D5: execute reviewed graph fold and publish C6 bound

PROOF_INDEX.md

@@ -24,6 +24,11 @@ The shared [public inventory](https://github.com/d6g8k5htny-coder/main/tree/main
 - D5 two-scale S6-S21: proof [frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md](frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md); review [reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md](reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md).
 - D5 inner-belt gradient density: proof [frontiers/axial_density_20260925/PROOF.md](frontiers/axial_density_20260925/PROOF.md); review [reviews/replacement_20260925_pr19_pr21/REVIEW.md](reviews/replacement_20260925_pr19_pr21/REVIEW.md) accepts corollary (1) on `|z|<=W r^2`. That acceptance is the density bound only.
 - D5 fixed-transverse chart: proof [reviews/downstream_boundary_20260925/TRANSVERSE_BOUND_CANDIDATE.md](reviews/downstream_boundary_20260925/TRANSVERSE_BOUND_CANDIDATE.md) (byte-for-byte import of commit `32b80ee085dc6a40113d1e46e333cda50d57ba21`, blob `024d927779f79fadaf932541ea6474f2995f8c50`); review [reviews/pr16_fixed_transverse_nonauthor_20260925/REVIEW.md](reviews/pr16_fixed_transverse_nonauthor_20260925/REVIEW.md).
+- D5 planar pin/collar/intermediate first moment: the [source-bound reconciliation](reviews/d5_reconciliation_20260929/RECONCILIATION.md) composes the punctured pin disks, nested microdisks, collar, fixed annulus, window-only intermediate shells, and remote window into D5-a–D5-f. The reviewed scope is fixed `d=2` and `T`, compact birth/gap marks with `k>=k_->0`, all frames and critical indices, existential constants, all heights for D5-a–D5-d and the height window `I_r` for D5-e–D5-f. The exact component nodes and 30 required evidence edges are in [the downstream graph](frontiers/downstream_gate_20260925/GRAPH.json). The xAI planar continuum check is [Math-#141 comment 5894512272](https://github.com/d6g8k5htny-coder/Math-/pull/141#issuecomment-5894512272); it grants no `d>2` transfer and no independent collar proof. The regional shrinking-witness mechanism, numerical constants and RN/24-jet/JETMOD remain outside this planar fold; no elder-selection or other register transition is inferred.
+- D5 every fixed dimension (separate packet, not folded into the planar graph here): [full proof](frontiers/d5_dimension_lift_20260929/PROOF.md), [continuum crosswalk](frontiers/d5_dimension_lift_20260929/CONTINUUM_CROSSWALK.md), and its [scope/review record](frontiers/d5_dimension_lift_20260929/README.md) give Theorems `P_d`, `C_d`, `I_d`, `G_d` for fixed `d>=2`, fixed torus and compact positive-gap marks. OpenAI reviews 5357858391 and 5357882570 accept the continuum rows at their stated source-exposed scope; Math-#141 merged the packet at `e1ca400b3414e5a7bec13b91bc4f1e5293df32be`. This source landing did not itself change `GRAPH.json` or a scientific register.
+- C6 planar Fourier upper bound: [full proof](frontiers/c6_fourier_cutoff_20260929/PROOF.md), [source-bound reading note](reviews/c6_fourier_completion_20260929/READING_NOTE.md), and [Anthropic nonauthor review 5356335148](https://github.com/d6g8k5htny-coder/Math-/pull/148#pullrequestreview-5356335148) record `E_{Q_r^W}N(N-1)<=C r^3 log(1/r)` for fixed planar `T`, compact positive-gap marks and existential constants, using the complete planar D5/I5 reading rule. This remains a separately reviewed upper theorem; it is not the later sharp route and does not close the regional witness-collision node.
+- C6 sharp Palm route (separate packet, not folded into this planar graph transition): [full proof](frontiers/c6_palm_route_20260929/PROOF.md) and [scope/review record](frontiers/c6_palm_route_20260929/README.md) give `E[(N)_q]<=C_q r^3` for fixed `q>=2` and `E[N(N-1)]=Theta(r^3)` in every fixed `d>=2`, conditional on the exact reviewed first-moment inputs. OpenAI reviews 5356233690 and 5358116559 accept the stated source-exposed sections; Math-#145 merged the packet at `820d4435c5f13c12b9c2f3590e859212d2648dc0`. Its global result does not resolve or move `math.rn-region.witness-collision`.
+- C6 rare-cluster consequences (separate conditional packet): [full proof](frontiers/c6_rare_cluster_laws_20260929/PROOF.md), [sharp coefficient addendum](frontiers/c6_rare_cluster_laws_20260929/SHARP_POISSON_COEFFICIENT.md), and [review record](frontiers/c6_rare_cluster_laws_20260929/REVIEW_RECORD.md) state the elementary consequences of the exact D5/C6 count interface, including the sharp ordinary-Poisson obstruction and an `O(r^6)` canonical compound-Poisson approximation with the actual unknown positive-count law. Anthropic review 5358565704 and xAI review 5358623521 accept their respective slices; Math-#153 merged the packet at `190cf2bd4f31c7caf219d5d9b3d1fa468c450ea6`. The limiting cluster law remains unidentified, and no graph/register transition follows.
 - Cumulative transfer correction: proof [reviews/collision_mechanism_20260925/CUMULATIVE_TRANSFER_CORRECTION.md](reviews/collision_mechanism_20260925/CUMULATIVE_TRANSFER_CORRECTION.md); review [reviews/d2_cumulative_correction_20260925/REVIEW.md](reviews/d2_cumulative_correction_20260925/REVIEW.md) accepts this correction only.
 - P15 demand-one extension: exact counterexample [frontiers/three_fronts_20260924/P15_PRICE_BOUNDARY.md](frontiers/three_fronts_20260924/P15_PRICE_BOUNDARY.md); review pointer in [claims/LANDING_CLAIMS.json](claims/LANDING_CLAIMS.json) is [main #67](https://github.com/d6g8k5htny-coder/main/issues/67), disposition EXACT_COUNTEREXAMPLE.
 - D6 P15 full price theorem: proof [frontiers/full_price_20260924/PROOF.md](frontiers/full_price_20260924/PROOF.md); [reviews/p15_full_price_nonauthor_20260926/REVIEW.md](reviews/p15_full_price_nonauthor_20260926/REVIEW.md) records ACCEPT for Theorem F on the stated realized disjoint-capacity/clutter family, with demands at least two, independent probabilities, and the same palette. That review leaves the landing disposition untouched; it does not accept arbitrary downsets, demand-one extension, or an unrestricted prize claim. ASCII `3e-2` in (F1)/(F11) means `3*e-2`; see [ASCII_3E_MINUS_2.md](frontiers/full_price_20260924/ASCII_3E_MINUS_2.md).
@@ -40,9 +45,7 @@ The shared [public inventory](https://github.com/d6g8k5htny-coder/main/tree/main
 
