scope clarification below; the registry itself is not edited.

What kind of premise this is

ADOPTED_PREMISE is the register kind. The located passage itself is a proposition about the chosen split algebra, not a sentence adopting that algebra. Appendix E separately locates the choice of algebra and trace form upstream of its selector. The distinction matters: a trace-signature calculation on a specified carrier is not a proof that physics must choose that carrier. The source supplies no retirement condition for the carrier choice here. Source status words: Trace-form signature discriminator; s215 (appendix_l_born_bell_foundations.tex:114).

Where the suite invokes it

Located invocations in the read excerpts, not an exhaustive full-source-tree census. Pages refer to saved Rev32.7 page-delimited text, not PDF-image authentication.

Arguments that rest on it

NO RECORD — trace-signature discriminator, appendix_l_born_bell_foundations.tex:114–119, kernel s215. Its decomposition is explicitly that of the split carrier. No carrying record is identified in the supplied candidates; no graph ADD is fabricated.

What breaks without it

NOT ASSESSED — the passage contrasts compact and split signatures, but does not derive consequences of removing the carrier choice from every subsequent argument. The calculation and the adoption should not be conflated.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: none (UNKNOWN, not INDEPENDENT). The lane's lines below describe the master as it was supplied to the lane (d0aa26db154ff43f), before these changes.

Declared today in the supplied material, Registrar master d0aa26db154ff43f: none (UNKNOWN, not INDEPENDENT). Draft dispositions — no ADD, CONFIRM or DISPUTE row; there is no declared edge to adjudicate. Unbound NO RECORD arguments are not graph ADDs. There are no declared or candidate records in this material. An empty list does not establish independence.

Tier and what this does not show

A premise is not a result, and invocation count is not importance. An ADD remains a proposal until house verification under R76; a DISPUTE goes to the PI. No record or premise is upgraded, downgraded, or edited. Unlocated dependencies remain unknown.

Sources

TeX: appendix_e_vacuum_selector.tex:509; appendix_l_born_bell_foundations.tex:114; appendix_l_born_bell_foundations.tex:114–119; appendix_l_born_bell_foundations.tex:117; appendix_l_born_bell_foundations.tex:118. Registrar: no carrying record identified in the supplied material. Premise: PRM-002. Suite-cited kernels: s215.