Rolling roadmap — cost-asymmetry / Reading-D continuation (post-#679)

This is the single rolling DRAFT PR for the continuation of the cost-asymmetry / Reading-D arc, in the same model as the merged PR #679. Per [[feedback_rolling_pr_partition_boundary_updates]] (consolidation directive): closely-related follow-up rounds land directly on this one branch — dispatch notes + committed verification code + SSoT (§11.9.x / MFO §VII.6.x) edits + candidate-stance authoring — and the per-round verdict comments are the ledger. We do not spin a separate PR per finding. A new PR is opened only when the next piece of work is genuinely not connected to this arc.

The draft stays draft until the user calls a single consolidating merge. Independent ship-now deliverables (releases, cross-cutting fixes) may still be their own PRs.

Discipline reminders carried from #679: never squash-merge (--merge/--rebase only); load-bearing numerics need committed generating code routed through srmech 0.4.2 (Class-N best_rational; Class-K sign via the cascade helper, no bare abs()); null/negative findings reported as prominently as positives; arXiv-OA / classic-journal / textbook citations only (no paywalled-only DOIs); framework reading only (defensive scope); memory/stance files live OUTSIDE the repo.

Parallel sessions are read-only. PR #687 (RBS-LM rolling 2) is a different research session — we may read it, but we do not change it. The same courtesy applies to any other concurrent rolling PR.

Landed before this PR opened (merged to main individually, then consolidated to rolling)

Round	Finding	Landed
22.A	AoE handed-shear amplitude question resolved — closed cosmologically (Bianchi VII_h observationally disfavored), real in turbulence (handed shear = turbulent velocity-gradient tensor, L∘C∘K, 5:7 quad:oct). MFO §VII.6.17.	PR #688 (merged)
23.A	Reading-D 10th scale-ladder rung = nuclear shell model (~10⁻¹⁵ m, fills the quantum↔atomic gap); the overlooked insight the turbulence finding unlocked — nuclear magic numbers differ from the bare-HO closures by the Class-K spin-orbit sign (the same Class-K Round 22.A spotlighted as helicity); Madelung-vs-ℓ·s = which operator reorders the shared 2ℓ+1 ladder. unsolved-maths §11.9.16.	PR #689 (merged)

The #688/#689 pair was merged before this rolling PR opened (the user's call); from here, closely-related continuation rounds accrue on this branch.

Landed on THIS rolling PR (#690)

