From 71772a8906cf6663d16be2cd5f63e5d4ebdcee2b Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 21:41:23 -0500 Subject: [PATCH] Add microscopic radial-rate expansion and sharp signed/unsigned metric asymptotics OpenAI author-side conditional consumer of the exact PR166 limiting point measure. Smooth fixed-domain reciprocal cutoff proves all-even tail expansion, explicit t^-13 correction, unsigned Pareto/height O(t^-2), signed latent joint Theta(t^-1), critical-moment finite part, and positive second coefficient for aligned planar exact periodic covariance. No original finite-r rate, spatial TV, whole-cluster tie rate or global status change. Fresh local40 tests per Python mode and8 semantic mutants per mode pass, all12 remote packet blobs and tree independently match. Actual historical source verification and nonauthor analytic review remain hosted obligations; no self-merge. --- .github/workflows/radial-rate.yml | 38 ++ frontiers/radial_rate_20260930/MANIFEST.json | 73 ++++ frontiers/radial_rate_20260930/PLAN.md | 29 ++ frontiers/radial_rate_20260930/PROOF.md | 334 ++++++++++++++++++ frontiers/radial_rate_20260930/README.md | 61 ++++ .../radial_rate_20260930/RECONNAISSANCE.md | 33 ++ frontiers/radial_rate_20260930/RESULTS.json | 21 ++ frontiers/radial_rate_20260930/SOURCES.json | 33 ++ frontiers/radial_rate_20260930/VALIDATION.md | 45 +++ frontiers/radial_rate_20260930/rate.py | 170 +++++++++ frontiers/radial_rate_20260930/test_rate.py | 137 +++++++ frontiers/radial_rate_20260930/test_verify.py | 102 ++++++ frontiers/radial_rate_20260930/verify.py | 104 ++++++ 13 files changed, 1180 insertions(+) create mode 100644 .github/workflows/radial-rate.yml create mode 100644 frontiers/radial_rate_20260930/MANIFEST.json create mode 100644 frontiers/radial_rate_20260930/PLAN.md create mode 100644 frontiers/radial_rate_20260930/PROOF.md create mode 100644 frontiers/radial_rate_20260930/README.md create mode 100644 frontiers/radial_rate_20260930/RECONNAISSANCE.md create mode 100644 frontiers/radial_rate_20260930/RESULTS.json create mode 100644 frontiers/radial_rate_20260930/SOURCES.json create mode 100644 frontiers/radial_rate_20260930/VALIDATION.md create mode 100644 frontiers/radial_rate_20260930/rate.py create mode 100644 frontiers/radial_rate_20260930/test_rate.py create mode 100644 frontiers/radial_rate_20260930/test_verify.py create mode 100644 frontiers/radial_rate_20260930/verify.py diff --git a/.github/workflows/radial-rate.yml b/.github/workflows/radial-rate.yml new file mode 100644 index 000000000..fa1a9abe5 --- /dev/null +++ b/.github/workflows/radial-rate.yml @@ -0,0 +1,38 @@ +name: Microscopic radial-rate checks + +'on': + pull_request: + paths: + - 'frontiers/radial_rate_20260930/**' + - '.github/workflows/radial-rate.yml' + workflow_dispatch: + +permissions: + contents: read + +jobs: + exact-and-source: + runs-on: ubuntu-latest + timeout-minutes: 10 + steps: + - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 + with: + persist-credentials: false + fetch-depth: 0 + - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 + with: + python-version: '3.11.16' + - name: Fetch exact public source objects + run: | + set -euo pipefail + git fetch --no-tags origin 80059a97cd8eb32d1a17a0ad9cb22cb2a0d7b337 + git fetch --no-tags origin 382c0f9ff2281f43651ddbdf2e9b36dd52e2c6bf + git fetch --no-tags origin 7a1cb09a9d58d179393e6d29146252f714b9c9bf + - name: Verify sources, packet and both Python modes + env: + PYTHONDONTWRITEBYTECODE: '1' + GIT_NO_REPLACE_OBJECTS: '1' + run: | + set -euo pipefail + python -B -S frontiers/radial_rate_20260930/verify.py + git diff --exit-code diff --git a/frontiers/radial_rate_20260930/MANIFEST.json b/frontiers/radial_rate_20260930/MANIFEST.json new file mode 100644 index 000000000..b06df6fa3 --- /dev/null +++ b/frontiers/radial_rate_20260930/MANIFEST.json @@ -0,0 +1,73 @@ +{ + "schema": 1, + "scientific_effect": "NONE", + "review_status": "NONAUTHOR_REVIEW_OPEN", + "files": [ + { + "path": "PLAN.md", + "bytes": 1772, + "sha256": "3a436b2f58a3b79bcb5471474d94fff7c07f5f4dce838525fed117cbb5d446db", + "git_blob": "db61274a4ce7f2e9e6c4b75303a285230f44d5db" + }, + { + "path": "PROOF.md", + "bytes": 15755, + "sha256": "a3693664900e23e1e763d88a0b5609936a6f31d844cbe6f18c7d0379b94ba710", + "git_blob": "65f24b1f9a7b80522a2ee059f5f6877c9f970f0d" + }, + { + "path": "README.md", + "bytes": 3186, + "sha256": "b31b309916639ce111f28f4c81fea061a62ac777c6a9f241185bcfd0f59655b8", + "git_blob": "cc0e2f5a45c76aa60a3782002321f0c47d0f3b17" + }, + { + "path": "RECONNAISSANCE.md", + "bytes": 2002, + "sha256": "54118b87d9a0dbe78ed9f2162ad413d1a9bfc1c1122c53855274b300751ede2b", + "git_blob": "3eb935b8d3fa2c10e8220c71c5243488beb25e31" + }, + { + "path": "RESULTS.json", + "bytes": 438, + "sha256": "c9cdb842befa92b8e26eb02831a1d20838cc75465f1db7840eba1c0eb1c70b4f", + "git_blob": "c7494046e449f30a6346572b2760cca6c1c62afb" + }, + { + "path": "SOURCES.json", + "bytes": 1396, + "sha256": "22b3064a278faff1d915dfb658e9d7e41ec5c4ee69f31e944d47a699a82f8a07", + "git_blob": "37f3dc7b5583bf2f4f0a8d1bb1fd5bd39ff12838" + }, + { + "path": "VALIDATION.md", + "bytes": 2898, + "sha256": "b14b2fb0576c7c7fd1a03baf3d7f479d901f186d0ef0a49dac5156805908409d", + "git_blob": "5a4a11b112723aaf9a67c1aeaafa3a216e5f17e8" + }, + { + "path": "rate.py", + "bytes": 6344, + "sha256": "e96be67c1703780dcd48113fa55809d98b87f0e498da132b162c9640d300577e", + "git_blob": "d213a2762e10a07f3290f9ae1b4dd9f8f73e5667" + }, + { + "path": "test_rate.py", + "bytes": 7286, + "sha256": "f2a096b91de1978dbaa6c1301ac1013d454cadcf96aa705fb66df3c43f53324f", + "git_blob": "4074549e593ad0f02f6931c6df211e25a02d84ea" + }, + { + "path": "test_verify.py", + "bytes": 5792, + "sha256": "1e8f2790b5861b520463ab1d44b87c29dd43ba46b652c46992889ecd001bd4c7", + "git_blob": "258288f8efa9039782432daf6dde77e2b594ef39" + }, + { + "path": "verify.py", + "bytes": 5169, + "sha256": "7f7006a1f3ba74964a00023dd418624612980e19f8e40a3506245ae43966119c", + "git_blob": "d5789cbe7b94b6243b55a62491ecd19bdeb9cbe0" + } + ] +} diff --git a/frontiers/radial_rate_20260930/PLAN.md b/frontiers/radial_rate_20260930/PLAN.md new file mode 100644 index 000000000..db61274a4 --- /dev/null +++ b/frontiers/radial_rate_20260930/PLAN.md @@ -0,0 +1,29 @@ +# Inverse-radius expansion: execution plan + +Goal: derive quantitative radius-tail and mark-law results from the exact R11 +integral of the already-formed limiting microscopic POINT intensity. The original +Gaussian-field limit r->0 is taken first. No whole-cluster maximum or finite-r +rate is to