Drift-kinetic island/layer solver#318
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…an under src/islands Design bundle for ISLET (Integrated SoLver for Evolving Tearing), a planned steady-state multi-species drift-kinetic solver for the resonant island/layer region, generalizing the Modified Rutherford Equation the way SLAYER generalized linear layer theory. Revised against the full Imada/Dudkovskaia/Leigh reference set in docs/resources/Drift_Kinetic_Island_References (see REVISION-2026-07-07). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…uthor-title convention Renames the nine PDFs under docs/resources/Drift_Kinetic_Island_References to the YEAR-Author-Title convention used by the rest of docs/resources, and extends the .gitignore resources-PDF negation to subdirectories (!docs/resources/**/*.pdf) so these tracked references match the existing docs/resources/*.pdf policy. Syncs the filename references in the ISLET reference-library doc (docs/08). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…e convention) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…n into in-repo layout
Drop the working acronym ISLET in favour of the plain module name Islands, and
record the module-naming convention (simple intuitive names, not standalone-code
acronyms) in the repo-root CLAUDE.md.
Reconcile the design bundle from its standalone-package assumptions into the
in-repo layout:
- module conventions -> src/Islands/CLAUDE.md
- overview -> docs/src/islands/index.md
- design docs 00-08 -> docs/src/islands/design/
- Physics Book / state / derivations / papers / notes / LOG / QUESTIONS
-> docs/src/islands/{,state,derivations,papers,notes}
- benchmarks + figures -> benchmarks/islands/{,figures}
- verify harness -> src/Islands/verify/
- tests -> test/runtests_islands_*.jl (top-level test/)
- regression cases -> integrated under regression-harness/ (islands_*)
Islands is a submodule of the GeneralizedPerturbedEquilibrium package (no separate
Project.toml), not a standalone subpackage; docs/03/06 updated accordingly.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
logan-nc
changed the title
… infrastructure Stand up the Islands submodule and the infrastructure the autonomous-run protocol (design doc 06) assumes: - src/Islands/Islands.jl (module Islands, skeleton) wired into the package - docs/src/islands/LOG.md + QUESTIONS.md (session memory + blocker queue; Q1 records that julia is not on the automation shell PATH) - .claude/settings.json + hooks (guard-bash PreToolUse, stop-check Stop) for unattended dontAsk runs; physics-verifier subagent as the [VERIFY] backstop - docs/src/islands/design/M1-launch-prompt.md (the milestone contract fed to the overnight loop) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…docs The exported Islands module carries a docstring, which checkdocs=:exports requires be covered in the manual. Add docs/src/islands.md with an @autodocs block and wire it into make.jl (API Reference), matching the other submodule pages. Fixes the missing_docs docs-build failure introduced by the module stub. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…tings.json /doctor flagged two deny rules as skipped: the :* prefix wildcard is only valid at the end of a pattern. Rewrite them with a mid-pattern wildcard so the rules load and again restrict the protected-branch pushes for any remote or flags.
A loaded OMFIT module leaks the conda env lib dir onto LD_LIBRARY_PATH, shadowing Julia's bundled artifacts (CHOLMOD, glib/Cairo/GR) and producing false 'broken build' blocks in the Stop hook. Strip the var for the julia smoke check via env -u; this is a no-op on a clean shell and in CI.
M1 needs forward-mode AD for the JVP/AD-compatibility checks (design docs/src/islands/design/04-numerics.md §9). Adds ForwardDiff to Project.toml (already present transitively in the manifest); removes nothing. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…ck + verify harness Land the milestone-M1 numerical skeleton (design 03 §1-2, 04; ladder A1/A2), structure only — no [VERIFY] physics coefficients assigned in src/. - phasespace/PhaseSpace.jl: the (x, ξ, y, E, σ) grids with layer-clustered maps. Fourier spectral ∂ξ; Fornberg high-order finite differences for ∂x/∂y on sinh-stretched grids (per-derivative window widths so D1 and D2 are both 4th-order including boundaries); composite-Simpson quadrature weights; Gauss-Laguerre energy nodes. Pure numerics. - operators/Operators.jl: AbstractTerm + apply! + residual! and the term structs of 03 §2 (ParallelStreaming, MagneticDrift with the :original/:improved toggle, ExBDrift as the (x,ξ) Poisson bracket, Collisions, GradientDrive, PerpTransport and RadiationSink L4 stubs, Quasineutrality field residual). Every physics coefficient is a supplied data field, never a literal; allocation-free and generic over eltype so ForwardDiff duals flow through. - verify/Verify.jl: manufactured-solution (MMS) + AD-vs-finite-difference JVP harness, plus allocation probes. Manufactured coefficients are arbitrary order-unity test values (not physics), exercising the discretization only. - Islands.jl: wire the three submodules. physics-verifier: PASS (no [VERIFY]-policy violation). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…to runtests test/runtests_islands_grids.jl and test/runtests_islands_operators.jl, included in test/runtests.jl: - A1 per-operator MMS: 4th-order convergence for the ∂x/∂y differential terms, machine precision for the Fourier ∂ξ (drift) term; assembled kinetic residual converges at 4th order. - A2: forward-mode-AD JVP of the (nonlinear) assembled residual matches the central finite-difference directional derivative to ~1e-9. - Allocation regression: every apply! and residual! hot path allocates 0 bytes. - Grid unit tests: Fourier exactness, mapped-FD order, Simpson/Gauss quadrature, layer-clustered packing, IslandGrid assembly and input validation. All 53 Islands tests pass. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…path) - docs/src/islands.md: document the M1 skeleton (PhaseSpace/Operators/Verify), restating the structure-only [VERIFY] discipline. - LOG.md: M1 session entry (what moved / blocked / next). - QUESTIONS.md: Q1 RESOLVED — julia is at the ncl2128 software dir and must be invoked with a clean LD_LIBRARY_PATH (OMFIT contamination); used here to run the suite locally. