From 52537045322452a968f2ffe79e97654d6c76b972 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 17:58:07 +0200 Subject: [PATCH 01/20] Open M1-ND salvage phase-diagram firewall --- ...M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md | 468 ++++++++++++++++++ 1 file changed, 468 insertions(+) create mode 100644 audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md new file mode 100644 index 00000000..15872cb9 --- /dev/null +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md @@ -0,0 +1,468 @@ +# P11/R32 — SW1 M1-ND SALVAGE-A0 Phase-Diagram Firewall + +> **Stand:** 1. September 2026 +> **Branch:** `research/sw1-m1-nd-salvage-phase-diagram` +> **Status:** Arbeitsdefinition / AI-GREEN candidate scope only; keine Promotion. +> **Input:** `M1-ND-IMG4-SMALLR: ✓[M]_neg`, IMG3 linear visibility, +> A7/A8 FREE graphing, IMG4 Mass-Transport/Reducing mechanism. + +--- + +## 1. Zweck + +Nach der negativen Promotion des expliziten Small-`R`-Witness ist die +universelle SW1-Injektivitätsfrage beendet. Die neue Frage ist nicht + +\[ +\ker\mathscr N_R=\{0\}\quad\text{auf ganz SW1?} +\] + +sondern: + +> Wo liegt die tatsächliche geometrische Degenerationsregion, und wo beginnt +> überhaupt ein Parameterbereich, in dem Transversalität noch möglich ist? + +Dieses Dokument verhindert insbesondere den Fehlschluss + +\[ +\boxed{ +\text{volle geometrische Sichtbarkeit} +\not\Longrightarrow +\ker\mathscr N_R=\{0\}. +} +\tag{S0.1} +\] + +--- + +## 2. Parameterraum und Defekt + +Im unteren SW1-Chamber betrachten wir + +\[ +0<\varepsilon<\Delta/2, +\qquad +00\}. +\] + +IMG4 liefert dort durch denselben Reducing-/Blindset-Mechanismus einen +nichttrivialen zulässigen Kernel. + +--- + +## 3. Drei logisch verschiedene Regime + +### BLIND + +\[ +\boxed{\beta>0.} +\] + +Dann existiert ein positiver Annulus-Blindsetanteil. Unter den bereits +promotierten IMG4-Gates folgt ein nichttrivialer zulässiger Kernel. + +### VISIBLE + +\[ +\boxed{\beta=0.} +\] + +Dies bedeutet ausschließlich geometrische Supportdeckung. + +Es folgt **nicht** + +\[ +\ker\mathscr N_R=\{0\}. +\] + +Koeffizientencancellation, lineare Abhängigkeit und fehlende Transversalität +bleiben möglich. + +### TRANSVERSAL + +Erst eine quantitative Operatorabschätzung der Form + +\[ +\boxed{ +\|\mathscr N_R(f,g)\| +\ge +c(\varepsilon,R,\sigma) +\bigl(\|f\|+\|g\|\bigr), +\qquad c>0, +} +\tag{S0.3} +\] + +oder eine äquivalente exakte Injektivitäts-/Coercivity-Aussage würde den +nichtdegeneraten Bereich schließen. + +Damit gilt die zwingende Reihenfolge + +\[ +\boxed{ +\text{BLIND} +\to +\text{VISIBLE} +\to +\text{TRANSVERSAL}. +} +\tag{S0.4} +\] + +Keine Stufe darf übersprungen werden. + +--- + +## 4. Wände und Randstrata + +Explizit getrennt zu behandeln sind mindestens + +\[ +\sigma=R, +\qquad +R=\varepsilon, +\qquad +\varepsilon=\Delta/2. +\] + +Der aktuelle SALVAGE-Angriff benutzt zunächst nur das offene untere Gebiet. +Der Rand \(R=\varepsilon\) darf als **monotone Majoranten-Geometrie** +verwendet werden, aber nicht als admissibler SW1-Punkt. + +--- + +## 5. Warum \(M_N\le288N+144\) keine uniforme Blindheit beweist + +IMG3 liefert für endliche Neumann-Tiefe \(N\) + +\[ +M_N^{\rm lin} +\le +288N+144 +\] + +mögliche affine Annulus-Samplingmaps und damit + +\[ +|W^{\rm vis}_{N}| +\le +(288N+144)R. +\tag{S0.5} +\] + +Für fixes \(N\) und \(R\downarrow0\) ist das stark. + +Für adaptive Tiefe \(N=N(R)\) folgt aber nur die notwendige +Deckungsbedingung + +\[ +(288N+144)R\ge S-R. +\] + +Insbesondere ist + +\[ +N=\Omega(1/R) +\] + +notwendig, aber die Phasenzahl allein erzwingt **keinen** +\(R\)-unabhängigen Blindanteil. + +Tatsächlich: Sobald + +\[ +(288N+144)R\ge T, +\] + +ist die reine Zähl-/Längeninformation mit einer vollständigen Überdeckung +eines Annulusintervalls der Länge \(0. +} +\tag{S0.8} +\] + +Der direkte Saturationsscan des tatsächlichen A7-Graphings bei der +Majorantenwahl \(R=\varepsilon\) zeigt einen auffälligen exakten +Kandidaten: + +\[ +\boxed{ +\varepsilon_c +:= +\frac h2 += +\frac{T-10\Delta}{8} +\approx +0.22123729809\,\Delta. +} +\tag{S0.9} +\] + +Für + +\[ +0<\varepsilon<\varepsilon_c +\] + +erscheinen vierzehn gleich breite blinde Intervalle mit Breite + +\[ +g_\varepsilon += +h-2\varepsilon += +\frac{T-10\Delta-8\varepsilon}{4}. +\tag{S0.10} +\] + +Die beobachteten linken Grundpositionen sind + +\[ +\mathcal C= +\{ +0,\Delta,2\Delta,3\Delta, +d,d+\Delta,d+2\Delta, +a,a+\Delta,a+2\Delta,a+3\Delta, +b,b+\Delta,b+2\Delta +\}. +\tag{S0.11} +\] + +Der natürliche Kandidat ist daher + +\[ +B_\varepsilon^{\rm cand} += +\bigcup_{c\in\mathcal C} +(c+\varepsilon,\ c+h-\varepsilon). +\tag{S0.12} +\] + +Falls die FREE-Sättigungs-/Hub-Exklusion für S0.12 exakt bewiesen wird, folgt + +\[ +|B_\varepsilon^{\rm cand}| += +14(h-2\varepsilon) += +\boxed{ +\frac72 +(T-10\Delta-8\varepsilon) +} +>0, +\tag{S0.13} +\] + +**unabhängig von \(R\)**. + +Das wäre ein wesentlich stärkerer No-Go-Wedge als der bisherige +Small-\(R\)-Union-Bound. + +### Status dieser Beobachtung + +S0.8–S0.11 sind exakt identifizierte Konstanten-/Musterkandidaten. + +Die entscheidende Inklusion + +\[ +B_\varepsilon^{\rm cand} +\cap +W^{\rm vis}(V_\varepsilon^{\max}) += +\varnothing +\tag{S0.14} +\] + +ist **noch nicht bewiesen**. + +Daher keine Promotion und noch keine Buchung als negativer Satz. + +--- + +## 8. Nächste Gates + +### SALVAGE-A1 — exact maximal-saturation cells + +Für + +\[ +0<\varepsilon<\varepsilon_c +\] + +die Sättigung von \(U_\varepsilon^{\max}\) unter allen neun A7-Maps +symbolisch als endliche Intervallzellen klassifizieren. + +### SALVAGE-A2 — 14-gap exclusion + +Für jede der sechs Hub-Source-Maps beweisen, dass ihre Bilder der +SALVAGE-A1-Sättigung S0.12 nicht treffen. + +Erst dann darf gebucht werden: + +\[ +\beta(\varepsilon,R,\sigma) +\ge +\frac72(T-10\Delta-8\varepsilon) +\] + +für den gesamten entsprechenden Wedge. + +### SALVAGE-A3 — true coverage threshold + +Nur außerhalb dieses Wedges die tatsächliche Nullstelle + +\[ +\beta(\varepsilon,R,\sigma)=0 +\] + +kartieren. + +### SALVAGE-A4 — transversality + +Nur auf \(\beta=0\) eine Coercivity-/Injektivitätsanalyse starten. + +--- + +## 9. Firewall + +- Die alte Schwelle \(T/28080\) ist nur ein grober hinreichender + Blindheitsbound. +- \(M_N\le288N+144\) beweist keine uniforme Blindheit bei adaptivem \(N\). +- \(\beta=0\) beweist keine Injektivität. +- S0.9–S0.14 sind aktuell **Kandidaten**, keine Promotion. +- Keine separate Aussage über \(\ker\Gamma_I\), Objekt X oder RH. From f1721fa07a6ca1989212a4051ead1e26c1881e33 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 17:58:24 +0200 Subject: [PATCH 02/20] Certify salvage counting firewall --- ..._sw1_m1_nd_salvage_a0_counting_firewall.py | 56 +++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py diff --git a/scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py b/scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py new file mode 100644 index 00000000..bcde6c4e --- /dev/null +++ b/scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py @@ -0,0 +1,56 @@ +#!