be inferred. + +Design: reciprocal radius z=1/Z makes the physical cutoff an interval with +explicit endpoints. Map it to [-1,1], prove a smooth even integrated function of +1/t using Gaussian derivative domination, and compute its first two coefficients. +Deduce radial and fixed latent-mark total-variation rates, keeping the sign- +retaining law separate. Preserve the complete original anisotropic covariance, +Haar factors and full normalizer. No original source or peer branch is edited. + +Execution: isolated new runtime directory and new additive GitHub branch. +Dylan's repeated autonomy instruction authorizes foreground work; no timers or +background agents are restarted. No subagent tool is available here. + +1. Read source R11-R13, exact Gaussian/spectral interface and current peer claims. +2. Write and observe failing tests for exact shape integrals and endpoint series. +3. Implement standard-library rational controls; test both signs and parity. +4. Write complete domination and coefficient proof, plus all scope exclusions. +5. Verify exact historical source identities, packet inventory and both Python + modes; include hostile Git fixtures and semantic mutants. +6. Publish a new source-bound candidate and request nonauthor analytic review. + +Separate supporting task: bounded nonauthor review of PR173 Route C; accept the +conditional count implication and repair its inadmissible fixed-R substitution +by a diagonal argument. No graph execution or parent revalidation. diff --git a/frontiers/radial_rate_20260930/PROOF.md b/frontiers/radial_rate_20260930/PROOF.md new file mode 100644 index 000000000..65f24b1f9 --- /dev/null +++ b/frontiers/radial_rate_20260930/PROOF.md @@ -0,0 +1,334 @@ +# Smooth inverse-radius expansion and sharp rates for microscopic extreme marks + +Object: OA-RADIAL-RATE-20260930-v1. Author: OpenAI / GPT-6 Astra Pro. +Disposition: AUTHOR-SIDE CONDITIONAL PROOF CANDIDATE; NONAUTHOR REVIEW OPEN. +Scientific effect NONE. No parent proof, register, Boolean, prize, or earlier +review is changed. This conversation authored SC/P and contributed to the +related cluster line; no independent revalidation of those premises is implied. + +## 1. Exact object and scope + +Fix d>=2, L>0, b real, k>0 and an orthonormal frame, under the original model +and full endpoint normalizer. This paper concerns the ALREADY-FORMED limiting +microscopic POINT intensity of [R]. First the original field radius r tends to +zero; only then does the microscopic distance threshold t tend to infinity. +No finite-r convergence rate is proved. Whole-cluster maximum selection and +its moving tie boundaries are not consumed or treated here. + +Exact source identities are in SOURCES.json. [R] is PR166 RADIAL_TAIL.md at +80059a97cd8eb32d1a17a0ad9cb22cb2a0d7b337, blob0f14417ef7038b9c6f50e4b01e393a58b7b5e3a4: +R7-R13 supply the root-resolved integral, Gaussian domination and positive leading +coefficient. [SC] is PR162 PROOF.md at382c0f9ff2281f43651ddbdf2e9b36dd52e2c6bf, +blob16c56821b52fd76b0be791622b9c3809eafde75a: the nondegenerate raw Gaussian contact +jet, orthogonal spectral convention and finite nonempty microscopic measure. +[P] is imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md at +7a1cb09a9d58d179393e6d29146252f714b9c9bf, blobdfed3b8d318a3ab1950957f393307733a4bef3f2: +only the exact periodized covariance and contact conditioning, used in Section7. +Neither PR169's whole-cluster candidate, its companion-ratio addendum, nor any +numerical coefficient note is a premise. Source reviews are not reviews here. + +Use [R]'s variables lambda=(a,h,O,xi), with ordered positive hard curvatures h, +normalized Haar O, and remaining cubic entries xi. Put + + A=a/(12k), gamma=sqrt(1+A^2), + beta0=a^2/(12k), c0=a^3/(144k^2), + A0=O diag(0,-h) O^T, + H(h)=product h_j^3 product_(i0 on S. + +For y=1/Z define + + g_lambda,u,v(y)=G_lambda(beta0+k b0 y^2, + c0+(a b0/4)y^2+2k(v-b0u)y^3). (2) + +[R, R11] says exactly that the tail F(t)=integral sum_i 1{|z_i|>t}dM is + + F(t)=K0 integral_(S,lambda) Q H + integral_R |Z|^-12 g(1/Z) + 1{(u-AZ)^2+Z^2>t^2}dZ du dv d lambda. (3) + +The multiplicity of roots is already correct in this formula. No extra factor +for a double cluster, pin density, or endpoint normalizer is introduced. + +## 2. A fixed-domain smooth even representation + +**Theorem 1.** There is a smooth even function C(delta), defined for +|delta|<2/3 and with every fixed derivative bounded on |delta|<=1/3, such that + + F(t)=t^-11 C(1/t), t>=3. (4) + +Smoothness also holds in L1 for the underlying UNSIGNED shape/parameter measures. +The claim is C-infinity, not analyticity or convergence of an infinite Taylor +series. Consequently for every fixed N>=0 there are finite coefficients C_(2j) +with + + F(t)=sum_(j=0..N) C_(2j) t^(-11-2j)+O_N(t^(-13-2N)), + -F'(t)=sum_(j=0..N)(11+2j)C_(2j)t^(-12-2j) + +O_N(t^(-14-2N)). (5) + +C_(0)>0 is [R]'s C_star. Constants are at the fixed source parameters; no growing +dimension, volume, vanishing-gap, or parameter-uniform claim is made. + +**Proof.** The reciprocal substitution in (3) gives |Z|^-12 dZ=|y|^10 dy on +both signs. For t>|u| the physical radius condition is + + (t^2-u^2)y^2+2uAy-gamma^2<0. + +Set delta=1/t and y=delta w. Its two endpoints in w are + + w_plus/minus(delta)=m(delta) +/- d(delta), + m(delta)=-uA delta/(1-u^2 delta^2), + d(delta)=sqrt(gamma^2-u^2 delta^2)/(1-u^2 delta^2). (6) + +Thus (4) holds with + + J_delta(u,v,lambda)=d(delta) integral_(-1)^1 + [m(delta)+d(delta)x]^10 + g(delta[m(delta)+d(delta)x]) dx, + C(delta)=K0 integral Q H J_delta du dv d lambda. (7) + +There is no moving integration boundary left. On |delta|<=delta0<2/3 the +denominator is uniformly positive and the square-root radicand is bounded +below by a positive constant, since |u|<=3/2 and gamma>=1. Each fixed derivative +of m,d is bounded by a polynomial in1+|a| with constants depending on delta0,k. + +For every fixed j the nondegenerate Gaussian contact density satisfies + + sup_(beta,c) |partial_(beta,c)^j G_lambda(beta,c)| + <= C_j exp[-c_j(|h|^2+a^2+|xi|^2)] (8) + +uniformly in O. Indeed each derivative is a polynomial times the same Gaussian; +absorb that polynomial into a weaker Gaussian exponent and then discard beta,c +from its quadratic lower bound. A bounded mean changes the constants only. +Uniform tensor norm equivalence under O supplies the displayed retained variables. +No inverse hard eigenvalue is used. This is an elementary derivative extension +of [R]'s raw Gaussian bound, not an extra stochastic assumption. + +The chain