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Set up the next milestone (M2 — L0 solve machinery) for the autonomous loop, mirroring the M1 launch-prompt bootstrap. - docs/src/islands/design/M2-launch-prompt.md: the M2 milestone contract. Scope = full L0 solve machinery (solvers/, moments/, frames/, fields/, species/, neoclassical-matching BCs) as AD-compatible allocation-free structure with every physics coefficient a [VERIFY]-gated parameter. DoD = the physics-free structural gates (A5 null, assembled solve-MMS, A8 y_c conditioning, A4 conservation, A3 parity, A7 ⟨∂²h/∂x²⟩=0) + suite + PR + Paper-I OUTLINE + the clearance queue. The York gates (B5a/b/c, B2, B4) are explicitly OUT — they need human-cleared physics; reaching one by hardcoding is a policy violation, not completion. - QUESTIONS.md: seed the parallel-human clearance queue — Q2 (ratify D7/D8), Q3 (clear the L0 [CHECKED] coefficient set with exact cites), Q4 (open [VERIFY]s: the psi-tilde q_s'/q_s typo, B5a collisionality, acquire WCHH96 + Park 2022). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Drop the overnight-loop framing (dontAsk/--continue header, unattended language, Stop-hook exit-criteria) — M2 is driven interactively via /goal in auto mode. Blocked coefficients are surfaced to the user to clear live rather than only parked in QUESTIONS.md. The contract (scope, DoD, [VERIFY] hard rule, gated York gates) is unchanged. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…ylov solver Matrix-free GMRES backend for the L0 solve (design docs/src/islands/design/04-numerics.md $5, $9). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
…es, fields, moments
Land the Level-0 solve structure (design 03 §1-3, 04 §3-5; M2 contract), every
physics coefficient a supplied [VERIFY]-gated parameter — no literal in src/:
- solvers/Solvers.jl: matrix-free Newton-Krylov (Krylov.jl GMRES on a
preallocated ForwardDiff JVP operator; Eisenstat-Walker forcing; backtracking
line search; convergence on both norm and max-norm per 04 §5), YBlockJacobi
physics-block preconditioner skeleton with TSVD-regularized pencil solves
(the explicit y_c treatment of 04 §3), dense tiny-grid debug Jacobian, and a
pseudo-arclength continuation scaffold with fold detection from day one.
- species/Species.jl: Species{AbstractBackground}, Maxwellian/SlowingDown,
Bulk/Trace roles, validation + trace-criteria check (warn, never degrade) —
the D3 first-class species plumbing (02 §1).
- frames/Frames.jl: Level0Parameters input vector (01 §5) and the frame
conversion FORMS with every sign/normalization a NaN-defaulted gated
FrameConvention field — an un-cleared convention poisons results instead of
guessing (QUESTIONS Q3).
- fields/Fields.jl: Q(Ω)/h(Ω) flattened-electron closure structure (prefactor
supplied), the coefficient-free A7 identity ⟨∂²h/∂x²⟩_Ω = 0, and the
NaN-gated ElectronClosure constant set.
- moments/Moments.jl: J̄_∥ assembly from charge-scaled weighted moments,
Δ_cos/Δ_sin projections with REQUIRED gated prefactors (ψ̃ open [VERIFY],
sin normalization unpinned — QUESTIONS Q4), Ω label + ⟨·⟩_Ω average +
channel-split diagnostics (pinned half-width convention).
- operators/: PitchAngleDiffusion in mimetic divergence form (exact discrete
particle conservation + entropy sign, ladder A4), FarFieldConditions
matching BCs (never bare Neumann, 01 §3), weighted_moment!, flat-index
helpers; IslandGrid now records y_c for the A8 monitor.
- verify/: solve-level MMS + zero-drive configurations (A5/A1-solve) and the
yc_block_sigma_min conditioning monitor (A8, the L23 §4.2 silent-noise
regression tripwire).
All new kernels pass a --check-bounds=yes run (M1 lesson).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…/A8 + solve-MMS) test/runtests_islands_solve.jl (67 tests, wired into runtests.jl): - A5 zero-drive null: residual exactly machine zero at g ≡ 0; Newton falls back to the zero state from a perturbation. - A1-solve: assembled Newton-Krylov solve recovers the manufactured state at design order (observed 3.98 on the nx = 17→33 pair). - A4: exact discrete particle conservation (≲1e-11) + entropy sign of the mimetic pitch-angle operator; allocation-free apply!. - A3: Δ_cos even / Δ_sin odd under ξ-reflection, spectrally exact projections. - A7: ⟨∂²h/∂x²⟩_Ω = 0 to 1e-10 across Ω and prefactors (coefficient-free). - A8: y_c-block σ_min monitor is finite/positive and detects an artificially singularized pencil. - Preconditioner gate: YBlockJacobi cuts GMRES iterations >2× at identical solutions; far-field BC rows; pseudo-arclength fold detection; species + gated-frames plumbing. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…ctural regression case - benchmarks/islands/ (+ figures/): the docs/05 B-ladder scripts B2 (large-w limits), B4 (polarization ω_E structure), B5a/b/c (York threshold triangle) — all SKIPPED, each naming the QUESTIONS.md entries (Q2-Q4) whose human clearance un-gates it. Un-skipping by filling in a coefficient is the forbidden action; the scripts say so. - regression-harness: new computed case islands_l0_structural tracking the structural numbers that silently move if the discretization/solver/quadratures drift — solve-MMS error + Newton/GMRES iteration counts (nx=17), the A7 closure identity, and the A8 y_c-block sigma_min. Verified locally: err=5.254e-2, 6 Newton / 1210 GMRES, A7=8.0e-17, sigma_min=0.1139. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
- docs/src/islands/papers/paper-1/OUTLINE.md: the Level-0 figure contract (docs/07 §3), claims → figures → ladder IDs. C1-C3 (discretization order, solver conditioning, conservation structure) are green as CI artifacts; C4-C8 (neoclassics, large-w limits, the York triangle, the Δ_pol(ω_E) reversal, the L23 electron-Δ_pol question) are gated on QUESTIONS Q2-Q4. - docs/src/islands.md: M2 status (all seven submodules, gating summary). - LOG.md: M2 session entry, including the solve-well-posedness lesson (generic y-diffusion without BCs is unstable; the mimetic degenerate form + far-field x-BCs are the correct structure). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…docs missing_docs) Documenter's checkdocs=:exports requires every exported docstring in the package (including submodules) to appear in a page; the islands.md @autodocs block only listed the top-level Islands module, so the PhaseSpace/Operators/ Verify exports failed the docs build. Add per-submodule @autodocs sections. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…tract (derivation lane) User decisions (2026-07-08): PR #324 merged; D7 and D8 ratified as written (Decision Log updated, Q2 RESOLVED); Q3 clearance mode = re-derivation first. M2b-launch-prompt.md is the next milestone contract: independent derivations of the L0 coefficient set into docs/src/islands/derivations/ with cross-check tables against the [CHECKED] transcriptions, item-by-item human sign-off (recorded in docs/01) clearing coefficients into a named-configuration builder, progressive un-skipping of the B-ladder with docs/05 reporting, and honest triage of any threshold disagreement. Provenance rules sharpened: [DERIVED] never presented as transcription, no unsigned coefficient in src/, no tuning to pass benchmarks. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…citation The docs/08 island-subfolder map missed the SLAYER paper sitting in the general GPEC library (docs/resources/2022-Park-Parametric dependencies...). Map and Q4 corrected; only WCHH96 (Wilson, Connor, Hastie & Hegna, Phys. Plasmas 3, 248 (1996), doi:10.1063/1.871830) remains to acquire. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…R-matching template - WCHH96 (Wilson, Connor, Hastie & Hegna, PoP 3, 248 (1996)) added to the island reference library by the user and promoted into the docs/08 primary table: first-hand source for the flattened-electron closure (docs/01 §2.4) and the large-w Eq. (85) target (ladder B2) — previously cited only via I19/L23/Diss19 transcriptions. - Burgess 2026 (toroidal Δ' + Park-2022 SLAYER two-fluid slab layer) recorded as B26: the outer/inner regime-generalized matching template that Islands extends from zero-width linear layers to finite-width islands (ladder D1). - Q4 acquisition sub-items resolved; remaining open: ψ̃ amplitude check and B5a run collisionality. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…caling-first)
User-flagged flaw: absolute literature numbers (w_c 2.76/8.73, 0.45/1.46 rho,
the kokuchou 0.440 fit, the -0.89 omega_dia reversal, D23a shaping widths) were
propagated as pass/fail targets, but reproducing an absolute number requires
every input of the source's exact scenario — which the lineage under-specifies
(B5a's own collisionality is internally contradictory: I19 §4.2 nu*=0.01 vs L23
nu*=1e-3).
Decision D9 (docs/00): four-tier target taxonomy in docs/05 —
T1 exact math; T2 internal cross-checks & toggle differentials (sharpest,
primary quantitative gates); T3 scalings/trends/existence vs literature
(primary literature-facing gates); T4 absolute reproduction (audit-gated,
never pass/fail without an input manifest, downgraded to T3 where the source
is under-specified). Plus a fifth triage outcome ("under-specified source
configuration") and three reporting rules (publish the manifest; prefer
ratios/differentials; sensitivity scans).
Applied across docs/05 (all B/C rows retagged, A7 constants marked T1), docs/00
(gate softened, D9 logged), Paper-I OUTLINE (C5-C7 scaling-first; new C9 = the
input-completeness audit as a methods deliverable), the three B benchmarks +
README (tier-labeled), the M2b prompt (new deliverable: per-source input
manifests; B-ladder DoD = T2 differential + T3 scalings, T4 only with
manifests), QUESTIONS (B5a collisionality reframed as the audit type specimen),
numerics.md and islands.md status. Docs-only; local docs build green. Aligns the
ladder with the SLAYER-validation precedent (Park 2022 / Burgess 2026).
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…closes the psi-tilde [VERIFY] First M2b derivation-lane chapter (Decision D7, re-derivation-first). Independent re-derivation of the island flux amplitude from the helical-flux island geometry: psi-tilde = (w_psi^2 / 4) (q_s' / q_s) [DERIVED: 2026-07-11] with q_s' = dq/dpsi. Three independent arguments give q_s'/q_s: (a) the helical flux chi_0 = psi - psi_tor/q_s has curvature chi_0'' = -q_s'/q_s; the constant-psi island half-width w_psi = 2 sqrt(psi-tilde/|chi_0''|) inverts to psi-tilde = (w_psi^2/4)|chi_0''|; (b) dimensional analysis makes q_s/q_s' impossible (it gives [psi]^3, not [psi]); (c) Omega = chi/psi-tilde reproduces the pinned Omega = 2(psi-psi_s)^2/w_psi^2 - cos xi exactly. Closes the open [VERIFY] (QUESTIONS Q4). First-hand check of I19: the paper as printed (print p.3, text after Eq.6) shows q_s/q_s', but its own Eq.(7) Omega requires q_s'/q_s and it defines L_q = q/q' — so I19 is internally inconsistent and the amplitude text is a published typo (docs/05 triage: their published- equation error, same class as the L23 §2.6 amendments). This is exactly the failure mode the re-derivation-first policy exists to catch. physics-verifier: PASS (provenance clean, logic verified, no src/ coefficient assigned — psi-tilde stays gated in Moments.delta_moments until human sign-off). Docs-only; local docs build green; wired into the Islands > Derivations nav. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…ned-off coefficient) Human sign-off 2026-07-11 of the psi-tilde derivation (D7). Records the clearance and un-gates the cleared relation: - docs/01 §1: [CHECKED: I19 Eq.5...] -> [CLEARED: sign-off 2026-07-11, derivation link]; the psi-tilde [VERIFY] marked RESOLVED (I19 published typo; physical form q_s'/q_s). - Moments.island_flux_amplitude(; w_psi, dq_dpsi, q_s) = (w_psi^2/4)(q_s'/q_s), anchored to the derivation, with 4 tests (value, w^2 scaling, half-width round-trip, q_s=0 guard). 71 islands-solve tests green. - delta_moments prefactors stay required/gated (mu_0 R + sin-normalization pin are separate open items); Frames/Fields NaN-gates untouched. physics-verifier: PASS (formula matches signed-off derivation; clearance recorded, not a silent promotion; nothing else un-gated). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…iginal/:improved toggle (D7)
Second M2b derivation-lane chapter. Independent re-derivation of the orbit-
averaged magnetic drift frequency from the guiding-centre drift (I19 Eq.8) and
p_phi conservation:
omega_hat_D = (sigma v_hat/(1+eps))[ (1/L_hat_q)<sqrt(1-yb)/b>
- (1/2)<(1/L_hat_B)(2-yb)/(b sqrt(1-yb))> ]
Two physical pieces: (1) the drift-orbit radial width x_D = rho_hat_theta_i
(sigma v_hat/(1+eps)) sqrt(1-yb)/b coupled to the safety-factor shear (1/L_q);
(2) the grad-B drift from dB/dpsi (1/L_B). The :original/:improved toggle is the
treatment of dB/dpsi: D21 Eq.(A2) gives dB/dpsi = -(B_phi/R_0^2 B_theta) cos theta
(low beta), so the cos theta orbit-averages to O(eps) => :improved sets
L_hat_B^-1 = 0; :original keeps it finite. This toggle is the highest-impact
physics item (the T2 ~x6 threshold-width differential; absolute 8.73->1.46 rho_bi
is T4/audit-gated, per D9).