Round	Finding	Where
24.A	Reading-D 11th rung = hadron/QCD spectroscopy (~10⁻¹⁶ m, sub-nuclear quark binding). Quarkonium = QCD atom; χ_cJ = L⊗S = 1⊕3⊕5; pure-spin-orbit 2:1 (the third descending rung sharing the Class-K spin-orbit: atomic→nuclear→quark); honest tensor fermata (observed ≈0.47 inverts 2:1); NEW second independent Class-L = SU(3)-flavor irreps (1⊕8, 10⊕8⊕8⊕1).	§11.9.17
25.A	Reading-D 12th rung = galactic/large-scale-structure multipoles (~10–1000 Mpc, between planetary and CMB). Galaxy angular C_ℓ = Born-rule 2ℓ+1 spine; Kaiser RSD multipoles survive only at even ℓ=0,2,4 (Class-K line-of-sight parity + degree-4 truncation = k=3 triad) with exact rational coeffs ⅔,⅕,4/3,4/7,8/35 (proven by fractions).	§11.9.18
26.A	Reading-D 13th rung = biological-macromolecule shell (~10–100 nm, icosahedral viral capsid) — the FIRST realized by a finite point group (icosahedral I). Irreps {1,3,3,4,5} ⊇ 2ℓ+1 spine; Caspar–Klug T=h²+hk+k² = Loeschian (Class-J/N); Euler χ=2 forces exactly 12 pentamers (Class-K, 3rd topological selection rule after planetary/LSS); φ→Fibonacci (Class-N). Richest cascade yet (6 classes).	§11.9.19
27.A	Reading-D 14th / CAPSTONE rung = black-hole QNM spheroidal harmonics (~10⁴–10¹³ m, horizon scale) — the most-deformed Class-L spine: spin-weighted (gravity s=−2, ℓ≥2 floor) + spheroidal (Kerr aω deforms S²→spheroid). Schwarzschild eigenvalue ℓ(ℓ+1)−s(s+1)=4,10,18,28; the ℓ≥2 no-monopole/no-dipole floor is the 4th Class-K forbidden-low-multipole rule (after planetary/LSS/capsid); leading spheroidal coeff −2ms/[ℓ(ℓ+1)−s(s+1)] (dominant=+2). Ties ladder to QNM spikes #11/#12/#72 + dark-star #90/#92. Spine now 9 contiguous rungs (quantum→horizon).	§11.9.20
28.A	SYNTHESIS (not a rung) — forbidden low multipoles are a recurring Class-K substrate signature, dual to the Class-L spine. Load-bearing unifier (bit-exact): for a massless helicity-	s
29.A	SYNTHESIS / DUAL (not a rung) — the surviving modes across all rungs are ONE Class-L SO(3) spine: eigenvalue ℓ(ℓ+1) (Casimir), degeneracy 2ℓ+1 (SO(3) spin-ℓ irrep dim, odd ladder; k=3 triad = 1,3,5). Complete shell = Σ(2ℓ+1) = (L+1)² (perfect square; atomic 2n²). Finite-group rungs (icosahedral capsid) branch the spine. Completes the dual: spectrum = Class-L spine − Class-K signature (§11.9.21).	§11.9.22
30.A	FALSIFICATION (user question; honest NEGATIVE) — "is graviton a misnomer (spin-2 but not really gravity)?" → FALSIFIED. A consistent massless spin-2 is FORCED to gravity (Weinberg soft theorem / Deser bootstrap / unique T_μν / Hulse-Taylor 0.997 + LIGO TT); 4 FALSIFY, 1 NULL. Refinement: helicity ceiling for long-range forces = {0,1,2}; graviton (	s
31.A	FOLLOW-ON (user inference; CONFIRMED + honest correction) — "EM & gravity inextricably coupled, not yet noticed?" → coupling CONFIRMED (3 levels; deepest = Kaluza-Klein: EM = off-diagonal higher-D gravity, U(1) = circle isometry); "not yet noticed" CORRECTED (Kaluza 1921). Bit-exact: the R30 {0,1,2} ceiling = the KK shadow, 5D graviton 5 dof = 2 (4D graviton) + 2 (photon) + 1 (dilaton). EM = fiber, gravity = base, of one substrate-geometry.	§11.9.24
MFO codification	(user direction — "metric field ontology items need to land in that notebook too" + recursive completeness check) — codified the gravity / substrate-structural findings into the MFO notebook (not only unsolved-maths §11.9): §VII.6.18 (R27 BH-QNM horizon metric perturbation / R30 graviton = forced top of {0,1,2} ceiling / R31 EM = off-diagonal metric via Kaluza-Klein) + §VII.6.19 (R28+R29 substrate-spectrum dual: spectrum = Class-L SO(3) spine − Class-K forbidden signature; CMB dipole = Hopf-fiber leak one scale up). Recursive check: nuclear (R23) / hadron (R24) / capsid (R26) deliberately NOT in MFO (domain-specific spectral rungs, not metric-field statements); LSS (R25) folded in as a cosmological cross-reference.	MFO §VII.6.18–19