rule in (7), for any fixed number of delta derivatives, now gives an +integrable majorant of the form + + C Q H (1+|a|)^M exp[-c(|h|^2+a^2+|xi|^2)], (9) + +on the bounded shape domain and x in[-1,1]. The actual shifted beta,c values +may be large: (8) is a supremum over them, not an invalid compactness assumption. +This proves differentiation under all integrals and smoothness in L1 as well +as for the total mass. The exact identities m(-delta)=-m(delta), +d(-delta)=d(delta), followed by x->-x, show J_(-delta)=J_delta. This cancellation +holds even when g(y) is not even; its cubic y^3 term is retained. + +Taylor's theorem with the integrated derivative bounds proves (5), including +its differentiated remainder. It is NOT obtained by formally differentiating +an unspecified big-O estimate. C(0) is the positive source coefficient. QED. + +## 3. Explicit second coefficient + +Write C_0=C_(0), C_2=C_(2), to distinguish coefficients from their tail powers11,13. +Set the differential operator acting on G_lambda at fixed a,h,O,xi + + D_a=k partial_beta+(a/4)partial_c. + +The pointwise density has expansion g(y)=G0+g2 y^2+g3 y^3+O(y^4), with + + g2=b0 D_a G0. (10) + +There is no linear y term. Expanding the exact endpoints, or differentiating +(7), gives + + j0=(2/11)gamma^11 G0, + j2=u^2 gamma^9(1+12A^2)G0+(2/13)b0 gamma^13 D_a G0, + J_delta=j0+j2 delta^2+O_L1(delta^4). (11) + +For the geometric part, write w_+=gamma-uA delta+ +[u^2 gamma-u^2/(2gamma)]delta^2+O(delta^3), with the corresponding reflected +negative endpoint. Then (w_+^11-w_-^11)/11 equals +2gamma^11/11+u^2 gamma^9(1+12A^2)delta^2+O(delta^4). +The g2 term contributes2g2 gamma^13 delta^2/13. The odd g3 term first contributes +at order delta^4 after the two physical sides are summed; it is not dropped +from the all-order argument. + +The necessary exact shape integrals are + + I=integral_S Q=246528/35, + U2=integral_S u^2 Q=240192/35, + B=integral_S b0 Q=-428544/7=3I-12U2, + Uabs=integral_S |u|Q=5898627/880. (12) + +They follow by integrating the polynomial Q in v and then on the strips cut +at u=-1/2 and u=0. The companion computes them in exact Fraction arithmetic. +In particular + + C_0=K0*(2I/11) integral H gamma^11 G0 d lambda, + C_2=K0 integral H [U2 gamma^9(1+12A^2)G0 + +(2B/13)gamma^13 D_a G0]d lambda. (13) + +Both integrals are finite by (8). C_0>0. No general sign or nonzero assertion +for C_2 is made in arbitrary dimension/frame; Section7 supplies an exact +noncancellation result at a narrower source scope. No numerical evaluation of +either Gaussian integral is claimed. + +## 4. Rates for the radial ratio and unsigned marks + +Let P_t be point-INTENSITY sampling conditioned on physical radius R>t. Define +q=R/t>=1 and retain Y=(u,v,lambda), but FORGET sign Z. These are the root-resolved +latent coordinates of [R], not a configuration-uniform selection. Define the +finite measures with densities + + dmu0=K0 Q H j0 dY, dmu2=K0 Q H j2 dY, + c=C_2/C_0. (14) + +mu0 has mass C_0 and mu2 mass C_2. The joint law of (q,Y) has the L1 expansion + + dP_t(q,Y)=11q^-12 dq dmu0(Y)/C_0 + +t^-2 [13q^-14 dq dmu2(Y)/C_0 + -11c q^-12 dq dmu0(Y)/C_0]+O_L1(t^-4). (15) + +In particular its total-variation distance to the stated independent limiting +product is O(t^-2). Projection to Y, or to the downward height +eta=u+1/2+v/6, retains this rate. This supplies an O(t^-2) TV rate for the +intensity-selected height law H_eta/I in [R, H1-H2]. No spatial-configuration +TV claim is made: the map to actual positions depends on t. + +Proof: for fixed Y, the radius tail density is t^-11 K0 QH J_(1/t). +Differentiate the smooth expression already justified in Section2; at tq its +radial density times t equals + +t^-11 K0 QH q^-12[11J_(1/(tq))+(1/(tq))J'_(1/(tq))]. + +Divide by F(t)=t^-11 C(1/t) and use the L1 Taylor estimates. The remainder is +bounded after integration by a constant times t^-4 q^-12, integrable on q>=1. +This proves (15) without differentiating a merely pointwise asymptotic. QED. + +Let Pareto_11 have density11q^-12 on q>=1. For the scalar radial ratio, (15) gives + + p_t(q)=11q^-12[1+c t^-2((13/11)q^-2-1)]+O_L1(t^-4). + +**Sharp scalar coefficient:** + + dTV(Law_(P_t)(R/t),Pareto_11) + =kappa |c| t^-2+O(t^-4), + kappa=(2/13)(11/13)^(11/2). (16) + +The same leading coefficient holds for the supremum distance of their CDFs. +The correction changes sign only at q0=sqrt(13/11). Its positive integral is +q0^-11-q0^-13=kappa; its total integral is zero. Half its L1 norm is therefore +kappa, proving (16). The uniform CDF remainder follows from the L1 remainder; +the maximum of q^-11(1-q^-2) is also kappa. If C_2=0 the stated error is O(t^-4), +not an unjustified claim of a nonzero second-order term. + +As another quantitative consequence, uniformly over q>=1, + + F(tq)/F(t)=q^-11[1+c t^-2(q^-2-1)]+O(t^-4 q^-11). (17) + +This is a source-specific second-order regular-variation statement. Generic +second-order tail theory is not claimed novel. + +## 5. Retaining the sign has a different, strictly slower sharp rate + +The cancellation in Section2 used both signs. Keep epsilon=sign Z and the +same Y. The two half integrals are exactly + + J_delta,epsilon=integral_0^(d+epsilon m) w^10 g(epsilon delta w)dw, + J_delta,epsilon=j0/2+epsilon h1 delta+O_L1(delta^2), + h1=-uA gamma^10 G0. (18) + +The linear term comes from the physical cutoff shift m. g'(0)=0, so no density +term cancels it. Applying the differentiated density argument to each half yields + + dTV(Law_(P_t)(epsilon,R/t,Y), + UniformSign x Pareto_11 x mu0/C_0) + =B_sign t^-1+O(t^-2), + B_sign=(K0/C_0) Uabs integral H |A|gamma^10 G0 d lambda>0. (19) + +Indeed the first signed correction has density +12 epsilon h1 q^-13 K0 QH/C_0; its half-L1 norm, summed over the two signs and +integrated over q, is the displayed B_sign because integral_1^infinity12q^-13dq=1. +Finiteness follows from (8); strict positivity follows from the full positive +Gaussian density on open sets with a!=0 and positive hard spectrum. The gauge +convention for O is exactly that in [R]; (19) is a result for those retained +latent variables, not a statement that a sign alone has a nonzero marginal bias. +Marginalizing can cancel a correction, and specifically forgetting epsilon +cancels this one. Thus signed and unsigned rates must not be conflated. + +## 6. A finite part for the critical eleventh moment + +Let M11(t)=integral sum_i min(R_i,t)^11 dM. The prior theorem gave its leading +logarithm. There is now a finite constant L11 such that + + M11(t)=11 C_0 log t+L11-(11/2)C_2 t^-2+O(t^-4). (20) + +One exact definition is + + L11=11 integral_0^1 x^10 F(x)dx + +11 integral_1^infinity[x^10 F(x)-C_0/x]dx. + +The first integral is finite by finite total point mass. The second converges +by (5) at N=1. Tonelli gives M11(t)=11 integral_0^t x^10 F(x)dx; subtracting +its limiting finite part and integrating the controlled remainder proves (20). +No numerical value for L11 is asserted. This is again after the r limit only. + +## 7. Exact positive second correction in the aligned planar periodic model + +**Theorem 2.