/usr/bin/env python3 +"""SW1 M1-ND SALVAGE-A0 counting firewall certificate. + +Purpose: +- certify the exact linear phase-count formula M_N=288N+144 already used by IMG3; +- certify that this count alone cannot imply an R-independent blind fraction + once N is allowed to depend on R. + +The script does NOT assert that the real phase locations cover the annulus. +It proves only that the cardinality/length estimate is compatible with full +coverage when N grows like 1/R, so actual phase geometry must be analyzed. +""" + +import sympy as sp + +print("SW1 M1-ND SALVAGE-A0 COUNTING FIREWALL") + +N=sp.symbols("N", integer=True, nonnegative=True) +M=72*(4*N+2) +assert sp.expand(M)==288*N+144 + +# Abstract positive constants. +T,R,sigma=sp.symbols("T R sigma", positive=True) + +# Restricted-tail condition sigma= T, then the raw count/length upper bound is already >= A. +# This makes the union bound non-informative: it cannot force beta>0. +margin=sp.expand(M*R-T) + +# Explicit adaptive choice R_N=T/M. Then M*R_N=T exactly. +RN=sp.simplify(T/M) +assert sp.simplify(M*RN-T)==0 + +# Choosing sigma_N=R_N/2 gives an annulus shorter than T. +sigmaN=RN/2 +AN=sp.simplify(T+sigmaN-RN) +assert sp.simplify(T-AN)==RN/2 +assert (sp.simplify(T-AN)).is_positive is True + +# For any fixed lower-chamber epsilon>0, RNT/epsilon. The exact integer ceiling is an elementary Archimedean step +# and is intentionally kept outside the finite CAS certificate. +eps=sp.symbols("eps", positive=True) + +print("M_N = 288*N + 144: PASS") +print("restricted tail sigma Date: Tue, 1 Sep 2026 17:58:59 +0200 Subject: [PATCH 03/20] Add salvage full-saturation phase diagram probe --- .../probe_sw1_m1_nd_salvage_phase_diagram.py | 199 ++++++++++++++++++ 1 file changed, 199 insertions(+) create mode 100644 scripts/probe_sw1_m1_nd_salvage_phase_diagram.py diff --git a/scripts/probe_sw1_m1_nd_salvage_phase_diagram.py b/scripts/probe_sw1_m1_nd_salvage_phase_diagram.py new file mode 100644 index 00000000..1086ea6f --- /dev/null +++ b/scripts/probe_sw1_m1_nd_salvage_phase_diagram.py @@ -0,0 +1,199 @@ +#!/usr/bin/env python3 +"""Exploratory full-FREE saturation probe for the M1-ND salvage phase diagram. + +This is deliberately NOT a certificate. It numerically saturates the maximal +KNF sampling set R=epsilon under all nine lower-chamber A7 maps, then computes +the exact physical six-branch Hub visibility on the positive annulus. + +The probe tests the candidate + h = (T-10 Delta)/4 = d-3 Delta, + epsilon_c = h/2, +and the 14 candidate blind gaps + (c+epsilon, c+h-epsilon) +for c in + 0,D,2D,3D, + d,d+D,d+2D, + a,a+D,a+2D,a+3D, + b,b+D,b+2D. + +Numerical agreement is discovery evidence only. SALVAGE-A1/A2 must replace +this probe by symbolic interval-cell and Hub-exclusion proofs before promotion. +""" + +from mpmath import mp + +mp.dps=80 + +L2=mp.log(2) +L3=mp.log(3) +a=L2/2 +b=L3/2 +T=L2 +d=b-a +Delta=L3-mp.mpf(3)/2*L2 +h=(T-10*Delta)/4 +epscrit=h/2 + +TOL=mp.mpf("1e-60") + +def merge(intervals): + xs=sorted((l,r) for l,r in intervals if r-l>TOL) + out=[] + for l,r in xs: + if not out or l>out[-1][1]+TOL: + out.append([l,r]) + elif r>out[-1][1]: + out[-1][1]=r + return [(l,r) for l,r in out] + +def inter(I,J): + l=max(I[0],J[0]) + r=min(I[1],J[1]) + return (l,r) if r-l>TOL else None + +def image(I,s,c): + l,r=I + return (l+c,r+c) if s==1 else (c-r,c-l) + +def saturation(eps,maxit=4000): + T0=T+eps + domains=[ + ( 1, a, [(0,a+eps)]), + ( 1,-a, [(a,T0)]), + ( 1, T, [(0,eps)]), + ( 1,-T, [(T,T0)]), + (-1, a, [(0,eps),(a-eps,a)]), + (-1, T, [(0,T)]), + (-1,3*a, [(a-eps,T0)]), + (-1,4*a, [(T-eps,T0)]), + (-1,2*b, [(2*d-eps,T0)]), + ] + V=merge([ + (a-eps,a+eps), + (b-eps,b+eps), + (T-eps,T+eps), + ]) + for it in range(1,maxit+1): + new=list(V) + for I in V: + for s,c,doms in domains: + for D in doms: + K=inter(I,D) + if K is None: + continue + J=inter(image(K,s,c),(mp.mpf("0"),T0)) + if J is not None: + new.append(J) + V2=merge(new) + if len(V2)==len(V) and all( + abs(x-u)TOL: + Q=inter((tau-K[1],tau-K[0]),ann) + if Q is not None: + images.append(Q) + if r>tau: + K=(max(l,tau),r) + if K[1]-K[0]>TOL: + Q=inter((K[0]-tau,K[1]-tau),ann) + if Q is not None: + images.append(Q) + # x+tau. + Q=inter((l+tau,r+tau),ann) + if Q is not None: + images.append(Q) + return merge(images),ann + +def