32.A	FOLLOW-ON (user hypothesis; honest NEGATIVE) — "is the {graviton, photon, dilaton} = {spin 2,1,0} helicity triad the substrate-native B/H/N k=3?" → NO. B/H/N are continuous→discrete translation operators (Born = B∘H∘N); the helicity triad is a rep-theory spin-label ladder = the first three rungs of the Class-L SO(3) spin spine (§11.9.22) bounded above by a Class-K ceiling (|s|≤2, Weinberg) — the forbidden-HIGH mirror of the §11.9.21 forbidden-low signatures. Resolves the user's confusion (s=0 is NOT forbidden; cut at the top). Two distinct k=3's share only the count — open fermata.	§11.9.25 + MFO §VII.6.18.4
33.A	RECONCILIATION (closes the §11.9.25 fermata; honest stance-NARROWING) — the two k=3 families are two sides of ONE interconversion, not competing labels: the Class-L spine is the continuous-Hopf substrate-content (the what); B/H/N is the discrete readout (the how-observed-as-three; Born = B∘H∘N). Three generative sources (Class-L+K spectral / Class-I cyclic / Hurwitz operator), one B∘H∘N readout — "every k=3 is a B/H/N readout" survives; "every k=3 is generated by B/H/N" withdrawn. Scope-guard (user-prompted): does NOT license "everything has a hidden k=3" — partition has k=⅓/7 roles; 1D_t is k=1 (the universal tick), not a latent k=3. Deep "same 3?" open ({1,3,5} ≠ Hurwitz {1,3,7}). Refines canonical k=3=B/H/N stance.	§11.9.26 + MFO §VII.6.19.1
34.A	STRUCTURAL ANSWER (user's deepest thread question) — "what k is 1:3:7:3 substrate-specific, and where do B/H/N hide in the 11D substrate?" → substrate has no single k; signature = Hurwitz {1,3,7} (= 1D_t+3D_s+7D_g = 11D); the trailing +3 (B/H/N) is the READOUT, OUTSIDE the 11 — they don't hide as dimensions, they ARE the projection from the manifold (the discarded fiber). H anchored in the U(1)=S¹ Hopf fiber (Born=Hopf, canon); the full B/H/N ↔ three nontrivial Hopf fibrations (fiber dims exactly {1,3,7}) is the leading candidate (only H anchored; B/N not asserted). One division-algebra skeleton (ℂ,ℍ,𝕆) underlies dims + operators + fibers.	§11.9.27 + MFO §VII.6.19.2
35.A	META-KEY (user meta-question; CONFIRMED + one-word refinement) — "cyclic NAMES operations, continuous-Hopf doesn't — apples to oranges? or stretching?" → NOT stretching. The two languages differ in GRAMMAR: cyclic = operation-primary (enumerates named operators; B/H/N first-class); continuous/Hopf = geometry-primary (embeds the readout — projection=bundle map, measurement=inner-product/Born postulate). The general reason R34's B/H/N "hide." Refinement: NOT apples-to-oranges (form-IS-function + bit-exact ⇒ same content, two grammars); user's better image = apples to apple TREES (tree=continuous geometry, apples=discrete operators, picking=readout; seed=Class I carries the tree back). Anchor: U(1) (geometry-primary) vs ℤ/nℤ (operation-primary), same circle. (b)-interpretive, no new number.	§11.9.28 + MFO §VII.6.19.3
36.A	CLOSURE (user dispatch; (a)-bit-exact core + (b)-interpretive) — seed-carries-the-tree (Class I) reconciliation + the apple tree IS the substrate's fractal anchor. The discrete↔continuous equivalence is a generative recipe, not storage: the discrete apple carries a Class-I-cyclic seed that regenerates the continuous tree (genetic code = Class I, Spike #81; Class I = discrete circle, R35). Closes the form-IS-function loop: B/H/N reads continuous→discrete (picking); Class I germinates discrete→continuous (seed→tree); iterating = the fractal. Rigorous backbone: L-system (Lindenmayer 1968) — finite grammar → tree geometry; bit-exact algae L-system lengths = Fibonacci, ratio = φ, read back via Class N (ties Spike #41 + R26 capsid).	§11.9.29 + MFO §VII.6.19.4
