From e3f10b390ae5ddd998d238206add5958d5b720bb Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Mon, 28 Sep 2026 18:01:06 -0500 Subject: [PATCH] Add fixed-dimensional elder lower-event candidate via raw Schur chart One O(r) physical-jet band, determinant-one shear, stable transverse complement and full W/Z tilt. Conditional sharp density/inverse-moment corollaries; exact finite controls, no scientific-status promotion. --- .github/workflows/elder-dimension-lift.yml | 33 ++ .../elder_dimension_lift_20260928/PROOF.md | 480 ++++++++++++++++++ .../elder_dimension_lift_20260928/README.md | 31 ++ .../RECONNAISSANCE.md | 35 ++ .../RESULTS.json | 8 + .../SOURCE_FILES.json | 54 ++ .../SOURCE_MAP.json | 42 ++ .../elder_dimension_lift_20260928/lift.py | 149 ++++++ .../test_lift.py | 146 ++++++ .../elder_dimension_lift_20260928/verify.py | 96 ++++ 10 files changed, 1074 insertions(+) create mode 100644 .github/workflows/elder-dimension-lift.yml create mode 100644 frontiers/elder_dimension_lift_20260928/PROOF.md create mode 100644 frontiers/elder_dimension_lift_20260928/README.md create mode 100644 frontiers/elder_dimension_lift_20260928/RECONNAISSANCE.md create mode 100644 frontiers/elder_dimension_lift_20260928/RESULTS.json create mode 100644 frontiers/elder_dimension_lift_20260928/SOURCE_FILES.json create mode 100644 frontiers/elder_dimension_lift_20260928/SOURCE_MAP.json create mode 100644 frontiers/elder_dimension_lift_20260928/lift.py create mode 100644 frontiers/elder_dimension_lift_20260928/test_lift.py create mode 100644 frontiers/elder_dimension_lift_20260928/verify.py diff --git a/.github/workflows/elder-dimension-lift.yml b/.github/workflows/elder-dimension-lift.yml new file mode 100644 index 000000000..fcb467a25 --- /dev/null +++ b/.github/workflows/elder-dimension-lift.yml @@ -0,0 +1,33 @@ +name: Elder dimension-lift exact controls + +'on': + pull_request: + paths: + - 'frontiers/elder_dimension_lift_20260928/**' + - '.github/workflows/elder-dimension-lift.yml' + push: + branches: [main] + paths: + - 'frontiers/elder_dimension_lift_20260928/**' + - '.github/workflows/elder-dimension-lift.yml' + workflow_dispatch: + +permissions: + contents: read + +jobs: + finite-dimension-lift: + runs-on: ubuntu-latest + timeout-minutes: 10 + steps: + - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 + with: + persist-credentials: false + - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 + with: + python-version: '3.11.16' + - name: Exact sources, both modes and intended semantic failures + run: | + set -euo pipefail + python -B -S frontiers/elder_dimension_lift_20260928/verify.py --output "${RUNNER_TEMP}/dimension-lift-${GITHUB_RUN_ID}-${GITHUB_RUN_ATTEMPT}" + git diff --exit-code diff --git a/frontiers/elder_dimension_lift_20260928/PROOF.md b/frontiers/elder_dimension_lift_20260928/PROOF.md new file mode 100644 index 000000000..7303bd791 --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/PROOF.md @@ -0,0 +1,480 @@ +# One soft transverse direction: an elder-failure lower event in every fixed dimension + +Object: OA-ELDER-DIMENSION-LIFT-20260928-v1. +Author: OpenAI / ChatGPT, foreground research continuation, 28 September 2026. +Disposition: AUTHOR-SIDE MATHEMATICAL CANDIDATE; source-bound nonauthor review required. +Scientific effect NONE. No existing proof, review verdict, registry, lemma flag or prize is changed. + +## 1. Model, precise claims, and dependence boundaries + +Fix d>=2, L>0, a compact birth interval B, and a compact gap interval +K=[k_-,k_+] with k_->0. Use exactly LP's variance-one periodized Gaussian field, + + Cov(f(x),f(y)) = sum_{n in Z^d} exp(-|x-y+Ln|^2/2) + / sum_{n in Z^d} exp(-|Ln|^2/2). + +All constants may depend on d,L,B,K. The dimension is fixed: no uniform-in-d +claim is made. All orthonormal pin frames R are allowed, without assuming the +periodized field is invariant under arbitrary rotations. Set u=R e_1 and + + M=-(r/2)u, S=(r/2)u; + f(M)=b, f(S)=b-k r^3, grad f(M)=grad f(S)=0. + +Q_r denotes continuous Gaussian regression on these original 2(d+1) observations. +Let F_j(H)=|det H| for a nonsingular Hessian with j negative eigenvalues, and zero +otherwise. Retain the ORIGINAL determinant tilt and FULL endpoint normalizer: + + W_r=F_d(H_M) F_(d-1)(H_S), Z_r=E_Qr W_r, + dQ_r^W=(W_r/Z_r)dQ_r. + +There is no adjacency conditioning. Let p_r(b,k,R) be the probability that S is +M's global ordinary superlevel elder-death partner, exactly as in LP Section 1. +On its generic locus the death height is the maximin from LP Section 8: + + d_f(M)=sup_{gamma(0)=M, f(gamma(1))>b} min_t f(gamma(t)). (A1) + +The already integrated planar source EL proves an explicit path obstruction in +d=2. This note extends that mechanism to all fixed d. The new issue is the raw +Gaussian mass of a nearly flat transverse direction coupled to d-2 stable +negative directions. Requiring every extra matrix entry to be O(r) would lose +the desired probability power. A Schur-complement coordinate chart avoids that. + +**Theorem A (direct lower event).** For all sufficiently small r, uniformly over +b,k,R in the specified ranges, there is an event E_r such that + + Q_r^W(E_r)>=c r^3, + E_r implies d_f(M)>=b-k r^3/4>f(S). (A2) + +In particular + + 1-p_r(b,k,R)>=c r^3. (A3) + +The event can be chosen also to contain two distinct additional critical points +of index d-1 and heights strictly between b-k r^3 and b, within distance C_d r +of the midpoint. If N_r counts all additional critical points in that height +window, then + + Q_r^W(N_r>=2)>=c r^3, + E_Qr^W[N_r(N_r-1)]>=c r^3. (A4) + +The second expectation may be extended-valued; this argument supplies no finite +upper bound. For d>2 it does NOT establish Q(N_r>=2)=Theta(r^3), a uniform lower +bound on Q(N_r>=2 | N_r>=1), or a global first-moment upper bound. Those would +need their own inputs. A torus-wide O(r^5) factorial bound is excluded by (A4). +The event lower bound is likewise an obstruction of order at least r^3 to any +approximation supported solely on empty and singleton configurations. + +**Corollary B (separate parent-dependent compositions).