** In d=2, with the axial coordinate aligned with one of the lattice +axes of [P]'s EXACT periodized kernel, C_2>0 for every fixed L,k>0 and b real. +Consequently the radial TV and CDF errors in (16) are genuinely Theta(t^-2), +with the positive coefficient in (16); not merely an upper bound. + +Proof: [P]'s kernel factors as K_L(x,z)=k_L(x)k_L(z). Let m2,m4,m6 be the even +spectral moments of the one-dimensional variance-one factor; m2>0 and the full +positive lattice spectrum gives m4-m2^2>0 and m6-m4^2/m2>0. At contact condition +on (f,fx,fxx,fxxx,fz,fxz)=(b,0,0,12k,0,0). + +Even-total-order jets and odd-total-order jets are independent. For the odd +soft cubic jets (a,beta,c)=(fxxz,fxzz,fzzz), separability and reflection in each +axis give a centered DIAGONAL conditional Gaussian with variances + + va=vbeta=m2(m4-m2^2), vc=m6-m4^2/m2. (21) + +For transparency: Cov(beta,(fx,fxxx))=(-m2^2,m2 m4) is -m2 times the first row +of Cov(fx,fxxx), so its conditional mean is -m2 fx=0 even though fxxx=12k. +a and c correlate only with fz in that odd conditioning block, with covariances +-m2^2 and -m4; their raw covariance m2 m4 is removed by that regression. Their +conditional covariance with beta vanishes by coordinate reflection. The diagonal +variances follow by subtracting these rank-one regressions. The even soft +curvature has its own strictly positive conditional density at zero and merely +multiplies this cubic Gaussian by a positive b-dependent scalar. + +Therefore on the cusp + + D_a G0=-[a^2/(12vbeta)+a^4/(576k^2 vc)]G0<=0. (22) + +In (13), U2>0, B<0 and G0>0. The geometric term is strictly positive and the +second term is nonnegative. Thus C_2>0, without replacing finite L by a continuum +covariance or numerically approximating a lattice sum. The same common even +b-dependent factor cancels from c=C_2/C_0 and B_sign at this planar aligned +scope. We do not extend this diagonal regression or noncancellation assertion +to arbitrary rotations or d>=3 without a separate argument. QED. + +## 8. Verification and review boundary + +A: reciprocal physical cutoff, fixed-domain map, C-infinity L1 Gaussian derivative +domination, exact parity and differentiated all-order asymptotic expansion. +B: j0/j2 coefficients, all four exact shape integrals, signed/unsigned TV and CDF +constants, finite-part moment, and aligned planar regression/noncancellation. + +The stdlib companion checks shape integrals, formal endpoint equations, exact +Taylor coefficients, cancellation and signed bias, independent scalar controls +and deliberately false variants. These are finite checks, not a formal proof +of any Gaussian input or differentiation under an infinite-dimensional integral. +No Lean formalization, global status change, coefficient enclosure or self-merge. + +No rate for r->0, no uniform simultaneous t(r)->infinity statement, no claim +about the remote singleton population, no convergence rate for whole-cluster +maximum selectors across ties, and no spatial independence/elder pairing is +added by this packet. Sign-forgetting is part of (15), not an optional omission. diff --git a/frontiers/radial_rate_20260930/README.md b/frontiers/radial_rate_20260930/README.md new file mode 100644 index 000000000..cc0e2f5a4 --- /dev/null +++ b/frontiers/radial_rate_20260930/README.md @@ -0,0 +1,61 @@ +# Microscopic radial rates and an even inverse-radius expansion + +OpenAI / GPT-6 Astra Pro. Source-bound conditional candidate; nonauthor review +OPEN. Scientific effect NONE. No self-merge or parent/status/graph modification. + +The earlier point-intensity result F(t)~C0 t^-11 is sharpened here to a smooth +even expansion in delta=1/t, with controlled derivatives to every fixed order. +The original field limit r->0 is taken FIRST. This is not a rate for that limit. + +Main manuscript PROOF.md: +- F(t)=C0 t^-11+C2 t^-13+O(t^-15), with an explicit finite Gaussian-derivative + formula for C2 and all-even fixed-order extensions. +- The radial ratio's Pareto(11) TV error has coefficient + (2/13)(11/13)^(11/2)|C2/C0| t^-2+O(t^-4). +- The unsigned shape/parameter/radial joint law has an L1 second-order expansion; + its height marginal consequently converges in TV at O(t^-2). +- RETAINING sign Z gives a strictly positive first-order joint TV coefficient, + Bsign t^-1+O(t^-2). Forgetting sign cancels that term. +- The capped eleventh moment has a finite renormalized limit and an explicit + t^-2 correction, not merely a leading logarithm. +- For the exact aligned PLANAR periodized kernel, Gaussian separability proves + C2>0 at every fixed L,k>0 and b real. Thus the radial error is genuinely + Theta(t^-2) at that narrower scope. No isotropic replacement is used. + +No numerical Gaussian coefficient, finite-r spatial moment/rate, simultaneous +radius limit, whole-cluster maximum rate, spatial TV convergence or independence +between pin pairs is asserted. All-rate statements concern the root-resolved +POINT measure. The parent whole-cluster and elder-geometry lanes are untouched. + +## Replay + +From a full checkout with the three pinned historical source objects: + + python -B -S frontiers/radial_rate_20260930/verify.py + +Standalone download: + + python -B -S verify.py --local-only + +The latter reports source_pins_checked=false. Real local Git fixtures test +custody behavior, not the actual project sources. The full workflow verifies +all source identities and the flat packet before replaying both Python modes, +deterministic results and eight semantic negative controls. No third-party +Python library is required by the shipped scripts. + +Forty local tests passed in each normal/optimized mode at author validation. +They include exact shape integrals, endpoint identities, signed/unsigned formal +series, a high-precision scalar diagnostic, planar Gaussian Schur complements, +and real Git replacement/noncommit/path/inventory attacks. Tests do not prove +the Gaussian domination, differentiation, or the new probability limits. + +## Review requests + +A: Sections2-3, exact physical-cutoff inversion, fixed-domain representation, +C-infinity L1 domination, parity, derivatives and explicit second coefficient. +B: Sections4-7, normalized joint/radial TV rates, signed first-order bias, finite +critical-moment part and exact planar regression/noncancellation. + +The author is exposed to SC/P and related source packets. New reviews must state +that exposure and bind the exact mathematical bytes; existing source verdicts +or green workflows are not automatic acceptance of these new deductions. diff --git a/frontiers/radial_rate_20260930/RECONNAISSANCE.md b/frontiers/radial_rate_20260930/RECONNAISSANCE.md new file mode 100644 index 000000000..3eb935b8d --- /dev/null +++ b/frontiers/radial_rate_20260930/RECONNAISSANCE.md @@ -0,0 +1,33 @@ +# Narrow primary-source reconnaissance — 30 September 2026 UTC + +Exact searches actually executed: +1. second order regular variation Pareto approximation total variation Hall class tail expansion paper +2. site.arxiv.org Palm theory extremes anchored tail processes Planinic 2104.03810 + +Primary records consulted: +- Hrvoje Planinic, Palm theory for extremes of stationary regularly varying time + series and random fields, arXiv:2104.03810v2 (14 March2023). + https://arxiv.org/abs/2104.03810 + Direct abstract/metadata open succeeded. It distinguishes typical exceedances + from typical clusters; no generic sampling/Palm principle is claimed new here. +- Second-order regular variation, convolution and the central limit theorem, + Stochastic Processes and their Applications69(2),139-159(1997), + DOI10.1016/S0304-4149(97)00042-2. + https://www.sciencedirect.com/science/article/pii/S0304414997000422 + The search response supplied the abstract describing second-order tail theory. + Direct open returned403. No full-text/theorem-level audit is claimed. +- L. de Haan and L. Peng, Rates of Convergence for Bivariate Extremes, + Journal of Multivariate Analysis61(2),195-230(1997), DOI10.1006/jmva.1997.1669. + https://doi.org/10.1006/jmva.1997.1669 + Search abstract states rates in total variation and uniform metrics under a + second-order regular-variation condition. Direct open returned403. + +This new packet derives its particular inverse-radius expansion from exact +GitHub source R11, not by importing an unchecked second-order tail theorem. +Generic second-order regular variation and metric convergence rates are prior +frameworks. No exhaustive novelty, priority, or absence claim is made. + +Consensus was not invoked in this pass: the user requested GitHub/Superpowers, +and prior actual repeated attempts had returned the quota error. No changed +quota status is asserted. All external access depth above is limited to the +actual returned abstracts/metadata. No PDF or full paper was inspected. diff --git a/frontiers/radial_rate_20260930/RESULTS.json b/frontiers/radial_rate_20260930/RESULTS.json new file mode 100644 index 000000000..c7494046e --- /dev/null +++ b/frontiers/radial_rate_20260930/RESULTS.json @@ -0,0 +1,21 @@ +{ + "mathematical_acceptance": false, + "passed": true, + "scientific_effect": "NONE", + "scope": "finite rational coefficient and parity controls only", + "series_cases": 12, + "shape_integrals": { + "ABS_U": "5898627/880", + "B": "-428544/7", + "I": "246528/35", + "U2": "240192/35" + }, + "signed_joint_rate": 1, + "tail_exponents": [ + 11, + 13, + 15 + ], + "tv_crossing_squared": "13/11", + "unsigned_radial_rate": 2 +} diff --git a/frontiers/radial_rate_20260930/SOURCES.json b/frontiers/radial_rate_20260930/SOURCES.json new file mode 100644 index 000000000..37f3dc7b5 --- /dev/null +++ b/frontiers/radial_rate_20260930/SOURCES.json @@ -0,0 +1,33 @@ +{ + "schema": 1, + "scientific_effect": "NONE", + "sources": [ + { + "id": "R", + "commit": "80059a97cd8eb32d1a17a0ad9cb22cb2a0d7b337", + "path": "frontiers/two_scale_cluster_geometry_20260929/RADIAL_TAIL.md", + "bytes": 12533, + "sha256": "250897858c8b314c0ff85ec1860a725efacfdae0ff7409fced4cadf7bfb85973", + "git_blob": "0f14417ef7038b9c6f50e4b01e393a58b7b5e3a4", + "use": "R7-R13 exact point-intensity integral/majorant; H1-H2 limiting height law." + }, + { + "id": "SC", + "commit": "382c0f9ff2281f43651ddbdf2e9b36dd52e2c6bf", + "path": "frontiers/spectral_cluster_closure_20260929/PROOF.md", + "bytes": 25006, + "sha256": "e971b2cbe50a8a06b47c1219191201e0d1037c9adac23e5e3b7d2051bb70c2eb", + "git_blob": "16c56821b52fd76b0be791622b9c3809eafde75a", + "use": "Raw nondegenerate contact Gaussian, orthogonal spectral conventions, finite microscopic measure. Author exposure." + }, + { + "id": "P", + "commit": "7a1cb09a9d58d179393e6d29146252f714b9c9bf", + "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md", + "bytes": 40261, + "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7", + "git_blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2", + "use": "Exact product-periodized covariance and contact pin vector; no new parent acceptance." + } + ] +} diff --git a/frontiers/radial_rate_20260930/VALIDATION.md b/frontiers/radial_rate_20260930/VALIDATION.md new file mode 100644 index 000000000..5a4a11b11 --- /dev/null +++ b/frontiers/radial_rate_20260930/VALIDATION.md @@ -0,0 +1,45 @@ +# Author validation and limits + +The initial eight-test mathematics scaffold returned seven failing assertions +(the zero odd-series test already passed on the zero scaffold). After exact +implementation all eight passed. Expanded mathematics tests total21. + +The nineteen-test custody scaffold returned25 failing assertions including +subtests. The implemented verifier passed all19. It rejects changed identities, +missing/duplicate/unexpected source IDs, unsafe or missing paths, noncommit tree +and tag objects, Git symlinks, replacement refs, and altered packet inventories. +The replacement fixture verifies that ordinary Git reads really see the forged +bytes before confirming that the protected verifier still authenticates only +the actual original source. This is a test fixture, not observed source tampering. + +Complete local result:40 tests PASS in each normal and optimized Python mode; +12 exact formal-series parameter cases; eight explicit semantic mutants rejected +with rc1 in each mode; unknown mutant rc2; deterministic baseline equal to +RESULTS.json. The source/packet verifier checks its inventory before and after +execution. No temporary output is placed in the packet during replay. + +Exact controls cover all four shape integrals, formal physical-cutoff equations, +odd-term cancellation, the signed first-order term, the density