Cross-checks (all first-hand): I19 Eq.(32), D21 Eq.(B1) [with the identity
V_par + lambda V^2/(2 V_par) = V(2-lambda B)/(2 sqrt(1-lambda B))], D21 Eq.(A2).
No discrepancy (unlike the psi-tilde typo).
physics-verifier: PASS (algebra (a)-(d) verified by hand, D21-B1 reconciliation
confirmed, provenance clean, no src/ change; MagneticDrift.c_D stays gated).
Docs-only; local docs build green.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…le; drift-model toggle usable) Human sign-off 2026-07-11 of the omega-hat-D derivation (D7). Records the clearance (docs/01 §2.1: [CHECKED] -> [CLEARED]) and implements the cleared coefficient: - New src/Islands/coefficients/Coefficients.jl: the home for human-cleared L0 physics coefficient builders (M2b fill-ins). magnetic_drift_frequency(...) computes omega-hat-D = (sigma v_hat/(1+eps))[inv_Lq A - (1/2) inv_LB G] via the orbit-average brackets A=<sqrt(1-yb)/b>, G=<(2-yb)/(b sqrt(1-yb))> (QuadGK; passing full-circuit, trapped bounce-integral with the integrable turning-point singularity). variant=:improved forces inv_LB=0 (D21 proxy). Wired into Islands.jl. - 13 tests: eps->0 analytic limit (A->sqrt(1-y), G->(2-y)/sqrt(1-y)), the toggle (:improved == :original with L_B=0), sigma-odd / v_hat-linear prefactor, trapped finiteness, forbidden-y and bad-variant guards. 84 islands-solve tests green. The toggle is a large effect at the test point (grad-B nearly cancels the shear term) -- the mechanism behind the ~x6 threshold differential. physics-verifier: PASS (formula matches signed-off derivation; clearance recorded; trapped branch sound; Frames/Fields NaN-gates and Moments prefactors untouched). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…deflection frequency + nu_star (D7) Third M2b derivation-lane chapter. Independent re-derivation of the Level-0 momentum-conserving pitch-angle (Lorentz) collision operator (I19 Eq.9), the deflection frequency (I19 Eq.11), and the nu_star normalization (L23 Eq.2.3.40): - The pitch operator is Lorentz scattering in self-adjoint form w^-1 d_lambda(P d_lambda) with diffusivity P(lambda)=lambda sqrt(1-lambda B) and measure w=B/sqrt(1-lambda B); the change of variables from the pitch cosine derives the exact 2 nu_jj prefactor. This is the same divergence form the mimetic PitchAngleDiffusion discretizes (conservation gate A4). - Deflection frequency nu_jj = nu_tilde[phi(v_hat)-G(v_hat)]/v_hat^3 (Chandrasekhar), with the :chandrasekhar/:vcubed sub-toggle. Low-v: phi-G -> (4/3 sqrt-pi) v_hat (LINEAR) so nu_jj ~ 1/v_hat^2 diverges -- the "nu_tilde ~ u^-2 divergence" of docs/01 §2.3 motivating the analytic average. - nu_star = nu_jj Rq/(eps^3/2 v_th) normalization. Two sub-items honestly DEFERRED (not asserted, policy rule 4): the analytic <nu_hat_ii>_u constant (L23 Eq.4.1.6, its own short derivation) and the discretized diffusivity profile (numerics, ties to A4). Review caught two errors, both fixed before sign-off: the §3 low-v limit (phi-G is linear, not cubic -> nu_jj diverges, not finite) -- caught independently by me and the physics-verifier -- and a §2 factor-of-2 in the change of variables (now derives the exact 2 nu_jj). Docs-only; local docs build green. Awaiting human sign-off. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
… src (P(lambda), deflection frequency) Human sign-off 2026-07-11 of the collision-operator derivation (D7). Records the clearance (docs/01 §2.3: [CHECKED] -> [CLEARED] for the operator structure, deflection frequency, and nu_star; the <nu_hat_ii>_u constant stays [CHECKED]- gated as a deferred sub-item) and un-gates the cleared building blocks: - Coefficients.pitch_diffusivity(lambda, B) = lambda sqrt(1-lambda B): the Lorentz operator's self-adjoint diffusivity P (feeds conservative_pitch_operator; vanishes at both endpoints, preserving the A4 gate). - Coefficients.deflection_frequency(v_hat; model): nu_jj = nu_tilde[phi-G]/v_hat^3 (:chandrasekhar) or nu_tilde/v_hat^3 (:vcubed), phi via QuadGK, G Chandrasekhar. - 11 tests: P endpoints/positivity/domain; deflection high-v (-> nu_tilde/v_hat^3, with the slow 1-1/2v_hat^2 approach) and low-v (-> (4/3 sqrt-pi)/v_hat^2 divergence, the derived linear phi-G limit); chandrasekhar < vcubed at low v; model/domain guards. 96 islands-solve tests green. The full discretized/orbit-averaged PitchAngleDiffusion assembly and the <nu_hat_ii>_u momentum-restoring constant remain deferred (docs/01 §2.3 note). Derivation physics-verifier: PASS (after review caught + fixed a low-v limit error and a change-of-variables factor). Un-gate implements the just-verified cleared forms directly, validated by the eps/velocity-limit tests. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…a) + amplitude (D7); fix Coefficients docs coverage Fourth M2b derivation-lane chapter (awaiting sign-off). Independent re-derivation of the flattened-electron profile function and its amplitude: - The closure constraint <d2h/dx2>_Omega = 0 (the A7 identity) gives the ODE 2 h'' <Omega+cos xi>_Omega + h' = 0; with <Omega+cos xi>_Omega = Q/(2Q') (Q=(1/2pi)∮sqrt(Omega+cos xi)dxi) this integrates to h'(Omega) = C/Q(Omega) -- i.e. h = Theta(Omega-1) C ∫_1^Omega dOmega'/Q. The already-green A7 gate IS this closure constraint. - Far-field matching h -> x (Q -> sqrt(Omega)) fixes the amplitude C = w_psi/(2 sqrt2), matching I19 Eq. 18 exactly. - The I19 Eq. 22 flow-relation structure is presented; the two constants k ~= -1.173 (Hirshman-Sigmar) and the 1.46 in f_p = 1 - 1.46 sqrt(eps) are honestly DEFERRED (their own short derivations), not asserted. physics-verifier: PASS (algebra (a)-(e) verified first-hand incl. h'=C/Q and the C=w_psi/2sqrt2 matching; provenance clean; deferred constants not asserted). Also FIXES the docs build (was red since the omega-D commit): the new Coefficients module's exported docstrings were not in the manual; added its @autodocs section to islands.md (checkdocs=:exports). Local docs build green. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…ts.h_amplitude) Human sign-off 2026-07-11 of the electron-closure derivation (D7). Records the clearance (docs/01 §2.4: h(Omega) form + amplitude [CLEARED]; the flow constants k ~= -1.173 and f_p's 1.46 stay [CHECKED]-gated as deferred sub-items) and un-gates the cleared amplitude: - Coefficients.h_amplitude(w_psi) = w_psi/(2 sqrt2): the flattened-electron profile prefactor C, derived from the flattening constraint (h'=C/Q) + far- field matching h->x. Feeds Fields.h_profile's prefactor. - 3 tests: the amplitude value; the far-field asymptote h_profile(Omega; C) -> (w_psi/sqrt2)(sqrt(Omega)-1) (a real check of the §3 derivation + the Q->sqrt(Omega) asymptotics); ElectronClosure k/f_p stay NaN. 98 islands-solve tests green. Derivation physics-verifier: PASS (h'=C/Q ODE and C=w_psi/2sqrt2 matching verified first-hand). Un-gate is a one-line cleared relation; far-field test validates it physically. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…), arbitrary tau (D7) Fifth M2b derivation-lane chapter (awaiting sign-off). Independent re-derivation of the Level-0 quasineutrality closure from the ion/electron density moments: - Ion moment n_i = n0(1-ePhi/T_i) + n0'(psi-psi_s) + dn_bar_i (from f_i, I19 Eq.23). - Electron moment n_e = n0(1+ePhi/T_e) + n0' h(Omega) (flattened closure; the v_par-odd term vanishes). - n_i=n_e => Phi_hat = tau/(tau+1)[dn_bar_i/n0 + L_n0^-1(x - h_hat)]. The denominator (tau+1)/tau is the SUM of ion+electron adiabatic shielding responses (1/T_i + 1/T_e) -- the origin of the "2" in 1/(2 L_n0). At tau=1 this reduces exactly to I19 Eq. A.11 [dn_i/n0 + x - h_hat]/(2 L_n0), and the derivation adds the arbitrary-tau generalization docs/01 §3 asks for. Initial pass surfaced a structural question (dn_i inside vs outside the 1/L_n0 factor); read I19 Eq. A.11 first-hand (print p.11) and resolved it: no discrepancy -- I19's normalized dn_i = L_n0 * (raw moment), a definitional convention, flagged openly. The invariant x-h_hat structure and the tau=1 coefficient match I19 exactly with nothing tuned. physics-verifier: PASS (algebra a-e verified first-hand incl. the (tau+1)/tau factor and tau=1 reduction; provenance clean, no src/ change; dn_i normalization honestly a convention). Local docs build green. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…tau+1)); triple-checked dn convention Human sign-off 2026-07-11 of the quasineutrality-closure derivation (D7), after an independent triple-check of the dn normalization. Records the clearance (docs/01 §3) and un-gates the coefficient: - Coefficients.quasineutrality_coefficient(tau) = tau/(tau+1): the closure coefficient (sum of ion+electron adiabatic responses; -> 1/2 at tau=1). - 4 tests: tau=1 -> 1/2, tau=2 -> 2/3, tau->inf -> 1, positivity guard. 102 islands-solve tests green. Triple-check resolution: the (x - h_hat) structure and the coefficient match I19 Eq. A.11 exactly; the only difference from I19's delta_n_i is a scaling by L_n0, which is PHYSICALLY FORCED (the raw moment is gradient-driven, delta_n_bar_i ~ L_n0^-1). Decisively, the code uses the RAW-MOMENT form (delta_n_bar_i = velocity_moment! output), so I19's delta_n_i normalization is a cross-check nuance only and does not enter src -- the un-gate is unambiguous. Also derived the arbitrary-tau generalization docs/01 §3 asked for. physics-verifier: PASS (derivation algebra a-e verified first-hand). Un-gate is a one-line cleared coefficient. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…tors (D7; sin-normalization pin) Sixth and final M2b main-derivation chapter (awaiting sign-off). Derives the output-moment prefactors: - Delta_cos = Delta_neo = -(mu0 R/2 psi_tilde) ∫∫ Jbar_par cos xi: the growth moment matched to the outer Delta' (stationarity Delta' + Delta_neo = 0). The prefactor is sourced piece by piece -- mu0 R from parallel Ampere, psi_tilde the ALREADY-CLEARED island_flux_amplitude, the 1/2 the adopted Diss19 Eq. 4.12 Rutherford matching convention (not re-derived from scratch, stated honestly). - Delta_sin = +(mu0 R/2 psi_tilde) ∫∫ Jbar_par sin xi: the sin normalization has no external Delta' to match, so it is a [DERIVED] CHOICE (docs/01 §4 flags it as such). Pinned SYMMETRICALLY to cos so Delta_cos + i Delta_sin is the natural complex growth+torque moment mapping to the linear-layer Delta(Q) (D1), and the A3 parity gate (cos even/sin odd) holds with matched normalization. physics-verifier: PASS (provenance clean, no src/ change, delta_moments prefactors stay required/gated; the cos attribution is honest -- adopted Diss19 convention, not overclaimed; the sin pin is honestly a [DERIVED] decision, consistent with the green A3 gate). Local docs build green. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…ation lane complete (6/6 cleared) Human sign-off 2026-07-11 of the Delta-prefactor derivation (D7). Records the clearance (docs/01 §4) and un-gates the prefactors: - Coefficients.delta_moment_prefactors returns (cos=-mu0R/2psi_tilde, sin=+mu0R/2psi_tilde); psi_tilde the cleared island_flux_amplitude; feeds Moments.delta_moments. Symmetric sin pin ([DERIVED]). 