** Consuming LP Theorem A +at its stated scope gives, in every fixed d>=2, + + c r^3<=1-p_r<=C r^3. (A5) + +Consuming additionally LP's compact-mark density identity, for positive-length +B,K, gives + + nu_cand(ell)-nu_eld(ell)=Theta(ell^(2/3)) (A6) + +for its COMPACT-MARK densities. The leading constant, a numerical c or r_*, +unrestricted-mark differences, and any identification with historical q-symbols +remain outside this statement. The d=3,L=24 specialization changes none of those +limitations. The direct lower (A3) does not consume the parent upper theorem. + +**Corollary C (sharp rejected-pair inverse-moment boundary).** Under the same +compact-mark density premises, let the nonselected counting measure count +candidate pairs which are not ordinary elder pairs. Directly on that measure, + + E sum_{nonselected, 00. In the finite regime it is Theta(t^(5/3-p)). At +p=5/3 the lower-cutoff divergence is logarithmic; above it it is a power. This +is not subtraction of two infinite individual inverse-moment expectations. + +The proof below uses only the positive spectrum/contact-frame and uniform +regression facts explicitly displayed in LP Sections 2-4, elementary Taylor +estimates, a stable negative block, and the original maximin definition. It does +not consume the pending remote pair/distance limits or a SARD-G theorem. + +## 2. Complete physical third-order jets after the pin frame + +Write the orthonormal local coordinates as (x,y), with x axial and y in R^m, +m=d-1. LP's nonsingular frame U_r is an invertible re-expression of the exact pins +for r>0; it has bounded target v_r and converges, uniformly in covariance and +fixed derivative cross-covariances, to + + U_0=(f,f_x,f_xx,f_xxx,f_y1,f_xy1,...,f_ym,f_xym) at 0. (A7) + +Append the physical midpoint vector J consisting of: + +- all independent entries A=D_y^2 f(0) of the transverse Hessian; +- all independent third-order derivatives T_alpha=partial^alpha f(0), |alpha|=3, + except f_xxx (which is already in U_0). + +At r=0 the entries of (U_0,J) are exactly every independent derivative of orders +0 through 3, once each. Their count is binom(d+3,3). No repeated symmetric entries +are presented as independent coordinates. + +Every Fourier weight of the periodized covariance is positive. A zero-variance +linear combination of these derivatives would give a polynomial vanishing at +every point of the rotated dual lattice. Pulling back by the invertible rotation +gives a polynomial vanishing on Z^d. Induction on dimension, using the univariate +root theorem on each lattice line, makes it identically zero. Thus the complete +jet covariance is positive definite in every frame. + +Continuity of U_r and compactness of O(d) give a uniform covariance floor and +ceiling for (U_r,J), for r in [0,r_1]. Schur complementation then gives a uniform +covariance sandwich for the Gaussian vector J under Q_r. Its mean is bounded +because v_r is bounded. Consequently, for EVERY fixed compact set of physical +J-targets, there is a uniform positive lower bound on its Lebesgue density there. +This is a bound for RAW jets, not for a falsely Gaussian nonlinear eigenvector +or normalized-Schur variable. + +## 3. A unit-Jacobian chart around one soft transverse direction + +For d=2 use the planar argument, or interpret the empty stable block below with +determinant one. We now give the new construction for d>=3. Write y=(z,w), +w in R^n, n=d-2, and decompose + + A = [[a, v^T], [v, D]], + sigma=a-v^T D^(-1)v. (A8) + +Restrict D to a fixed positive-volume box of symmetric matrices near -I_n, with + + -3I_n/2 < D < -I_n/2. + +Restrict v to a sufficiently small fixed box of positive volume, independent of +r, such that q=D^(-1)v satisfies ||q||<=1/9. The possible physical jets remain +bounded on this domain. Use the deterministic linear shear, frozen separately +for each realization of these midpoint jets, + + y = S(z,w) = (z,w-qz), + S=[[1,0],[-q,I_n]], det S=1, + S^T A S=diag(sigma,D). (A9) + +The full coordinate transformation is L=diag(1,S) after the orthonormal pin +frame. Its determinant has absolute value one. It preserves the axis x and the +original pin points. Both L and its inverse have uniformly bounded norms. It is +not generally orthogonal, and no rotation-invariance argument is applied to it. + +Define tilde f(x,z,w)=f(R L(x,z,w)). Here R,L are CONSTANT in spatial variables +within each realization. Thus differentiating tilde f does not differentiate a +randomly varying frame. Its midpoint transverse mixed quadratic terms are zero +exactly, its stable Hessian is D, and its soft second derivative is sigma. + +Let tau be the third derivatives of tilde f, except tau_xxx. For fixed v,D the +map from the original third derivatives to tau is invertible. Explicitly + + partial_z(tilde f)= (partial_z-q.partial_w)f, + partial_w(tilde f)=partial_w f, partial_x(tilde f)=partial_x f. + +On symmetric third-derivative coordinates this substitution is triangular with +unit diagonal when ordered by z degree. The pure xxx coordinate is fixed and +uncoupled; deleting it leaves determinant one. This observation is about finite +coordinate transformations, not the law of the resulting random variables. + +The map + + (sigma,v,D,tau) -> (a,v,D,T), + a=sigma+v^T D^(-1)v (A10) + +therefore has absolute Jacobian one. Its derivative is block triangular: the +Hessian part has derivative one in sigma and identity in the other coordinates; +the cubic part has determinant one, although it depends on v,D. Only D is +inverted; the chart remains regular when A is singular at sigma=0. + +This is the step preventing a dimension-dependent loss. Neither v nor the other +n(n+1)/2 stable entries has a shrinking width. The raw entry a itself need NOT +be O(r): it follows the O(1) surface v^T D^(-1)v within an O(r) band. + +## 4. The raw rare set has volume and probability of order r + +Fix a small epsilon>0, eventually independent of r, and retain the fixed D,v +boxes. In the chart require + + |sigma+(3k/2)r|=c_J r. (A13) + +The sheared jets need not be jointly Gaussian. We integrate the RAW Gaussian +density using the explicitly justified Jacobian; we never assign an independent +or rotation-invariant distribution to sigma, v, D or tau. Replacing sigma by +sigma/r without its r Jacobian would be incorrect. + +## 5. Remainder control is conditioned after ALL the physical jets + +Regress the full smooth field on V=(U_r,J) at each target (v_r,j) in the raw set. +For one unconditioned copy F the conditional realization is + + F(z)+Cov(F(z),V)Cov(V)^(-1)((v_r,j)-V). (A14) + +The normalized pin rows are integral averages of derivatives of order at most +three. Positive-spectrum rapid Fourier summability supplies uniform derivative +cross-covariance bounds through C^4, and all finite C^4 supremum moments of F. +The joint inverse covariance from Section 2 is bounded. The targets j lie in a +fixed compact set. Therefore, for each fixed finite p, + + sup E[||f||_C4^p | U_r=v_r,J=j] < infinity. (A15) + +Choose K_4 finite so the conditional probability of ||f||_C4<=K_4 is at least +1/2 at EVERY target in the raw rare set. Integrating (A15) over that set yields + + Q_r{rare jets AND ||f||_C4<=K_4} >= (c_J/2)r. (A16) + +The bounded shear converts this to a uniform local bound on ||tilde f||_C4. +There is no assertion of independence between the jet event and the remainder. +Subtracting a fixed unconditioned tail from a mass of order r is not used. + +The constants can be selected without circularity. Fix the D,v boxes and a +compact raw-target container valid for all epsilon<=1 and small r. Choose a +uniform K_4 from that container. Then choose epsilon for the planar stability +margins, and finally reduce r_* using K_4 and those margins. The positive c_J +may shrink with epsilon, but is fixed independently of r. + +## 6. Exact pinned planar normal form on the sheared plane + +Restrict to w=0, and put + + F_r(X,Z)=[tilde f(rX,rZ,0)-b]/r^3, + s=sigma/r, a_3=tau_xxz, beta=tau_xzz, c_3=tau_zzz. + +The original axial height and gradient pins, including the transverse gradient +pins in the sheared direction, are still exact. Taylor expansion as in the +planar source gives + + F_r = 2kX^3-3kX/2-k/2+(s/2)Z^2 + +(a_3/2)(X^2-1/4)Z+(beta/2)XZ^2+(c_3/6)Z^3 + + O_C2(B3)(r K_4), (A17) + +with a dimension-dependent constant absorbing the shear norm. For clarity the +potentially dangerous coefficients follow from the pin identities: + + tilde f_xxx(0)=12k+O(rK_4), + tilde f_x(0)=-(r^2/8)tilde f_xxx(0)+O(r^3K_4), + tilde f_z(0)=-(r^2/8)tilde f_xxz(0)+O(r^3K_4), + tilde f_xx(0), tilde f_xz(0)=O(r^2K_4), + tilde f(0)-b=-(r^3/24)tilde f_xxx(0)+O(r^4K_4). + +The second-derivative z^2 coefficient is sigma, not the raw a. No stable +quadratic term survives on w=0 because (A9) eliminates it exactly. +The term -a_3 Z/8 is necessary for the transverse gradient pins. + +On (A11), the polynomial part is O(epsilon k)-close in C^2(B3) to + + G_k(X,Z)=k(2X^3-3X/2-1/2-3Z^2/4-XZ^2). (A18) + +Choose epsilon and then r_* so the C^0 difference is strictly below k/64 and the +C^2 difference meets the endpoint and saddle stability tolerances below. +The higher-dimensional directions have introduced no extra r^-1 remainder. + +## 7. Stable path above the death pin + +Use the fixed polygonal path in the sheared plane + + (-1/2,0) -> (-3/4,0) -> (-3/4,9/4) -> (-1,9/4). (A19) + +Dividing by k, the restrictions of G_k to its three consecutive segments are + + -3t^2/16-t^3/32, + -7/32, + -7/32+51t/64-9t^2/32-t^3/32, 0<=t<=1. + +Their minimum is -7/32 and the final value is 17/64. The first is nonincreasing; +the third has derivative at least 9/64. Every segment is inside B(0,3), since +the maximal endpoint squared norm is 97/16<9 and the ball is convex. +A perturbation below k/64 leaves the path above -15k/64>-k/4 and its endpoint +above k/4. After applying the fixed shear, rotation and physical r scaling, the +path starts at the actual M and ends at a point above b, entirely above +b-k r^3/4. It remains inside an embedded O(r) ball by reducing r_*. + +This is a path in the physical torus, not a separatrix claim. It proves the +second statement in (A2) for every field in the event of (A16). The use of a +plane chosen from midpoint jets causes no probabilistic problem: existence of +ONE such path suffices, and the chart is a smooth measurable function of those +jets on the chosen stable-block domain. + +## 8. Full endpoint Hessians: only two directions are soft + +In the (x,z;w) shear frame, the physical endpoint Hessians have blocks + + H_i^tilde = [[r P_i+O(r^2 K_4), C_i], [C_i^T,D_i]], + ||C_i||<=C r K_4, D_i=D+O(r K_4), (A20) + +where P_i is the Hessian of the polynomial in (A17) at the corresponding scaled +endpoint. To verify the cross-block bound, at the midpoint tilde f_zw=0 exactly +by the shear, and tilde f_xw=O(r^2K_4) by the zero endpoint w-gradients. Moving +to either endpoint changes these entries by O(rK_4). The stable block remains +uniformly negative with bounded inverse for small r. + +The exact Schur complement is + + K_i=r P_i+O(r^2 K_4)-C_i D_i^(-1) C_i^T, + K_i/r=P_i+O(r K_4+r K_4^2). (A21) + +The correction must be included. The fact that it is smaller than r, rather +than zero, is what makes the construction stable. The target two-dimensional +endpoint Hessians are diag(-6k,-k/2) and diag(6k,-5k/2), with determinants 3k^2 +and -15k^2. Uniform smallness of epsilon and r preserves their indices and +strict determinant floors after (A21). + +Block congruence gives inertia(H_i^tilde)=inertia(D_i)+inertia(K_i), and + + det H_i^tilde = det D_i det K_i. (A22) + +Hence the physical endpoints have precisely the required indices d and d-1, +and EACH determinant has magnitude at least c r^2. The d-2 stable eigenvalues +remain O(1), not O(r). Because the shear determinant has absolute value one, +physical and sheared Hessian determinants agree; general invertible congruence +preserves their inertia as well. Thus on the event + + W_r >= c_W r^4. (A23) + +The r^4 power is independent of fixed d. Replacing it by r^(2d) would correspond +to incorrectly shrinking every spatial direction's curvature. + +For the FULL normalizer, the original endpoint gradient pins give zero averages +of H u along the axial segment. Thus ||H_i u||<=C r ||f||_C3. Hadamard yields +|det H_i|<=C r (1+||f||_C3)^d, so + + Z_r <= C_Z r^2 (A24) + +by the endpoint-conditioned moment bounds of LP Section 4. The positive event +(A16),(A23) ensures Z_r>0. No restricted normalizer is used. Combining gives + + Q_r^W(E_r) >= (c_J c_W/(2C_Z)) r*r^4/r^2 = c r^3. (A25) + +Together with the path, this