 ## Open obligations without a complete proof yet
 
-- D5 pin neighborhoods: retained derivations are [reviews/d5_finite_r_hermite_repair_20260925/REPAIR.md](reviews/d5_finite_r_hermite_repair_20260925/REPAIR.md) and [reviews/d5_finite_r_hermite_repair_20260925/C6_REMAINDERS.md](reviews/d5_finite_r_hermite_repair_20260925/C6_REMAINDERS.md), with M1–M7 and S1–S4 accepted in [reviews/replacement_20260925_pr19_pr21/REVIEW.md](reviews/replacement_20260925_pr19_pr21/REVIEW.md). The newer public [PR53 reconnaissance note](https://github.com/d6g8k5htny-coder/Math-/blob/9a6f8a660d4508ec273b67d67e6b3871ddf2aa19/reviews/pin_neighborhood_recon_20260926/NOTE.md) has an [AMEND review in PR55](https://github.com/d6g8k5htny-coder/Math-/blob/4e188e25b1e1ef560f3eeb75c0d354d2ccf0ea22/reviews/d5_pin_neighborhood_20260926/REVIEW.md). These sources are on unmerged branches. **NO COMPLETE PROOF YET:** the inner microdisk bound and the open collar to the reviewed annulus are not supplied by that reconnaissance. [Math #58](https://github.com/d6g8k5htny-coder/Math-/issues/58) tracks the microdisk derivation; the claimed summed pin-neighborhood bound remains AMEND.
-- D5 intermediate scale r << |x| << rho: bounded on opposite sides by [frontiers/remote_window_20260924/PROOF.md](frontiers/remote_window_20260924/PROOF.md) and by the reviewed fixed-annulus proofs [frontiers/rn_annulus_bridge_20260925/PROOF.md](frontiers/rn_annulus_bridge_20260925/PROOF.md) and [frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md](frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md). NO COMPLETE PROOF YET: uniform growing-scaled-radius bridge.
-- D5 shrinking multiple-witness collision: fixed-separation machinery is [frontiers/remote_window_20260924/PROOF.md](frontiers/remote_window_20260924/PROOF.md) section 6, (15)–(16), at fixed `eta>0`. NO COMPLETE PROOF YET: shrinking-separation factorial-moment/collision estimate.
+- D5 shrinking multiple-witness collision: fixed-separation machinery is [frontiers/remote_collision_20260928/PROOF.md](frontiers/remote_collision_20260928/PROOF.md). The reviewed [Fourier upper bound](frontiers/c6_fourier_cutoff_20260929/PROOF.md) and the later merged [sharp Palm route](frontiers/c6_palm_route_20260929/PROOF.md) establish global count statements by routes that do not identify this regional shrinking-separation mechanism. **NO COMPLETE REGIONAL PROOF YET:** `math.rn-region.witness-collision` remains `OPEN_ACTIVE`; the global `Theta(r^3)` result is not a proof of that node.
 - D0 historical CH-LIFT/Piece-2/24-jet obligations outside reviewed regional bypasses: see [frontiers/downstream_gate_20260925/GRAPH.json](frontiers/downstream_gate_20260925/GRAPH.json). NO COMPLETE PROOF YET where not explicitly superseded; absent historical carriers remain ABSENT.
 
 ## Repository rule