multiplier13, +the TV crossing at sqrt(13/11), and exact planar Schur regressions. A Decimal +scalar diagnostic checks the constant-density endpoint remainder at three +thresholds; it is a finite diagnostic, not a Gaussian coefficient enclosure. +Exploratory SymPy integration reproduced the shape constants, but SymPy is not +a shipped dependency or a substitute for the analytic derivation. + +Local runtime Python3.13.5, Git2.47.3. The workflow requests Python3.11.16, as in +the actual upstream workflows. All shipped syntax uses standard-library3.11 +features. The local raw.githubusercontent.com request failed with DNS resolution +error, so no complete upstream checkout was obtained. Local-only replay states +source_pins_checked=false. The real three-source authentication remains a +HOSTED requirement, not inferred from local Git fixtures or manifest strings. +No hosted pass is anticipated in this author-time record. + +The full Gaussian derivative domination and L1 smoothness are written analytic +obligations. There is no Lean formalization of this new packet. No numerical +value of C0,C2,Bsign or the critical-moment finite part is evaluated. The retained +sign and the order r->0 before t->infinity are load-bearing qualifications. + +Peer support actually delivered: native review5360751376 accepts PR173 §3 Route C +at its conditional count-estimate scope and requests an explicit diagonal repair +of the alternate fixed-R/moving-cutoff reading. It does not authorize graph +execution or count as an independent review of this conversation's source proofs. diff --git a/frontiers/radial_rate_20260930/rate.py b/frontiers/radial_rate_20260930/rate.py new file mode 100644 index 000000000..d213a2762 --- /dev/null +++ b/frontiers/radial_rate_20260930/rate.py @@ -0,0 +1,170 @@ +"""Exact finite controls for the inverse-radius asymptotic candidate. + +Standard library only. Series calculations are formal algebra, not authentication +of Gaussian premises or a proof of domination/total-variation convergence. +""" +import argparse +from fractions import Fraction as F +import json +from math import comb + +MUTANTS=('omit-shift','omit-density-term','drop-a-shear','odd-term-survives', + 'unsigned-is-signed','wrong-b-integral','wrong-density-factor','wrong-tv-root') + + +def rational(x): + if type(x) not in (int,F): raise TypeError('exact int/Fraction required') + return F(x) + + +def add(a,b): + out=dict(a) + for i,x in b.items():out[i]=out.get(i,F(0))+x + return {i:x for i,x in out.items() if x} + + +def scale(a,c): return {i:x*c for i,x in a.items() if x*c} + + +def mul(a,b): + out={} + for i,x in a.items(): + for j,y in b.items():out[i+j]=out.get(i+j,F(0))+x*y + return {i:x for i,x in out.items() if x} + + +def power(a,n): + out={0:F(1)} + for _ in range(n):out=mul(out,a) + return out + + +def integral(a,lo,hi): + return sum((x*(hi**(i+1)-lo**(i+1))/F(i+1) for i,x in a.items()),F(0)) + + +def shape_integrals(): + b={0:F(3),2:F(-12)};u={1:F(1)};hi={0:F(3),1:F(-6)} + # Q=(4v^2-b^2)(b-4uv); dictionary index is v power. + Q={3:scale(u,-16),2:scale(b,4),1:scale(mul(u,power(b,2)),4),0:scale(power(b,3),-1)} + ans={key:F(0) for key in ('I','U2','B','ABS_U')} + for lo_u,hi_u,sgn_b,sgn_u in ((F(-3,2),F(-1,2),-1,-1),(F(-1,2),F(0),1,-1),(F(0),F(1,2),1,1)): + low=scale(b,F(sgn_b,2));vint={} + for j,c in Q.items(): + difference=add(power(hi,j+1),scale(power(low,j+1),-1)) + vint=add(vint,scale(mul(c,difference),F(1,j+1))) + for key,weight in [('I',{0:F(1)}),('U2',{2:F(1)}),('B',b),('ABS_U',{1:F(sgn_u)})]: + ans[key]+=integral(mul(vint,weight),lo_u,hi_u) + return ans + + +def smul(a,b,n): + out=[F(0)]*(n+1) + for i,x in enumerate(a[:n+1]): + for j,y in enumerate(b[:n+1-i]):out[i+j]+=x*y + return out + + +def spow(a,m,n): + out=[F(1)]+[F(0)]*n + for _ in range(m):out=smul(out,a,n) + return out + + +def endpoints(u,A,g,n): + u,A,g=map(rational,(u,A,g)) + if type(n) is not int or not 0<=n<=12: raise ValueError('series order 0..12 required') + if g<=0 or g*g!=1+A*A: raise ValueError('positive exact gamma^2=1+A^2 required') + inv=[F(0)]*(n+1);root=[F(0)]*(n+1) + binom=F(1) + for j in range(n//2+1): + inv[2*j]=u**(2*j) + if j:binom*= (F(1,2)-(j-1))/j + root[2*j]=g*binom*(-u*u/(g*g))**j + d=smul(inv,root,n) + m=[F(0)]+[-u*A*x for x in inv[:n]] + plus=[x+y for x,y in zip(m,d)];minus=[x-y for x,y in zip(m,d)] + return plus,minus + + +def validate_phi(phi,n): + if not isinstance(phi,dict) or any(type(j) is not int or j<0 for j in phi): + raise ValueError('nonnegative polynomial orders required') + return {j:rational(x) for j,x in phi.items() if j<=n} + + +def tail_series(u,A,g,phi,n): + plus,minus=endpoints(u,A,g,n);phi=validate_phi(phi,n) + out=[F(0)]*(n+1) + for j,c in phi.items(): + p=spow(plus,11+j,n-j);m=spow(minus,11+j,n-j) + for i in range(n-j+1):out[i+j]+=c*(p[i]-m[i])/F(11+j) + return out + + +def half_series(u,A,g,phi,n,sign): + if type(sign) is not int or sign not in (-1,1): raise ValueError('sign must be +/-1') + plus,minus=endpoints(u,A,g,n);phi=validate_phi(phi,n) + endpoint=plus if sign==1 else [-x for x in minus] + out=[F(0)]*(n+1) + for j,c in phi.items(): + p=spow(endpoint,11+j,n-j) + for i in range(n-j+1):out[i+j]+=c*sign**j*p[i]/F(11+j) + return out + + +def density_series(coeffs):return [(11+j)*x for j,x in enumerate(coeffs)] + + +def predicted_second(u,A,g,phi0,phi2): + return u*u*g**9*(1+12*A*A)*phi0+F(2,13)*g**13*phi2 + + +def check(mutant=None): + vals=shape_integrals() + expected={'I':F(246528,35),'U2':F(240192,35),'B':F(-428544,7),'ABS_U':F(5898627,880)} + if mutant=='wrong-b-integral': vals['B']=-vals['B'] + if vals!=expected: raise ValueError('shape integral mismatch') + cases=0 + for u in (F(-5,4),F(-3,4),F(-1,4),F(1,4)): + for p in (F(-1,2),F(0),F(1,3)): + A=2*p/(1-p*p);g=(1+p*p)/(1-p*p) + phi={0:F(2),2:F(-3),3:F(5),4:F(7)} + got=tail_series(u,A,g,phi,6) + if got[0]!=2*g**11*phi[0]/11:raise ValueError('leading coefficient') + guess=predicted_second(u,A,g,phi[0],phi[2]) + if mutant=='omit-shift':guess-=10*u*u*A*A*g**9*phi[0] + if mutant=='omit-density-term':guess-=F(2,13)*g**13*phi[2] + if mutant=='drop-a-shear':guess=predicted_second(u,F(0),F(1),phi[0],phi[2]) + if got[2]!=guess:raise ValueError('second coefficient mismatch') + odd=[got[i] for i in (1,3,5)] + if mutant=='odd-term-survives':odd[0]=1 + if any(odd):raise ValueError('odd inverse powers do not cancel') + hplus=half_series(u,A,g,phi,6,1);hminus=half_series(u,A,g,phi,6,-1) + if [a+b for a,b in zip(hplus,hminus)]!=got:raise ValueError('half sum') + h1=-u*A*g**10*phi[0] + if mutant=='unsigned-is-signed':h1=F(0) + if hplus[1]!