105 tests green. Completes the M2b derivation lane: all six main L0 coefficient families derived (D7), signed off, cleared. Deferred sub-constants (<nu_hat_ii>_u, k, f_p) stay [CHECKED]-gated. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…dit + docs infra) Next milestone after the completed M2b derivation lane: assemble the six cleared coefficient families into a runnable L0 configuration, produce the D9 input- completeness audit (docs/09), stand up docs/07 infra (STATE dashboard + anchor-sync), and scaffold the B-ladder to the assembly. Autonomous-mode: un-gate nothing new (deferred sub-constants stay gated), draft deferred derivations only if rigorous else escalate to QUESTIONS, never guess. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…9 deliverable) Per-source input manifests (I19, D21, D23a/b, L23) auditing which published NTM-threshold configurations pin down every required input. Type specimen: I19's run collisionality is internally contradictory (0.01 vs 10^-3) and its Delta' value is unspecified, so B5a's absolute threshold downgrades to T3 (existence). L23 (thesis) is the only clean T4 candidate. This is itself a reproducibility result for Paper I C9. Added to docs nav. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…coeffs wired, gated families escalated) configure_level0 (src/Islands/configure/Configure.jl) assembles the Level-0 named configuration: it wires the CLEARED coefficient builders onto the operator stack and takes every uncleared family as a supplied gated input (never guessed). Cleared wiring (verified faithful): - c_D from magnetic_drift_frequency, node-for-node (Δ=0.0), with the :original/:improved toggle and forbidden-region (y >= 1/b_min) zeroing; - the pitch-collision shapes from pitch_diffusivity + deflection_frequency; - the Δ-moment prefactors from delta_moment_prefactors. Gated/supplied (GatedLevel0Inputs, escalated to QUESTIONS Q5): parallel streaming, E×B c_E, gradient drive, quasineutrality α, collision magnitude (⟨ν̂_ii⟩_u/ν_star), orbit-averaged pitch measure, neoclassical far field. The assembly surfaced a structural gap — the quasineutrality operator lacks the L̂_n0⁻¹(x−ĥ) field source the cleared closure requires — so no Level-0 physics run is possible until that lands; M2c delivers the assembly scaffold, verified STRUCTURALLY (level0_placeholders → Newton-Krylov converges, 5 iters ‖F‖=1.3e-9). 184 islands tests green (new runtests_islands_configure.jl). The y=0 orbit-average guard was relaxed (y>0 → y>=0): a domain-boundary fix, no y>0 value changes. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…ding wired to the assembly #3a STATE dashboard (docs/07 §1.3): Verify.write_state_dashboard + ladder_status generate docs/src/islands/state/STATE.md (auto-generated, do-not-hand-edit) — the docs/05 ladder as a status table (8 A-ladder rows green via the test suite; B/C physics rows gated on QUESTIONS). Nav-wired. #4 B-ladder scaffolding: benchmarks/islands/benchmark_B{2,4,5}*.jl wired to Islands.Configure.configure_level0 with a one-line un-skip (const UNGATED = true), kept skipped on QUESTIONS Q3/Q5. B5 carries the full T2 :original/:improved toggle scaffold; the physics w_c extraction stays gated on the Q5 far field + QN source. Also fixes a latent docs-CI breakage: cross-module @refs in the Coefficients delta_moment_prefactors docstring (island_flux_amplitude, Moments.delta_moments) do not resolve from the Coefficients module context — converted to plain code spans. build_docs_local.jl now green. 184 islands tests green. Remaining M2c: the anchor-sync CI check (#3b) is deferred — it needs the as-implemented Physics Book chapters + operator anchors (a larger docs deliverable). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…d assembly docs #3b anchor-sync (docs/07 §1.1): Verify.check_anchor_sync enforces the bidirectional operator<->docs sync — forward (every AbstractTerm operator is named by an 'Implemented by:' marker in numerics.md) and reverse (every marker symbol resolves to a real Islands binding). A new operator without docs, or a doc naming a deleted symbol, fails the check. Tested with negative controls. #6 as-implemented docs: numerics.md gains the Level-0 configuration-assembly section (configure_level0, the cleared wiring vs the Q5-gated families) and 'Implemented by:' markers over the operator stack. This completes the autonomous portion of M2c: #1 assembly, #2 audit, #3 docs infra (STATE dashboard + anchor-sync), #4 B-ladder scaffolding, #6 numerics.md. Remaining M2c is human-gated by design: Q5 (the un-cleared coefficient families + the QN operator structural fix) gates any Level-0 physics run and the B-ladder physics gates; the deferred sub-constants (#5) need a sign-off session. 189 islands tests green; build_docs_local.jl green. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…tion (awaiting sign-off) derivations/passing-fraction.md [DERIVED] derives the electron-closure passing fraction f_p ~= 1 - 1.46*sqrt(eps) from the effective trapped-fraction integral (Lin-Liu-Miller / Wesson) in the pinned b(theta) convention, shows the eps->0 all-passing limit analytically (B(2,1/2)=4/3), and NUMERICALLY confirms the leading coefficient c1 = 1.4624 — matching the sources' quoted 1.46 to 3 s.f. DRAFTED, NOT CLEARED: f_p stays NaN-gated in Fields.ElectronClosure (no src change); awaits human sign-off with one open reviewer item (confirm I19 Eq. 22 uses the same effective-trapped-fraction definition). The companion deferred constants <nu_ii>_u and Hirshman-Sigmar k are left escalated (QUESTIONS Q3/Q5) — each needs its specific source integrand, not derived speculatively. This is the M2c #5 deliverable (draft where rigorously possible; escalate the rest). Wired into the derivations index + nav + QUESTIONS Q5. build_docs_local.jl green. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…y closure (Phi now driven) Closes the M2c-surfaced quasineutrality structural gap (QUESTIONS Q5). The closure was signed off in M2b, but Operators.Quasineutrality carried only R_Phi = M[g] - alpha*Phi (no drive), so the Level-0 potential collapsed to zero. Implemented the full cleared closure (physics-verifier PASS): - Operators.Quasineutrality gains an optional source field; apply! adds it (R_Phi = M[g] - alpha*Phi + S). Backward-compatible Quasineutrality(alpha). - Configure.configure_level0 builds alpha = (tau+1)/tau (= 1/quasineutrality_ coefficient(tau), the reciprocal, = 2 at tau=1) and the drive S = inv_Ln0*(x - h(Omega)) via the new Configure.quasineutrality_source, from the cleared h_amplitude/h_profile with one width w=w_psi for both Omega and the h prefactor (electron-closure.md §3 far-field matching). - Added inv_Ln0 to Level0Physics; removed alpha from GatedLevel0Inputs and level0_placeholders; :quasineutrality moved from gated to cleared. Verified: max|Phi| ~= 5.7 after the placeholder solve (was ~0). 194 islands tests green (new testset asserts the reciprocal alpha, the wired source, and a nonzero solved Phi). Doc-first: docs/01 §3, quasineutrality-closure.md §6, numerics.md, QUESTIONS Q5 amended. build_docs_local.jl green. The kinetic Q5 families (streaming, E×B, gradient drive, <nu_ii>_u, pitch measure, far field) remain gated; a physics threshold still needs those. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…fficients
Re-derived the island-streaming channel from the master DKE (I19 Eq. 32, L23
§2.6-amended trapped mask) — derivations/parallel-streaming.md, human sign-off.
The two coefficients factor EXACTLY into {Omega, g} flux-surface advection:
a_xi = (inv_Lq/rho_hat_theta_i)*x*Theta(y_c-y)
a_x = -(inv_Lq*w^2/4rho_hat_theta_i)*sin(xi)*Theta(y_c-y)
= (inv_Lq*w^2/4rho_hat_theta_i)*Theta*{Omega, .} -- a coefficient-free structural
check that leaves no freedom (streaming must advect along Omega-contours).
Passing-only via Theta(y_c-y). Normalization (divide by -m*rho_hat_theta_i) chosen
so the already-cleared c_D = omega_hat_D is UNCHANGED.
Implemented as Configure.streaming_coefficients with a new
Level0Physics.rho_hat_theta_i; :streaming moved gated -> cleared; a_xi/a_x removed
from GatedLevel0Inputs and level0_placeholders. physics-verifier PASS (forms,
signs, {Omega,g} structure, c_D unchanged, no guessed coefficient all checked
vs the signed-off derivation). 1494 islands assertions green (new per-node
{Omega,g} structure testset). Doc-first: docs/01 §2, QUESTIONS Q5, numerics.md
§2/§8, derivations index + nav. build_docs_local.jl green.
Cleared now: streaming, drift, collision shapes, quasineutrality field, Delta
prefactors. Still gated (Q5): E×B, gradient drive, <nu_ii>_u, pitch measure,
far field.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…= far-field BC) Read I19 first-hand (Eqs. 8, 23-32) to derive the Level-0 gradient drive. Finding (derivations/gradient-drive.md, draft): the master orbit-averaged equation (I19 Eq. 32) is HOMOGENEOUS in G0 -- no interior source term. The gradient drive enters as the FAR-FIELD BOUNDARY CONDITION: far from the island G0 -> p_phi*(omega_si^T/omega_ci)*(n'/n)*F_Mi (Eq. 29), the diamagnetic-driven distribution. Consequence: Operators.GradientDrive is ZERO at Level 0, and the Q5 'gradient_drive' and 'far_field' items merge into one physical object -- the diamagnetic far field g_drive = D_dia*x*[1+(vhat^2-3/2)*eta_i]*F_Mi. The x-linearity, the (vhat^2-3/2)eta_i temperature correction, and the Maxwellian are cleared structure; the normalized amplitude D_dia bundles the frame convention Frames.C_dia (still NaN-gated) -- clearing the drive = clearing C_dia (the ion omega_dia normalization) in the same sign-off. Nothing entered src/ (docs-only draft). QUESTIONS Q5, derivations index + nav, LOG updated. build_docs_local.jl green. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
Signed off derivations/passing-fraction.md and cleared Coefficients.passing_fraction(eps) = 1 - 1.4624*sqrt(eps) -- the effective trapped-fraction coefficient (Lin-Liu-Miller / Wesson), derived analytically (eps->0 all-passing limit) and numerically confirmed (c1 = 1.4624, matching the sources' quoted 1.46 to 3 s.f.). Authorizes Fields.ElectronClosure.f_p. physics-verifier PASS (constant matches the derivation's converged value, form matches I19 Eq. 22, k correctly stays gated). 1499 islands assertions green (limits + monotonicity + the 1.46 match). Doc-first: docs/01 §2.4 [CLEARED], QUESTIONS Q3/Q5 RESOLVED, derivations index/nav, Fields.ElectronClosure docstring. build_docs_local.jl green. The companion Hirshman-Sigmar k ~= -1.173 remains deferred (own derivation). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…o frame convention) Completed the gradient drive by re-reading I19 Eq. 29 first-hand. CORRECTION: the earlier draft misread the ratio as omega_si^T/omega_ci (=> would need the frame convention); it is omega_si^T/omega_si = 1 + (vhat^2-3/2)*eta_i, a dimensionless TEMPERATURE factor, not a frequency ratio. So NO frame convention is needed. The drive is the standard neoclassical p_phi*F'_Mi, imposed as the FAR-FIELD boundary condition (master eq is homogeneous -- I19 Formulation A), not an interior source. Cleared: Operators.GradientDrive = 0 (zero interior source) and Configure.gradient_far_field builds g_far = x*inv_Ln0*[1+(E-3/2)*eta_i] (Phi_far = 0 at omega_E=0), with a new Level0Physics.eta_i. Both :gradient_drive and :far_field moved gated->cleared; drive/bc dropped from GatedLevel0Inputs. physics-verifier PASS -- re-read the PDF first-hand and CONFIRMED Eq. 29 is omega_si^T/omega_si (not omega_ci), validating the correction; far-field form, zero source, Phi_far=0, no frame convention, no guessed literal all checked. 1511 islands assertions green (the assembly now solves with the physical far field). Doc-first: gradient-drive.md signed off, docs/01 §2, QUESTIONS Q5, numerics.md, derivations index/nav. build_docs_local.jl green. Remaining gated (Q5): E×B coupling, collision magnitude <nu_ii>_u, orbit-averaged pitch measure. Plus the deferred k ~= -1.173. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…STIONS Q5) Captured the E×B derivation core for the next session: c_E = (1/2)<1/vhat_par>_theta (the orbit transit-time weight, NOT frame-entangled), plus the three wrinkles to finish carefully -- velocity-dependent coefficient (operator change), the new <1/sqrt(1-yb)> orbit bracket, and the passing-vs-trapped sigma-parity. Paused before implementing to give the sigma subtlety a fresh look rather than end-of-session attention. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…, trapped ≡ 0) Derive and clear the E×B coupling c_E = ½⟨1/v̂_∥⟩_θ (human sign-off, derivation exb-coupling.md). Matching the master-eq E×B braces to the ExBDrift Poisson bracket in the c_D=ω̂_D normalization (÷ −m ρ̂_θi, ρ̂_θi cancels — no new physics parameter) fixes the coefficient with no sign freedom. σ-parity (the crux): passing (y<y_c) is σ-odd c_E = (σ/2√E)B₁(y) with a new orbit bracket B₁(y)=⟨1/√(1−yb)⟩_θ; trapped (y>y_c) is identically 0 — the σ-odd 1/v̂_∥ cancels between the two banana legs under Σ_σ. Required (not chosen) by the published drift-island label S ∝ p̂ for trapped (docs/01 §2.2). E×B is a passing-particle effect, like island-streaming. - Coefficients.orbit_average_exb_bracket — B₁(y), passing-only, same y_c-layer handling as the drift G bracket. - Configure.exb_coupling_table — c_E[ix,iξ,iy,iE,iσ], passing-only Θ(y_c−y). - Operators.ExBDrift generalized to a velocity-dependent array coefficient (scalar path retained for manufactured tests). - :exb moved gated→cleared; c_E removed from GatedLevel0Inputs. physics-verifier PASS; 1566 islands assertions green; build_docs_local.jl green. The M2c structural-solve assertion switched to the grid-independent max-norm (04 §5 criterion): the now-active E×B spreads a ~1e-8 residual across ~N unknowns, inflating the √N L2 norm past 1e-7 (per-equation residual 4.5e-8; not a physics change). Doc-first: docs/01 §2 (+ fixed the §2 line-107 orbit-average convention to match both cleared code paths), QUESTIONS Q5, numerics.md §2/§8, derivations index/nav. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
…ntum-restoring ⟨ν̂_ii⟩_u)
Derive and clear the two remaining pieces of the Level-0 collision magnitude
(human sign-off, derivation collision-magnitude.md), completing the deferred
sub-item of the signed-off collision-operator derivation (§7).
Read L23 Eqs. 4.1.4–4.1.6 (p. 87–88) first-hand and derived the
momentum-restoring speed average
⟨ν̂_ii⟩_u = (4ε^{3/2}ν_★/3√π)(√2 − ln(1+√2))
from L23's reduced integrand: the reduction u⁴ν̃_jj = u·erf − erf/2u + e^{−u²}/√π
plus three standard integrals (∫u e^{−u²}erf = 1/2√2, ∫e^{−2u²} = ½√(π/2),
∫u⁻¹e^{−u²}erf = ln(1+√2) = arcsinh(1)). Verified independently (QuadGK): all
three integrals and the u⁴ν̃ reduction exact to 15 digits, ⟨1⟩_u = 1
(normalized), and the full value reproduces L23's own unit-test 1.267537e-4
(ε=0.1, ν_★=0.01) to all 7 digits.
- Coefficients.momentum_restoring_average — the ⟨ν̂_ii⟩_u constant (the
restoring operator term is a separate future addition; this clears its
magnitude).
- Level0Physics.nu_star — the banana-regime collisionality ν_★, a scenario scan
input (Decision D7).
- Configure builds nu_tilde = ε^{3/2}ν_★ (the already-signed-off §4
normalization) and wires it into the collision coefficient; :nu_tilde moved
gated→cleared; nu_tilde removed from GatedLevel0Inputs (now B_profile-only).
This un-gates the collision operator magnitude — only the orbit-averaged pitch
measure B_profile remains gated at Level 0. physics-verifier PASS; 1577 islands
assertions green; build_docs_local.jl green. Doc-first: docs/01 §2.3,
QUESTIONS Q5, numerics.md §2/§8, collision-operator.md §7, derivations
index/nav.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016pUwoFRo9a5AjF8HuwcZMr
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Design plan (docs only) for Islands, a new GPEC submodule (
src/Islands/): a steady-state, multi-species drift-kinetic solver for the resonant island/layer region that returns the growth moment Δ_cos(w, ω; p) and torque moment Δ_sin(w, ω; p) for arbitrary parameters — replacing the sum of regime-specific Modified Rutherford Equation terms with a single calculation, and in its small-amplitude limit reducing to the linear layer response so that error-field shielding, penetration, seeded-NTM onset, and island saturation become faces of one solution manifold.Draft: this PR lands the design docs (
docs/src/islands/, module conventions insrc/Islands/CLAUDE.md) and the drift-kinetic reference library, revised against the Imada / Dudkovskaia / Leigh source set. No solver code yet.🤖 Generated with Claude Code