proves (A2)-(A3), in every fixed d>=3; EL covers +d=2. No parent upper selection theorem entered this argument. + +## 9. Two additional saddles with a stable negative complement + +A planar restriction critical point is NOT automatically a full-dimensional +critical point. We explicitly correct the stable coordinates. + +Near either planar saddle P_+ or P_- of G_k, with + + P_+/-=(-3/4,+/-sqrt(15/8)), G_k(P_+/-)=-7k/32, + det H_2 G_k(P_+/-)=-15k^2/2, + +write x=rX, z=rZ, w=r^2 W. Consider the rescaled FULL gradient map + + H_r(X,Z,W)=r^(-2) grad tilde f(rX,rZ,r^2W). (A26) + +On bounded (X,Z,W) sets, Taylor and the pin identities give in C^1 + + H_r = (grad P(X,Z), D W+Q(X,Z)) + O(r C(K_4)), (A27) + +where P is the two-dimensional polynomial in (A17), and the stable-vector +quadratic polynomial is + + Q_j(X,Z)=(tau_xxwj/2)(X^2-1/4) + +tau_xzwj XZ+(tau_zzwj/2) Z^2. (A28) + +In particular the -tau_xxwj/8 term comes from tilde f_wj(0), and is retained. +All its coefficients lie in fixed small boxes. The absence of an order-r +linear z term in the stable gradient uses tilde f_zw(0)=0 exactly. The two soft +gradient components have no O(1) dependence on W because their physical mixed +Hessian is O(r); varying w by r^2 W contributes only O(r) after /r^2. +The C^1 estimates require at most the uniform C^4 bound, not an assumed exact +cubic random field. + +For epsilon small, P has one nondegenerate saddle near each P_+/- by ordinary +C^2 stability. At such a point p, the limit vector map in (A27) has a zero at +(p,-D^(-1)Q(p)). Its derivative is block triangular with diagonal blocks H_2P(p) +and D, so its inverse is uniformly bounded over the compact jet boxes. These +zeros persist for the C^1-small perturbation (A27), uniformly after reducing r_*. +This can equivalently be obtained by a quantitative inverse-function argument +on fixed disjoint neighborhoods. The solutions have w=O(r^2); they are not +assumed to lie exactly in the w=0 plane. + +Their physical heights are b+r^3[G_k(P_+/-)+O(epsilon k)+O(r C(K_4))], strictly +inside the height window for small epsilon,r. Their full Hessian has a negative +stable block and a two-dimensional Schur complement with one negative and one +positive eigenvalue, just as in (A20)-(A22). Both therefore have index d-1. +Their physical positions lie in an O(r) ball and are distinct from each other +and the original pins. This proves the additional event in (A4); the factorial +inequality follows from N(N-1)>=2 on that event. + +Uniformity here is on the compact family of jets and stable blocks for a FIXED +d. It does not assert a uniform number of all critical points or the persistence +pairing of either extra saddle. The separate strict path gives the elder +obstruction; mere extra-point existence would not do so. + +## 10. Parent-dependent selection and density consequences + +LP Theorem A gives the opposite inequality 1-p_r<=C r^3. When consumed with +(A3), it proves (A5) and shows the Gaussian order r^3 is sharp at every fixed +d, not merely for the matrix relaxation or the planar model. + +For LP's ordered compact-mark candidate/elder densities, its exact radial ledger +is r A_r(b,k,u) dr db dk d sigma(u), with A_r uniformly positive and bounded, +and ell=k r^3. Consequently the density difference is + + ell^(-1/3)/3 * integral k^(-2/3) A_((ell/k)^(1/3))(b,k,u) + [1-p_((ell/k)^(1/3))(b,k,u)] d sigma dk db. + +The lower factor (A3) contributes ell/k. The upper factor is supplied separately +by LP Theorem A. Both bounding integrands are proportional to +ell^(2/3) k^(-5/3), integrable and of positive integral on positive-length compact +B,K and the ordinary sphere measure. This proves (A6). Integrating over +0-1, proving +(A6a). At p=5/3, truncation to eta5/3 it +gives Theta(eta^(5/3-p)) as eta decreases to zero for fixed small t. In the +finite regime the result is Theta(t^(5/3-p)), not a claimed leading constant. +The ordinary candidate and elder inverse-moment threshold 2/3 from LP Section 12 +is different. Here a rejected-pair measure is used, never infinity minus infinity. +For d=2 this is already a consequence of the integrated planar lower and LP; +for d>2 it additionally uses the new dimensional lower proof. + +For d>2 we do not import the PLANAR global first-moment estimate (IW I5) to +claim a global multiple-occurrence upper bound or conditional nonuniqueness +bounded away from zero. Only (A4) and the corresponding unconditioned TV lower +obstruction follow without another global upper input. This is intentionally +weaker than those extra planar conclusions in LOCAL_MULTIPLICITY.md. + +## 11. What is new, what is checked, and what remains for review + +The planar cubic, path and raw-jet conditioning mechanism are credited to the +unchanged EL/LOCAL sources. The new step is the full-dimensional raw Schur chart: +one shrinking scalar band, determinant-one data-dependent shear, all other +coordinates in fixed-volume boxes, and a stable negative complement. The +Gaussian law is never changed to an independently rotated or sheared ensemble. + +The exact suite checks nonorthogonal shear cancellation, the chart through a +singular contact Hessian, unit cubic-jet Jacobians, the complete nonduplicated +jet list, a finite polynomial-lattice unisolvence illustration, exact planar +pins, the path, full-dimensional Hessian determinants/inertia, the cross-block +Schur correction, stable-coordinate displacement scaling, and exponent ledgers. +It deliberately rejects replacing r by r^(d-1), r^4 by r^(2d), dropping the raw +band Jacobian, dropping transverse pin terms, and reversing the stable sign. + +Finite checks do NOT prove covariance floors, uniform conditional C^4 estimates, +uniform inverse-function neighborhoods or the Gaussian probability inequality. +Those arguments are the written Sections 2-9 and require an actual nonauthor +analytic review. The finite Fourier illustration is not substituted for positivity +of the infinite exact periodized spectrum. The code is a new shear/Schur module, +not recovery or a retry of the blocked author algebra.py from #116. + +Source identities, limited primary-source reconnaissance, and the precise role +of each parent are in SOURCE_MAP.json and RECONNAISSANCE.md. This candidate +changes no old source or canonical scientific status and claims no historical +priority. All constants and cutoffs in the Gaussian result remain existential. diff --git a/frontiers/elder_dimension_lift_20260928/README.md b/frontiers/elder_dimension_lift_20260928/README.md new file mode 100644 index 000000000..716c27595 --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/README.md @@ -0,0 +1,31 @@ +# Dimensional lift of the direct elder-failure lower event + +Author-side candidate; nonauthor analytic review required. Scientific effect NONE. + +[PROOF.md](PROOF.md) extends the original planar cubic/path mechanism to every +fixed d>=2 using a physical Hessian Schur chart and a determinant-one shear. +Only one raw scalar band has width O(r); stable transverse modes stay O(1). +The proposed direct result is 1-p_r>=c r^3 under the original full determinant +tilt. Two additional index-(d-1) window critical points persist after correcting +the stable coordinates by O(r^2). + +With separately named LP upper/density premises: the r^3 order and compact-mark +ell^(2/3) density loss are sharp in every fixed dimension. The rejected-pair +inverse-moment threshold is p<5/3; its endpoint divergence is logarithmic. +This does not assert any new all-height/global factorial upper bound, uniform-in-d +constant, numerical cutoff, unrestricted-mark difference or legacy q/p identity. + +Run the complete source/finite-control verification: + + python -B -S verify.py --output /path/to/new-output + python -B -O -S verify.py --output /path/to/other-new-output + +The output directory must be new and outside this source directory. Each runner +checks exact membership/bytes/SHA256/Git blob identities, executes both Python +modes, and requires every semantic negative to fail the intended assertion with +valid JSON and no execution errors. The 18 finite tests and 10 semantic mutants +are not proofs of the Gaussian uniformity or inverse-function arguments. + +[Source map](SOURCE_MAP.json) separates direct inputs from conditional corollary +inputs. [Reconnaissance](RECONNAISSANCE.md) records the limited literature read +and Consensus quota limitation. No frozen source or review is rewritten. diff --git a/frontiers/elder_dimension_lift_20260928/RECONNAISSANCE.md b/frontiers/elder_dimension_lift_20260928/RECONNAISSANCE.md new file mode 100644 index 000000000..dd56b21f2 --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/RECONNAISSANCE.md @@ -0,0 +1,35 @@ +# Limited primary-source reconnaissance — 28 September 2026 + +Scope: derivative geometry and critical-point correlations near collisions; +not a claim of novelty, first discovery, or an exhaustive priority audit. + +Consensus was called for Gaussian critical points, higher-dimensional Hessian +Schur complements and elder persistence. It returned its monthly 30-search quota +error with an October 1 reset. No result was invented or cited from that call. + +The following primary-source abstracts/publisher records were inspected with web +search. No external theorem is used as an unexamined replacement for this proof: + +1. Jean-Marc Azaïs and Céline Delmas, *Mean number and correlation function of + critical points of isotropic Gaussian fields and some results on GOE random + matrices*, arXiv:1911.02300; Stochastic Processes and their Applications 150 + (2022), 411-445, DOI 10.1016/j.spa.2022.04.013. + https://arxiv.org/abs/1911.02300 + This already studies adjacent-index short-range correlation effects in the + unconditioned isotropic setting. Such adjacency by itself is not a novelty + claim for this project. It does not by its abstract establish this exact + pair-conditioned full-tilt elder obstruction or its compact-window loss. +2. Louis Gass and Michele Stecconi, *The number of critical points of a Gaussian + field: finiteness of moments*, Probability Theory and Related Fields 190 + (2024), 1167-1197, DOI 10.1007/s00440-024-01273-5. + https://doi.org/10.1007/s00440-024-01273-5 + The record addresses finite moments under jet nondegeneracy. Its conclusions + are not automatically uniform at this coalescing conditioned pair, and no + global O(r^3) first moment or factorial upper bound is imported from it. + +The actual positive-spectrum, pin-frame and uniform-regression ingredients are +read from the exact LP source in SOURCE_MAP.json. The new construction is proved +thereafter with a raw physical-jet chart, not an assumed isotropic GOE law or +independent soft eigenvector. Schur complementation, congruence, Taylor bounds, +and nondegenerate-zero stability are classical; the proof writes out their role. +The generic peer-review and governing status boundaries remain separate. diff --git a/frontiers/elder_dimension_lift_20260928/RESULTS.json b/frontiers/elder_dimension_lift_20260928/RESULTS.json new file mode 100644 index 000000000..457fcb8bc --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/RESULTS.json @@ -0,0 +1,8 @@ +{ + "tests_per_mode": 18, + "semantic_mutants_per_mode": 10, + "identical_output_pairs": 11, + "all_intended_failures": true, + "scientific_effect": "NONE", + "gaussian_analysis_verified_by_code": false +} diff --git a/frontiers/elder_dimension_lift_20260928/SOURCE_FILES.json b/frontiers/elder_dimension_lift_20260928/SOURCE_FILES.json new file mode 100644 index 000000000..11a80bd6d --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/SOURCE_FILES.json @@ -0,0 +1,54 @@ +{ + "schema": 1, + "scientific_effect": "NONE", + "files": [ + { + "path": "PROOF.md", + "bytes": 23971, + "sha256": "b529fe3780e1909014b3cb144b9a74156d976bbdc19b6711d0c5b1a1da9e5669", + "git_blob": "7303bd791a68a1139251f0f6e403a9f7cc89b006" + }, + { + "path": "README.md", + "bytes": 1771, + "sha256": "64950f041cee272079f4dd5e04dcf2293f5ed6d8c3ee231df8817d2d10fce2ac", + "git_blob": "716c275954910521102d1e154ef526360f19d908" + }, + { + "path": "RECONNAISSANCE.md", + "bytes": 2214, + "sha256": "d6f0bb97f4555ebb44b06df5d35d12f90fb746bbef45fb2053b8294d6621ed28", + "git_blob": "dd56b21f2da20be803f431357c5de49e6efbf452" + }, + { + "path": "RESULTS.json", + "bytes": 205, + "sha256": "57dba071afd0e53e1317f165b5170dd0a69a456fef41d50b2f775d33ffd123f5", + "git_blob": "457fcb8bc2bcd84ad0b25c67be8869fefb9681b8" + }, + { + "path": "SOURCE_MAP.json", + "bytes": 