=h1:raise ValueError('signed first-order bias') + den=density_series(got) + expected_den=13*got[2] + if mutant=='wrong-density-factor':expected_den=11*got[2] + if den[2]!=expected_den:raise ValueError('radial density coefficient') + cases+=1 + crossing2=F(13,11) if mutant!='wrong-tv-root' else F(11,13) + if F(13,11)/crossing2!=1:raise ValueError('TV crossing root') + return {'passed':True,'mathematical_acceptance':False,'scientific_effect':'NONE', + 'scope':'finite rational coefficient and parity controls only', + 'shape_integrals':{k:str(v) for k,v in expected.items()}, + 'series_cases':cases,'tail_exponents':[11,13,15], + 'unsigned_radial_rate':2,'signed_joint_rate':1,'tv_crossing_squared':str(crossing2)} + + +def main(): + parser=argparse.ArgumentParser(description=__doc__);parser.add_argument('--mutant',choices=MUTANTS) + args=parser.parse_args() + try:result=check(args.mutant) + except ValueError as exc: + print(json.dumps({'passed':False,'error':str(exc)},sort_keys=True));raise SystemExit(1) + print(json.dumps(result,sort_keys=True,indent=2)) + +if __name__=='__main__':main() diff --git a/frontiers/radial_rate_20260930/test_rate.py b/frontiers/radial_rate_20260930/test_rate.py new file mode 100644 index 000000000..4074549e5 --- /dev/null +++ b/frontiers/radial_rate_20260930/test_rate.py @@ -0,0 +1,137 @@ +from fractions import Fraction as F +import unittest +import rate + +class InitialTests(unittest.TestCase): + def test_shape_mass(self): self.assertEqual(rate.shape_integrals()['I'],F(246528,35)) + def test_shape_u2(self): self.assertEqual(rate.shape_integrals()['U2'],F(240192,35)) + def test_shape_b(self): self.assertEqual(rate.shape_integrals()['B'],F(-428544,7)) + def test_shape_abs_u(self): self.assertEqual(rate.shape_integrals()['ABS_U'],F(5898627,880)) + def test_leading_boundary(self): + c=rate.tail_series(F(-3,4),F(3,4),F(5,4),{0:F(1)},4) + self.assertEqual(c[0],2*F(5,4)**11/11) + def test_second_boundary(self): + u,A,g=F(-3,4),F(3,4),F(5,4) + c=rate.tail_series(u,A,g,{0:F(1),2:F(2)},4) + self.assertEqual(c[2],u*u*g**9*(1+12*A*A)+F(4,13)*g**13) + def test_even_series(self): + c=rate.tail_series(F(-3,4),F(3,4),F(5,4),{0:F(1),2:F(2),3:F(7)},6) + self.assertEqual([c[i] for i in (1,3,5)],[0,0,0]) + def test_signed_first_coefficient(self): + u,A,g=F(-3,4),F(3,4),F(5,4) + c=rate.half_series(u,A,g,{0:F(1),2:F(2),3:F(7)},4,1) + self.assertEqual(c[1],-u*A*g**10) + + +class ExtendedTests(unittest.TestCase): + def test_endpoint_equation(self): + for u in (F(-5,4),F(-1,2),F(1,4)): + for p in (F(-1,2),F(0),F(1,3)): + A=2*p/(1-p*p);g=(1+p*p)/(1-p*p);n=8 + for B in rate.endpoints(u,A,g,n): + square=rate.smul(B,B,n) + for j in range(n+1): + value=square[j]-(u*u*square[j-2] if j>=2 else 0) + value+=2*u*A*B[j-1] if j>=1 else 0 + value-=g*g if j==0 else 0 + self.assertEqual(value,0) + def test_general_polynomial_parity(self): + phi={0:F(1),1:F(3),2:F(-5),3:F(7),4:F(2),5:F(-1)} + got=rate.tail_series(F(-4,3),F(3,4),F(5,4),phi,10) + self.assertTrue(all(got[j]==0 for j in (1,3,5,7,9))) + def test_half_reflection(self): + u,A,g=F(-3,4),F(3,4),F(5,4);phi={0:F(2),2:F(-3),3:F(5)} + plus=rate.half_series(u,A,g,phi,8,1);minus=rate.half_series(u,A,g,phi,8,-1) + self.assertEqual(minus,[x*(-1)**j for j,x in enumerate(plus)]) + def test_cubic_density_term_first_enters_at_four(self): + args=F(-3,4),F(3,4),F(5,4) + x=rate.tail_series(*args,{0:F(1)},6);y=rate.tail_series(*args,{0:F(1),3:F(5)},6) + self.assertEqual(x[:4],y[:4]);self.assertNotEqual(x[4],y[4]) + def test_shear_zero_removes_first_signed_bias(self): + got=rate.half_series(F(-3,4),F(0),F(1),{0:F(1),2:F(3),3:F(5)},6,1) + self.assertEqual(got[1],0);self.assertNotEqual(got[3],0) + def test_density_multiplier(self): + coeff=[F(2),0,F(3),0,F(5)] + self.assertEqual(rate.density_series(coeff),[F(22),0,F(39),0,F(75)]) + def test_b_integral_relation(self): + c=rate.shape_integrals();self.assertEqual(c['B'],3*c['I']-12*c['U2']) + def test_constant_density_decimal_remainder(self): + from decimal import Decimal,localcontext + with localcontext() as ctx: + ctx.prec=70;D=Decimal;u=D('-0.75');A=D('0.75');g=D('1.25') + c0=2*g**11/11;c2=u*u*g**9*(1+12*A*A) + vals=[] + for t in (D(40),D(80),D(160)): + delta=1/t;disc=(g*g-u*u*delta*delta).sqrt();den=1-u*u*delta*delta + bp=(-u*A*delta+disc)/den;bm=(-u*A*delta-disc)/den + J=(bp**11-bm**11)/11 + vals.append(abs((J-c0-c2*delta*delta)/delta**4)) + self.assertTrue(all(x0 for x in expected)) + def test_second_correction_positive_in_aligned_case(self): + vals=rate.shape_integrals() + for a in (F(0),F(1),F(-3)): + for k in (F(1,2),F(1),F(2)): + vbeta,vc=F(2),F(6);da=-(a*a/(12*vbeta)+a**4/(576*k*k*vc)) + self.assertGreater(vals['U2'],0) + self.assertGreaterEqual(vals['B']*da,0) + +if __name__=='__main__':unittest.main() diff --git a/frontiers/radial_rate_20260930/test_verify.py b/frontiers/radial_rate_20260930/test_verify.py new file mode 100644 index 000000000..258288f8e --- /dev/null +++ b/frontiers/radial_rate_20260930/test_verify.py @@ -0,0 +1,102 @@ +"""Custody regressions on real local Git objects, never on invented upstream data.""" +import copy +import hashlib +import json +import os +from pathlib import Path +import subprocess +import tempfile +import unittest +import verify as v + + +def entry(path,data,**kw): + return dict(path=path,bytes=len(data),sha256=hashlib.sha256(data).hexdigest(), + git_blob=hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest(),**kw) + +class SourceTests(unittest.TestCase): + def setUp(self): + t=tempfile.TemporaryDirectory();self.addCleanup(t.cleanup);self.repo=Path(t.name) + self.root=self.repo/'frontiers'/'packet';self.root.mkdir(parents=True) + self.git('init','-q');self.data=b'fixture\n' + for name in ('R','SC','P'):(self.repo/(name+'.md')).write_bytes(self.data) + self.git('add','R.md','SC.md','P.md');self.git('commit','-qm','fixture') + self.commit=self.git('rev-parse','HEAD').decode().strip() + self.es=[entry(x+'.md',self.data,id=x,commit=self.commit) for x in ('R','SC','P')];self.write() + def git(self,*args): + env=os.environ.copy();env.pop('GIT_NO_REPLACE_OBJECTS',None) + return subprocess.run(['git','-c','user.name=Fixture','-c','user.email=fixture@example.invalid',*args], + cwd=self.repo,env=env,check=True,capture_output=True,timeout=15).stdout + def write(self,es=None): + (self.root/'SOURCES.json').write_text(json.dumps({'sources':self.es if es is None else es})) + def test_valid_nested(self):self.assertEqual(v.sources(self.root),3) + def test_identity_fields(self): + for k,val in (('bytes',0),('bytes',True),('sha256','0'*64),('git_blob','0'*40)): + es=copy.deepcopy(self.es);es[0][k]=val;self.write(es) + with self.subTest(k=k,val=val),self.assertRaises(ValueError):v.sources(self.root) + def test_missing_and_duplicate_inventory(self): + for es in ([],self.es[:-1],self.es+[self.es[0]]): + self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_wrong_id(self): + es=copy.deepcopy(self.es);es[0]['id']='X';self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_unsafe_paths(self): + for p in ('../R.md','/R.md','./R.md','x//R.md','x/../R.md',''): + es=copy.deepcopy(self.es);es[0]['path']=p;self.write(es) + with self.subTest(path=p),self.assertRaises(ValueError):v.sources(self.root) + def test_missing_file(self): + es=copy.deepcopy(self.es);es[0]['path']='missing.md';self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_noncommit_tree(self): + es=copy.deepcopy(self.es);es[0]['commit']=self.git('rev-parse','HEAD^{tree}').decode().strip();self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_annotated_tag(self): + self.git('tag','-a','tag','-m','tag');es=copy.deepcopy(self.es) + es[0]['commit']=self.git('rev-parse','tag').decode().strip();self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_missing_commit(self): + es=copy.deepcopy(self.es);es[0]['commit']='0'*40;self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_leaf_symlink(self): + (self.repo/'R.md').unlink();(self.repo/'R.md').symlink_to('SC.md');self.git('add','R.md');self.git('commit','-qm','link') + es=copy.deepcopy(self.es);es[0]['commit']=self.git('rev-parse','HEAD').decode().strip();self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + def test_replacements_disabled(self): + changed=b'forged bytes\n';(self.repo/'R.md').write_bytes(changed);self.git('add','R.md');self.git('commit','-qm','changed') + newer=self.git('rev-parse','HEAD').decode().strip();self.git('replace',self.commit,newer) + self.assertEqual(self.git('show',self.commit+':R.md'),changed) + self.assertEqual(v.sources(self.root),3) + es=copy.deepcopy(self.es);es[0].update(entry('R.md',changed));self.write(es) + with self.assertRaises(ValueError):v.sources(self.root) + +class PacketTests(unittest.TestCase): + def setUp(self): + t=tempfile.TemporaryDirectory();self.addCleanup(t.cleanup);self.root=Path(t.name);self.data=b'payload\n' + (self.root/'proof.md').write_bytes(self.data) + self.entries=[entry('proof.md',self.data)];self.write() + def write(self): (self.root/'MANIFEST.json').write_text(json.dumps({'files':self.entries})) + def test_valid(self):self.assertEqual(v.inventory(self.root),1) + def test_changed(self): + (self.root/'proof.md').write_bytes(b'changed') + with self.assertRaises(ValueError):v.inventory(self.root) + def test_extra(self): + (self.root/'extra').write_bytes(b'x') + with self.assertRaises(ValueError):v.inventory(self.root) + def test_missing(self): + (self.root/'proof.md').unlink() + with self.assertRaises(ValueError):v.inventory(self.root) + def test_duplicate(self): + self.entries+=self.entries;self.write() + with self.assertRaises(ValueError):v.inventory(self.root) + def test_symlink_payload(self): + (self.root/'proof.md').unlink();(self.root/'proof.md').symlink_to('MANIFEST.json') + with self.assertRaises(ValueError):v.inventory(self.root) + def test_symlink_manifest(self): + p=self.root/'MANIFEST.json';p.rename(self.root/'real');p.symlink_to('real') + with self.assertRaises(ValueError):v.inventory(self.root) + def test_json_duplicate(self): + p=self.root/'MANIFEST.json';p.write_text('{"files":[],"files":[]}') + with self.assertRaises(ValueError):v.inventory(self.root) + +if __name__=='__main__':unittest.main() diff --git a/frontiers/radial_rate_20260930/verify.py b/frontiers/radial_rate_20260930/verify.py new file mode 100644 index 000000000..d5789cbe7 --- /dev/null +++ b/frontiers/radial_rate_20260930/verify.py @@ -0,0 +1,104 @@ +"""Exact packet replay; --local-only does not authenticate upstream Git sources.""" +import argparse +import hashlib +import json +import os +from pathlib import Path, PurePosixPath +import re +import subprocess +import sys + +IDS={'R','SC','P'} +MUTANTS=('omit-shift','omit-density-term','drop-a-shear','odd-term-survives', + 'unsigned-is-signed','wrong-b-integral','wrong-density-factor','wrong-tv-root') + + +def read_json(path): + if path.is_symlink() or not path.is_file():raise ValueError('regular JSON file required') + def unique(pairs): + ans={} + for k,v in pairs: + if k in ans:raise ValueError('duplicate JSON key') + ans[k]=v + return ans + ans=json.loads(path.read_text(encoding='utf-8'),object_pairs_hook=unique) + if not isinstance(ans,dict):raise ValueError('JSON object required') + return ans + + +def path_parts(path): + if not isinstance(path,str) or not path:raise ValueError('nonempty path required') + p=PurePosixPath(path) + if p.is_absolute() or str(p)!=path or any(x in ('.','..') or not re.fullmatch('[A-Za-z0-9_.-]+',x) for x in p.parts): + raise ValueError('unsafe path') + return p.parts + + +def identity(data,e): + blob=hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest() + if type(e['bytes']) is not int or len(data)!=e['bytes'] or hashlib.sha256(data).hexdigest()!=e['sha256'] or blob!=e['git_blob']: + raise ValueError('identity mismatch: '+e['path']) + + +def git(root,*args): + run=subprocess.run(['git','--no-replace-objects',*args],cwd=root, + env=dict(os.environ,GIT_NO_REPLACE_OBJECTS='1'),capture_output=True,timeout=45) + if run.returncode:raise ValueError('Git object read failed: '+run.stderr.decode(errors='replace')[:200]) + return run.stdout + + +def sources(root): + es=read_json(root/'SOURCES.json')['sources'] + if not isinstance(es,list) or len(es)!=len(IDS) or {e['id'] for e in es}!=IDS: + raise ValueError('missing, duplicate or unexpected source IDs') + seen=set() + for e in es: + parts=path_parts(e['path']);commit=e['commit'] + if not isinstance(commit,str) or not re.fullmatch('[0-9a-f]{40}',commit):raise ValueError('exact commit required') + pair=(commit,e['path']) + if pair in seen:raise ValueError('duplicate source binding') + seen.add(pair) + if git(root,'cat-file','-t',commit).strip()!=b'commit':raise ValueError('not a commit object') + for j in range(1,len(parts)+1): + prefix='/'.join(parts[:j]);records=git(root,'ls-tree','--full-tree','-z',commit,'--',prefix).split(b'\0') + records=[x for x in records if x] + if len(records)!=1:raise ValueError('missing or ambiguous source path') + meta,name=records[0].split(b'\t',1);mode,kind,blob=meta.decode().split() + if name.decode()!=prefix:raise ValueError('path mismatch') + if j