A registered result in its source context

E8.UNMAPPED.BANDWIDTH.01

Original ledger classification: Bandwidth search [E]/[C]/[O] (forced set-level structure sum=128=spinor/product=|W|/exponents=totatives; subchain flagged; per-degree matches declined; no new physical hit; reconciles v66+v354)

Original claim text

A DISCIPLINED BANDWIDTH SEARCH OF THE UNMAPPED E8 REGION (2026-06-22, the next step after v354). The natural follow-up -- 'search that region for hits and structures we overlooked' -- is itself the numerology temptation v354 warns about: a rich object like E8 yields a numerical match for almost anything. So this scan uses a STRICT discriminator: a candidate is real ONLY if it is a FORCED identity (a theorem about E8), never a coincidence. It also RECONCILES v66 (the 8 degrees coincide with TFPT's load-bearing integers) with v354 (only 2,8,30 are primary readouts). [E] FORCED SET-LEVEL (the genuinely overlooked structure, collective not per-number): sum(degrees)=128=dim S^+ the SPINOR half of 248=120+128 (theorem: sum of degrees=#pos roots+rank=120+8; v66 saw 2^7, the spinor reading is deeper -- the invariant budget equals the fermion content the carrier reads); sum(exponents)=120=#pos roots; product(degrees)=|W(E8)|=696729600; exponents={1,7,11,13,17,19,23,29}=the phi(30)=8 totatives of 30 (v223), so the unmapped degrees' exponents {11,13,17,19,23} are part of the forced totative set; max(degree)=30=h(E8). [C] SUGGESTIVE, NOT A THEOREM (the discriminator at work): 12=h(E6),18=h(E7),30=h(E8) are all degrees of E8 (the 2T/2O/2I McKay ladder, v219), but 'deg(E8) contains its subalgebras' Coxeter numbers' is not a general theorem, so the pattern is flagged, not claimed. [O] DECLINED (the numerology temptation): the per-degree atom matches 14=dim G2, 20=det L, 24=|W(A3)|=4!, 12=|R(A3)|, 18=p4(a)=2+2^4 (v66, which already flagged 12,18 as fittable) each admit >=2 readings from the frozen atoms with no forced selector, and the extra prime 7 in |W(E8)|=2^14 3^5 5^2 7 '=' the scalaron exponent g+n-1 is one of many readings of 7 -- all declined. [E] RECONCILIATION + HONEST CONCLUSION: the unmapped region yields NO new forced physical readout; its genuine content is collective (set-level, already in v66/v223) plus the Coxeter number, and the per-degree atom coincidences are unforced -- so v66 and v354 are both right once forced set/subchain structure is separated from unforced per-degree matches. The disciplined decline IS the anti-numerology result.

Original classification detail

[E] the set-level forced identities and the reconciliation; [C] the subchain Coxeter pattern; [O] the explicit declines. A self-critical search whose main finding is that there is nothing forced left to find per-number -- the correct outcome of an honest reverse audit; sharpens v354 (no PRIMARY readout, not 'unmapped'), reconciles v66.

Dependencies as recorded

E8.REVERSE.AUDIT.01; v354; v66; v223; v219; v305