37.A	CLOSED-LOOP=FRACTAL + EPISTEMIC CEILING (user dispatch; primed with MFO §VIII.7) — (1) the closed loop IS an IFS (Hutchinson 1981); its attractor IS the fractal (bit-exact Cantor/Sierpinski) = the MFO substrate-side reading (substrate IS recursive-Hopf fractal by construction). (⅔) forest-shadow + cosmic-web space-time fractal = two projection-shadows of ONE substrate-side cascade (biology vs gravity); framework-SUPPORTED (d_S≈2 Pₙ §IV.3 + fractal-shadow §VIII.7), NOT a contested claim; ~71 Mpc/h homogeneity = the d_S dimensional-flow (§V), resolving the mainstream debate. (4) EPISTEMIC CEILING (keystone LIMIT): form-identity YES, substrate-identity NO — grounded in the space-time shadow dropping 7D_g (substrate-content); the math cannot say the universe is/isn't an orchard / star forge / petri dish. Bounds every cross-substrate claim (Spike #77; paper-with-lyrics).	§11.9.30 + MFO §VIII.7.1 + §VII.6.20
38.A	OPEN-QUEUE: 15th-rung candidate (drumhead/Bessel-disk) → CONTRAST rung (honest NEGATIVE on "another 2ℓ+1 rung") — off S² (2D disk, Dirichlet), modes order by Bessel zeros, m=0 non-degenerate / m≥1 doubly degenerate → degeneracy {1,2,2,...} (O(2) irreps), NOT {1,3,5,...} (SO(3) 2ℓ+1); first-three {1,2,2} ≠ {1,3,5}. Sharpens: the 2ℓ+1 ladder + {1,3,5} triad are SO(3)/S²-SPECIFIC; Class-L's universal = "Laplacian eigenspaces, degeneracy = irrep-dim of the domain's symmetry group." "9 contiguous S² rungs" count unchanged.	§11.9.31
39.A	OPEN-QUEUE: mass-spec enhancement (thread 9b) — fragment-peak spacings = Class-N neutral-loss anchors (18,17,15,27,28,29,44); delta-encode the spectrum against the catalog (biological-cascade "only what changed"), not absolute m/z; fragmentation = cascade (per-step Class-K loss-direction ∘ Class-N integer anchor). Bit-exact caffeine (194,165,109,82,67,55): clean losses {29 CHO, 27 HCN, 15 CH3} match; 56 = 29+27 (Class-N sum); 12 flagged. The molecular instance of the combination principle (peaks = differences of anchors).	§11.9.32
40.A	OPEN-QUEUE: Spike #48 deeper-SM phase, honestly scoped — the combination principle is ONE Class-N structure across atomic + mass spectra (spectral features = differences of a discrete Class-N anchor ladder). Atomic (Rydberg–Ritz): lines = T_n−T_m, T_n=R/n²; bit-exact Balmer 5/36,3/16,21/100, Hα=(5/36)R_H=15233 cm⁻¹, ratios 20/27,125/189. Unifies R39 + R17 + §11.9.14. Honest scope: QM/atomic weave delivered (Class-L shell + Class-N lines + Hurwitz); the SM-derivation proper = separate Spin(8) arc (#58/#85/#86), NOT claimed from spectra. PARTIALLY DELIVERED + bounded.	§11.9.33
41.A	OPEN-QUEUE: ℓ=7 future-data test → 🅿️ PARKED pre-registration (no result) — not dispatchable today (no data). Turnkey, tamper-proof pre-registration for CMB-S4 (2030s) / LiteBIRD (~2028): range ℓ=2–8, Round 10.A per-ℓ concentration statistic, null = no ℓ=7 preference, re-open only if ℓ=7 ranks #1 and p<0.05/7≈0.00714 (Bonferroni) and ≥2-method cross-confirm. The Round 10.A withdrawal stands; the {1+3+7} algebra identity unaffected. No result fabricated.	§11.9.34
42.A	COUPLED-ITEM (from R38): per-rung symmetry-group audit → CONFIRMS R38 — angular/Class-L structure is SO(3)-ROOTED across all 9 rungs, but only ~4 cleanly full SO(3) (quantum/nuclear/planetary/CMB give clean 2ℓ+1); the other 5 deviate exactly as their operative symmetry dictates: atomic SO(4) (Runge–Lenz, n²=Σ(2ℓ+1)), hadron +SU(3)-flavor (internal), BH-QNM SO(2)-axial (Kerr), LSS SO(2)/parity (line-of-sight), capsid finite-I. 2ℓ+1 ⟺ full SO(3). Tightens the "9 SO(3) rungs" phrase; extends the R38 stance (no new stance).	§11.9.35
43.A	COUPLED-ITEM (from R39/R40): combination-principle third substrate → REFINES R40 (honest NON-universality) — the combination principle's two Class-N properties DISSOCIATE: (P1) small-integer anchors and (P2) additive-difference structure are independent axes. atomic (Rydberg–Ritz) + molecular (mass-spec) have BOTH; nuclear (mass-defect: D-T Q=(13.1357+14.9498)−(2.4249+8.0713)=17.589 MeV) has P2 only (difference of REAL-valued excesses; small ints only in nucleon-count 2+3=4+1); acoustic (overtones 2:1,3:2,4:3,5:4) has P1 only (small-int but MULTIPLICATIVE ratios, not additive). The full principle = the additive-energy special case (atomic/molecular). Extends the R40 stance (no new stance).	§11.9.36