2106, + "sha256": "8cdedee5300ecc64bc5e38ea94d9bf263f0d87c4b75ccba67fb108edcf7013b1", + "git_blob": "713cad893e3d922c971a866f9b6accd89758f6d1" + }, + { + "path": "lift.py", + "bytes": 5514, + "sha256": "e17fa8384b6d5e516223499efff26354da0d84de9ba3e9ea3d96cfe75373ee9d", + "git_blob": "03d6827ac66afeb04f70153108aa195668e58a22" + }, + { + "path": "test_lift.py", + "bytes": 6109, + "sha256": "6901d40a216db622ee6cf82dc2092cdd7cd7dae261ea81b2c00fbb72a6f4a02b", + "git_blob": "c3ff861519c6b522ad8ca049c2f1aebecebae623" + }, + { + "path": "verify.py", + "bytes": 4910, + "sha256": "f79ba38b27c40ec86b5d2bbec4f5c9891fbe27c62ba328b6d58769b6f04469dd", + "git_blob": "7bbd0612ebae56c8b05c97d22142f0086a3549cd" + } + ] +} diff --git a/frontiers/elder_dimension_lift_20260928/SOURCE_MAP.json b/frontiers/elder_dimension_lift_20260928/SOURCE_MAP.json new file mode 100644 index 000000000..713cad893 --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/SOURCE_MAP.json @@ -0,0 +1,42 @@ +{ + "scientific_effect": "NONE", + "source_repository": "d6g8k5htny-coder/Math-", + "source_commit": "d39dbbc25c25a7bc3f6c15b21f957a7fcac30615", + "inputs": [ + { + "id": "LP", + "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md", + "bytes": 40261, + "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7", + "git_blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2", + "direct_use": "Exact model, original pins/tilt/selector, Sections 2-4 positive spectrum and contact regression; Section 8 generic locus/maximin.", + "conditional_corollary_use": "Theorem A upper bound and Sections 9-12 compact-mark density ledger/moments; not required for the new direct lower proof." + }, + { + "id": "EL", + "path": "frontiers/window_multiplicity_laws_20260928/ELDER_LOWER_AND_DENSITY_GAP.md", + "bytes": 10229, + "sha256": "8ce05a43bde8e0d718f09e2da1ffe75d3ec5893489254afdbf5b58b602cdba0c", + "git_blob": "aaefc8da9668e819591dd9db0b34442394f2362e", + "use": "Unchanged planar cubic/path and lower event; basis of d=2 and credited mechanism, not an assumed d>2 proof." + }, + { + "id": "LOCAL", + "path": "frontiers/window_multiplicity_laws_20260928/LOCAL_MULTIPLICITY.md", + "bytes": 13100, + "sha256": "e6272e8709835ca6290fecb7034fa84832dde08c3c4cc990a48b8019e89e7c8d", + "git_blob": "b5c18aac5529c5f975ee5bb056b304debafc6697", + "use": "Planar normal-form and extra-saddle data. Its planar global first-moment upper estimate is NOT imported for d>2." + } + ], + "new_obligations": [ + "Complete physical-jet covariance floor in every fixed dimension", + "Nonlinear raw Schur/shear chart with unit Jacobian and one shrinking coordinate", + "Conditional C4 control on raw jets before choosing the spatial shear", + "Full-dimensional endpoint Schur bounds and anisotropic saddle persistence" + ], + "pending_pair_distance_sources_consumed": false, + "historical_blocked_code_consumed_or_retried": false, + "nonauthor_acceptance": false, + "governing_status_changed": false +} diff --git a/frontiers/elder_dimension_lift_20260928/lift.py b/frontiers/elder_dimension_lift_20260928/lift.py new file mode 100644 index 000000000..03d6827ac --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/lift.py @@ -0,0 +1,149 @@ +"""Exact finite helpers for the one-soft-transverse-direction construction. + +No Gaussian continuum claim follows from these computations. Standard library only. +""" +from fractions import Fraction as F +from itertools import product +from math import factorial + +MUTANT=None + +def eye(n): return [[F(int(i==j)) for j in range(n)] for i in range(n)] +def tr(A): return [list(c) for c in zip(*A)] +def mm(A,B): + return [[sum((x*y for x,y in zip(row,col)),F(0)) for col in zip(*B)] for row in A] + +def solve(A,b): + n=len(A) + if n==0 or len(b)!=n or any(len(row)!=n for row in A): + raise ValueError('nonempty square linear system required') + W=[[F(x) for x in row]+[F(b[i])] for i,row in enumerate(A)] + for j in range(n): + p=next((i for i in range(j,n) if W[i][j]),None) + if p is None: raise ValueError('singular matrix') + W[j],W[p]=W[p],W[j] + pivot=W[j][j]; W[j]=[x/pivot for x in W[j]] + for i in range(n): + if i!=j: + v=W[i][j]; W[i]=[x-v*y for x,y in zip(W[i],W[j])] + return [row[-1] for row in W] + +def det(A): + n=len(A) + if not n:return F(1) + W=[[F(x) for x in row] for row in A]; out=F(1) + for j in range(n): + p=next((i for i in range(j,n) if W[i][j]),None) + if p is None:return F(0) + if p!=j:W[j],W[p]=W[p],W[j];out=-out + pivot=W[j][j];out*=pivot + for i in range(j+1,n): + z=W[i][j]/pivot + for k in range(j+1,n):W[i][k]-=z*W[j][k] + return out + +def rank(A): + W=[[F(x) for x in row] for row in A] + if not W:return 0 + h=0 + for j in range(len(W[0])): + p=next((i for i in range(h,len(W)) if W[i][j]),None) + if p is None:continue + W[h],W[p]=W[p],W[h];pivot=W[h][j] + for i in range(h+1,len(W)): + z=W[i][j]/pivot + if z: + for k in range(j,len(W[0])):W[i][k]-=z*W[h][k] + h+=1 + if h==len(W):break + return h + +def chart(D,v,sigma): + q=solve(D,v);n=len(D) + sign=-1 if MUTANT=='wrong-schur-sign' else 1 + a=F(sigma)+sign*sum((x*y for x,y in zip(v,q)),F(0)) + A=[[a,*v]]+[[v[i],*D[i]] for i in range(n)] + S=eye(n+1) + for i in range(n):S[i+1][0]=F(0) if MUTANT=='omit-shear' else -q[i] + return A,S + +def multiindices(d,degree,upto=False): + return [a for a in product(range(degree+1),repeat=d) if sum(a)<=degree] if upto else [a for a in product(range(degree+1),repeat=d) if sum(a)==degree] + +def monomial(x,a): + out=1 + for u,p in zip(x,a):out*=u**p + return out + +def jet_labels(d): + zero=(0,)*d; e=[tuple(int(i==j) for j in range(d)) for i in range(d)] + plus=lambda a,b:tuple(x+y for x,y in zip(a,b)) + ex=e[0]; two=plus(ex,ex);three=plus(two,ex) + U=[zero,ex,two,three] + for j in range(1,d):U += [e[j],plus(ex,e[j])] + J=[a for a in multiindices(d,3,upto=True) if a not in U] + if MUTANT=='duplicate-cubic-pin':J[-1]=three + return U,J + +def _pmul(P,Q): + R={} + for a,c in P.items(): + for b,e in Q.items(): + k=tuple(x+y for x,y in zip(a,b));R[k]=R.get(k,F(0))+c*e + return {a:c for a,c in R.items() if c} + +def cubic_change(d,q): + """Map third-derivative coordinates by f -> f(x,z,w-q z); pure xxx stays fixed.""" + labels=multiindices(d,3);M=[[F(0) for _ in labels] for _ in