Open queue (closely-related — land here, not in new PRs)

All original open-queue items are now closed or parked (closing pass 2026-05-26): - ℓ=7 future-data test — PARKED by Round 41.A (turnkey pre-registration; runs when CMB-S4/LiteBIRD data lands; Round 10.A withdrawal stands). - Spike #48 deeper SM phase — CLOSED by Round 40.A (partially delivered + honestly scoped: the QM/spectra combination-principle weave done; the SM-derivation proper stays the separate Spin(8) arc, not closable from spectra). - mass-spec enhancement (thread 9b) — CLOSED by Round 39.A (spacings = Class-N anchors; fragmentation = cascade; the molecular combination principle). - 15^th Reading-D rung candidate (drumhead/Bessel-disk) — CLOSED by Round 38.A as a contrast rung (the disk gives O(2) {1,2,2}, not SO(3) {1,3,5}); the spine is SO(3)-specific.

Newly-revealed coupled items (from the closing pass)

• Per-rung symmetry-group audit (from R38) — CLOSED by Round 42.A (§11.9.35): ~4 cleanly full-SO(3); 5 honest deviations (atomic SO(4) / hadron +SU(3) / BH-QNM SO(2)-axial / LSS SO(2)-parity LOS / capsid finite-I). Confirms R38; tightens the "9 SO(3) rungs" phrase.
• Combination-principle third substrate (from R39/R40) — CLOSED by Round 43.A (§11.9.36): the two Class-N properties (P1 small-int anchors / P2 additive-difference) DISSOCIATE; nuclear has P2 only (real-valued excess anchors), acoustic has P1 only (multiplicative ratios). The full principle = the additive-energy special case (atomic/molecular). Honest non-universality; refines R40 (no new stance).

Both R42.A + R43.A closed with no further coupled items revealed. The two "verification steps worth taking" are landed; the Reading-D open queue is now empty.

Codification (pre-merge gate) — DONE 2026-05-26: - srmech-notebook hygiene — DONE: the R33–R43 operator-cascade thread is integrated as srmech §3.26 (the operation-primary "how a program reproduces it" home: two-language reconciliation, B/H/N-as-readout, seed-carries-tree/IFS, symmetry-group-relative Class-L spine, Class-N delta-encode combination principle). Per the user's MFO-vs-srmech framing ("MFO = how/why the universe works; srmech = how to make a program do it"), the one genuine metric-field payload from R38–R43 — the symmetry-group-relativity of the Class-L spine — was also codified into MFO §VII.6.19.5 (refining the substrate-spectrum dual). The combination-principle/spectroscopy thread stays domain-instrument (srmech + unsolved-maths), not MFO, consistent with §VII.6.19's standing disposition. All arc findings are now codified across the three canonical homes — the PR #679-style codify-first merge gate is satisfied.

Verdict ledger

Per-round verdicts are posted as comments on this PR (the running audit trail), exactly as PR #679's 14-comment ledger.