labels] + unit=[tuple(int(i==j) for j in range(d)) for i in range(d)] + substitutions=[{u:F(1)} for u in unit] + for j,v in enumerate(q):substitutions[j+2][unit[1]]=-v + def mf(a): + out=1 + for x in a:out*=factorial(x) + return out + for j,a in enumerate(labels): + P={(0,)*d:F(1,mf(a))} + for i,power in enumerate(a): + for _ in range(power):P=_pmul(P,substitutions[i]) + for i,b in enumerate(labels):M[i][j]=P.get(b,F(0))*mf(b) + return labels,M + +def rare_power(d):return d-1 if MUTANT=='rare-every-direction' else 1 +def weight_power(d):return 2*d if MUTANT=='all-directions-soft' else 4 +def band_width(r,k,epsilon):return 2*epsilon*k*(1 if MUTANT=='drop-band-jacobian' else r) + +def plane(X,Z,k,s,a,beta,c): + lin=0 if MUTANT=='drop-transverse-linear' else F(1,4) + value=2*k*X**3-F(3,2)*k*X-k/2+s*Z*Z/2+a*(X*X-lin)*Z/2+beta*X*Z*Z/2+c*Z**3/6 + dx=6*k*X*X-F(3,2)*k+a*X*Z+beta*Z*Z/2 + dz=s*Z+a*(X*X-lin)/2+beta*X*Z+c*Z*Z/2 + return value,[dx,dz] + +def blocks(A,C,D): + return [list(A[i])+list(C[i]) for i in range(len(A))]+[list(row)+list(D[i]) for i,row in enumerate(tr(C))] + +def schur(A,C,D): + invC=tr([solve(D,row) for row in C]);Q=mm(C,invC) + if MUTANT=='ignore-cross-schur':Q=[[F(0) for _ in A] for _ in A] + return [[A[i][j]-Q[i][j] for j in range(len(A))] for i in range(len(A))] + +def endpoint_model(d,r,k): + stable=1 if MUTANT=='positive-stiff' else -1 + def diag(vals):return [[v if i==j else F(0) for j in range(d)] for i,v in enumerate(vals)] + return diag([-6*k*r,-k*r/2]+[F(stable)]*(d-2)),diag([6*k*r,-5*k*r/2]+[F(stable)]*(d-2)) + +def inertia(A): + """Exact Descartes signs for a real-rooted characteristic polynomial of a symmetric matrix.""" + n=len(A);coef=[F(1)];B=eye(n) + for k in range(1,n+1): + AB=mm(A,B);c=-sum(AB[i][i] for i in range(n))/k + coef.append(c);B=[[AB[i][j]+(c if i==j else 0) for j in range(n)] for i in range(n)] + asc=list(reversed(coef));z=0 + while z0 for i,v in enumerate(asc) if v] + neg=sum(a!=b for a,b in zip(signs,signs[1:])) + return neg,z + +def loss_powers(): + return (F(-1,3)+(0 if MUTANT=='omit-loss-factor' else 1),F(-2,3)-1) diff --git a/frontiers/elder_dimension_lift_20260928/test_lift.py b/frontiers/elder_dimension_lift_20260928/test_lift.py new file mode 100644 index 000000000..c3ff86151 --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/test_lift.py @@ -0,0 +1,146 @@ +"""Finite exact controls, not a Gaussian-field theorem checker.""" +import itertools +import unittest +from fractions import Fraction as F +import lift as m + +class LiftTests(unittest.TestCase): + def test_nonorthogonal_shear_cancels_midpoint_cross_terms(self): + D = [[F(-2), F(1,5)], [F(1,5), F(-3)]] + v = [F(1,4), F(-1,7)] + sigma = F(-3,200) + A, S = m.chart(D,v,sigma) + wanted = [[sigma,F(0),F(0)], [F(0),*D[0]], [F(0),*D[1]]] + self.assertEqual(m.mm(m.tr(S),m.mm(A,S)),wanted) + self.assertNotEqual(m.mm(m.tr(S),S),m.eye(3)) + self.assertEqual(m.det(S),1) + + def test_raw_soft_entry_need_not_be_order_r(self): + A,_ = m.chart([[F(-1)]],[F(1,5)],F(-1,100)) + self.assertEqual(A[0][0],F(-1,20)) + self.assertEqual(A[0][0]-F(1,5)**2/F(-1),F(-1,100)) + + def test_chart_extends_through_singular_contact(self): + A,S = m.chart([[F(-1)]],[F(1,5)],F(0)) + self.assertEqual(m.det(A),0) + self.assertEqual(m.det(S),1) + + def test_full_dimension_determinant_identity(self): + for n in range(1,5): + D = [[-F(i+2) if i==j else F(0) for j in range(n)] for i in range(n)] + v = [F(i+1,20) for i in range(n)] + A,_ = m.chart(D,v,F(-1,17)) + self.assertEqual(m.det(A),F(-1,17)*m.det(D)) + + def test_cubic_tensor_change_has_unit_jacobian(self): + for d in range(3,6): + labels,T = m.cubic_change(d,[F(i+1,20) for i in range(d-2)]) + self.assertEqual(m.det(T),1) + pure = labels.index((3,)+(0,)*(d-1)) + self.assertEqual(T[pure],[F(int(j==pure)) for j in range(len(labels))]) + reduced = [[v for j,v in enumerate(row) if j!=pure] + for i,row in enumerate(T) if i!=pure] + self.assertEqual(m.det(reduced),1) + + def test_raw_chart_volume_is_one_power_of_r(self): + for d in range(2,9): + self.assertEqual(m.rare_power(d),1) + r = F(1,13) + self.assertEqual(m.band_width(r,F(6,5),F(1,100)),F(12,6500)) + + def test_complete_contact_jet_labels(self): + for d in range(2,8): + U,J = m.jet_labels(d) + self.assertEqual(len(U),2*(d+1)) + self.assertEqual(len(U+J),len(set(U+J))) + self.assertEqual(set(U+J),set(m.multiindices(d,3,upto=True))) + + def test_polynomial_lattice_unisolvence(self): + for d in (2,3,4): + labels = m.multiindices(d,3,upto=True) + V = [[m.monomial(n,a) for a in labels] for n in itertools.product(range(4),repeat=d)] + self.assertEqual(m.rank(V),len(labels)) + self.assertEqual(m.rank([row+[row[0]] for row in V]),len(labels)) + + def test_plane_pins_with_free_transverse_cubic(self): + k,s,a,beta,c = F(6,5),F(-2),F(3,7),F(-4,5),F(2,3) + for X,val in ((F(-1,2),0),(F(1,2),-k)): + f,g = m.plane(X,F(0),k,s,a,beta,c) + self.assertEqual(f,val) + self.assertEqual(g,[0,0]) + + def test_plane_path_polynomials(self): + k=F(6,5) + for t in [F(i,16) for i in range(17)]: + pts=[(-F(1,2)-t/4, F(0)),(-F(3,4),9*t/4),(-F(3,4)-t/4,F(9,4))] + want=[-3*t*t/16-t**3/32,F(-7,32),-F(7,32)+51*t/64-9*t*t/32-t**3/32] + for (X,Z),w in zip(pts,want): + f,_=m.plane(X,Z,k,-3*k/2,0,-2*k,0) + self.assertEqual(f,k*w) + self.assertGreater(F(-7,32)-F(1,64),F(-1,4)) + self.assertGreater(F(17,64)-F(1,64),0) + + def test_path_survives_bounded_spatial_shear(self): + q=F(1,9) + maxnorm=F(97,16) + self.assertLess((1+q)**2*maxnorm,16) + + def test_two_extra_saddle_data(self): + X,z2=F(-3,4),F(15,8) + self.assertEqual(6*X*X-F(3,2)-z2,0) + self.assertEqual(F(3,2)+2*X,0) + self.assertEqual(2*X**3-F(3,2)*X-F(1,2)-(F(3,4)+X)*z2,F(-7,32)) + self.assertEqual(-4*z2,F(-15,2)) + self.assertLess(X*X+z2,4) + + def test_stiff_modes_do_not_change_weight_power(self): + for d in range(2,9): + self.assertEqual(m.weight_power(d),4) + for r in (F(1,4),F(1,16),F(1,64)): + HM,HS=m.endpoint_model(d,r,F(1)) + self.assertEqual(abs(m.det(HM)*m.det(HS)),45*r**4) + self.assertEqual(m.inertia(HM),(d,0)) + self.assertEqual(m.inertia(HS),(d-1,0)) + + def test_endpoint_cross_blocks_need_schur_correction(self): + D=[[F(-2),F(0)],[F(0),F(-3)]] + for r in (F(1,4),F(1,16),F(1,64)): + A=[[-6*r,F(0)],[F(0),-r/2]] + C=[[r/7,r/11],[r/13,r/17]] + H=m.blocks(A,C,D) + K=m.schur(A,C,D) + self.assertEqual(m.det(H),m.det(D)*m.det(K)) + self.assertNotEqual(K,A) + self.assertEqual(m.inertia(H),(4,0)) + error=max(abs((K[i][j]-A[i][j])/r) for i in range(2) for j in range(2)) + self.assertLess(error,r) + + def test_stiff_elimination_is_order_r_squared(self): + D=[[F(-2),F(0)],[F(0),F(-3)]] + Q=[F(1,7),F(-2,9)] + z=m.solve(D,Q) + for r in (F(1,4),F(1,16),F(1,64)): + ell=[r*r*v for v in Q] + w=[-r*r*v for v in z] + for i in range(2): + self.assertEqual(sum(D[i][j]*w[j] for j in range(2))+ell[i],0) + correction=sum(w[i]*D[i][j]*w[j]/2 for i in range(2) for j in range(2))+sum(ell[i]*w[i] for i in range(2)) + self.assertEqual(correction/r**3,-r*sum(Q[i]*z[i] for i in range(2))/2) + + def test_determinant_tilt_ledger_all_dimensions(self): + for d in range(2,9): + self.assertEqual(m.rare_power(d)+m.weight_power(d)-2,3) + + def test_density_loss_ledger(self): + self.assertEqual(m.loss_powers(),(F(2,3),F(-5,3))) + self.assertEqual(F(2,3)+1,F(5,3)) + # ell=u^3 gives ell^(2/3-p) d ell = 3 u^(4-3p) du. + self.assertEqual(4-3*F(5,3),-1) + self.assertGreater(4-3*F(3,2),-1) + self.assertLess(4-3*F(2),-1) + + def test_singular_stable_block_is_excluded(self): + with self.assertRaises(ValueError): + m.chart([[F(0)]],[F(1)],F(1)) + +if __name__=='__main__': unittest.main() diff --git a/frontiers/elder_dimension_lift_20260928/verify.py b/frontiers/elder_dimension_lift_20260928/verify.py new file mode 100644 index 000000000..7bbd0612e --- /dev/null +++ b/frontiers/elder_dimension_lift_20260928/verify.py @@ -0,0 +1,96 @@ +"""Source-bound exact finite controls; not a verification of Gaussian analysis.""" +import argparse +import hashlib +import io +import json +from pathlib import Path +import subprocess +import sys +import unittest + +ROOT=Path(__file__).resolve().parent +MUTANTS={ + 'wrong-schur-sign':'test_nonorthogonal_shear_cancels_midpoint_cross_terms', + 'omit-shear':'test_nonorthogonal_shear_cancels_midpoint_cross_terms', + 'rare-every-direction':'test_raw_chart_volume_is_one_power_of_r', + 'all-directions-soft':'test_stiff_modes_do_not_change_weight_power', + 'drop-band-jacobian':'test_raw_chart_volume_is_one_power_of_r', + 'duplicate-cubic-pin':'test_complete_contact_jet_labels', + 'drop-transverse-linear':'test_plane_pins_with_free_transverse_cubic', + 'ignore-cross-schur':'test_endpoint_cross_blocks_need_schur_correction', + 'positive-stiff':'test_stiff_modes_do_not_change_weight_power', + 'omit-loss-factor':'test_density_loss_ledger', +} + +def require(ok,message): + if not ok:raise ValueError(message) + +def decode(text): + def unique(items): + d={} + for k,v in items: + require(k not in d,'duplicate JSON key: '+k);d[k]=v + return d + return json.loads(text,object_pairs_hook=unique) + +def ident(path): + require(path.is_file() and not path.is_symlink(),'regular source required') + data=path.read_bytes() + return {'bytes':len(data),'sha256':hashlib.sha256(data).hexdigest(), + 'git_blob':hashlib.sha1(f'blob {len(data)}\0'.encode()+data).hexdigest()} + +def sources(): + ident(ROOT/'SOURCE_FILES.json') + entries=decode((ROOT/'SOURCE_FILES.json').read_text())['files'] + names=[e['path'] for e in entries] + require(len(names)==len(set(names)) and all(Path(n).name==n and n!='SOURCE_FILES.json' for n in names),'unique flat paths required') + require(sorted(p.name for p in ROOT.iterdir())==sorted(names+['SOURCE_FILES.json']),'source membership differs') + for e in entries:require(ident(ROOT/e['path'])=={k:e[k] for k in ['bytes','sha256','git_blob']},'source identity differs: '+e['path']) + return {p.name:ident(p) for p in sorted(ROOT.iterdir())} + +def child(mutant): + import lift + import test_lift + lift.MUTANT=mutant + result=unittest.TextTestRunner(stream=io.StringIO()).run(unittest.defaultTestLoader.loadTestsFromModule(test_lift)) + print(json.dumps({'tests':result.testsRun,'passed':result.wasSuccessful(), + 'failures':sorted(t.id().rsplit('.',1)[-1] for t,_ in result.failures), + 'errors':sorted(t.id().rsplit('.',1)[-1] for t,_ in result.errors)},sort_keys=True)) + return 0 if result.wasSuccessful() else 1 + +def replay(out): + out=out.resolve() + require(not out.exists() and not out.is_relative_to(ROOT),'new output outside source required') + before=sources();out.mkdir(parents=True) + records={} + for case in ['baseline',*MUTANTS]: + pair=[] + for mode,flags in [('normal',[]),('optimized',['-O'])]: + command=[sys.executable,'-B',*flags,'-S',str(ROOT/'verify.py'),'--child'] + if case!='baseline':command+=['--mutant',case] + proc=subprocess.run(command,capture_output=True,timeout=30) + (out/(case+'_'+mode+'.stdout')).write_bytes(proc.stdout) + (out/(case+'_'+mode+'.stderr')).write_bytes(proc.stderr) + result=decode(proc.stdout.decode()) + require(not proc.stderr and not result['errors'],'execution error: '+case) + require(result['tests']==18,'wrong test count') + if case=='baseline':require(proc.returncode==0 and result['passed'] and not result['failures'],'baseline failed') + else:require(proc.returncode==1 and not result['passed'] and MUTANTS[case] in result['failures'],'intended semantic failure absent: '+case) + pair.append(proc.stdout) + require(pair[0]==pair[1],'Python modes disagree: '+case) + records[case]=decode(pair[0].decode()) + summary={'tests_per_mode':18,'semantic_mutants_per_mode':10,'identical_output_pairs':11, + 'all_intended_failures':True,'scientific_effect':'NONE','gaussian_analysis_verified_by_code':False} + require(summary==decode((ROOT/'RESULTS.json').read_text()),'stored summary differs') + require(sources()==before,'sources changed during replay') + report={**summary,'source_identities':before,'sources_unchanged':True,'cases':records} + (out/'REPORT.json').write_text(json.dumps(report,sort_keys=True,indent=2)+'\n') + print(json.dumps(summary,sort_keys=True,indent=2)) + return 0 + +if __name__=='__main__': + p=argparse.ArgumentParser(description=__doc__);g=p.add_mutually_exclusive_group(required=True) + g.add_argument('--child',action='store_true');g.add_argument('--output',type=Path) + p.add_argument('--mutant',choices=MUTANTS);a=p.parse_args() + require(a.child or a.mutant is None,'mutant requires child mode') + raise SystemExit(child(a.mutant) if a.child else replay(a.output))