blind_measure(W,ann): + cur=ann[0] + total=mp.mpf("0") + gaps=[] + for l,r in W: + if l>cur+TOL: + gaps.append((cur,l)) + total += l-cur + cur=max(cur,r) + if cur0 + cand=[(c+eps,c+h-eps) for c in C] + + # Candidate gaps must lie in (eps,T) and be pairwise separated. + for l,r in cand: + assert l>=eps-TOL and r<=T+TOL and r-l>0 + + # Numerical disjointness from actual visible union. + for B in cand: + for J in W: + assert inter(B,J) is None + + lower=14*g + assert beta+mp.mpf("1e-50") >= lower + + print( + "eps/Delta=",frac, + "iters=",it, + "Vcells=",len(V), + "Wcells=",len(W), + "beta=",mp.nstr(beta,18), + "14g=",mp.nstr(lower,18), + ) + +# Just above the candidate threshold the majorant scan reaches full support. +eps=mp.mpf("0.23")*Delta +assert eps>epscrit +V,it=saturation(eps) +W,ann=hub_visibility(V,eps) +beta,_=blind_measure(W,ann) +print("eps/Delta=0.23 exploratory beta =",mp.nstr(beta,18)) +assert abs(beta) < mp.mpf("1e-50") + +print("DISCOVERY: 14-gap candidate survives every tested epsilon Date: Tue, 1 Sep 2026 17:59:11 +0200 Subject: [PATCH 04/20] Run salvage phase-diagram firewall and probe --- .../sw1-m1-nd-salvage-phase-diagram.yml | 42 +++++++++++++++++++ 1 file changed, 42 insertions(+) create mode 100644 .github/workflows/sw1-m1-nd-salvage-phase-diagram.yml diff --git a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml new file mode 100644 index 00000000..9ebd4aaf --- /dev/null +++ b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml @@ -0,0 +1,42 @@ +name: SW1 M1-ND salvage phase diagram + +on: + push: + branches: + - research/sw1-m1-nd-salvage-phase-diagram + paths: + - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md' + - 'scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py' + - 'scripts/probe_sw1_m1_nd_salvage_phase_diagram.py' + - '.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml' + workflow_dispatch: + +jobs: + salvage: + runs-on: ubuntu-latest + steps: + - name: Checkout + uses: actions/checkout@v4 + + - name: Set up Python + uses: actions/setup-python@v5 + with: + python-version: '3.12' + + - name: Install SymPy + run: python -m pip install sympy==1.14.0 + + - name: Record provenance + run: | + python --version + python -c "import sympy; print('sympy='+sympy.__version__)" + git rev-parse HEAD + git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md + git hash-object scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py + git hash-object scripts/probe_sw1_m1_nd_salvage_phase_diagram.py + + - name: Run counting firewall certificate + run: python scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py + + - name: Run full-saturation phase diagram probe + run: python scripts/probe_sw1_m1_nd_salvage_phase_diagram.py From db1f0b58077be2d932b36c397f1f81b3699656fc Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:03:10 +0200 Subject: [PATCH 05/20] Certify uniform blind wedge geometry --- ...m1_nd_salvage_a1_a2_uniform_blind_wedge.py | 300 ++++++++++++++++++ 1 file changed, 300 insertions(+) create mode 100644 scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py diff --git a/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py b/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py new file mode 100644 index 00000000..b8142435 --- /dev/null +++ b/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py @@ -0,0 +1,300 @@ +#!/usr/bin/env python3 +"""Exact SALVAGE-A1/A2 certificate: an R-independent blind wedge. + +Claimed geometric scope: + 0 < epsilon < epsilon_c := (T-10*Delta)/8, + 0 < R < epsilon, + 0 < sigma < R. + +Define + h = (T-10*Delta)/4 = d-3*Delta > 0. + +Construct 24 open forbidden Horizon gaps F_epsilon. Their complement +K_epsilon contains the maximal KNF sampling set U_epsilon^max. +The script proves, uniformly for the whole open epsilon interval: + +1. the 24 gaps are positive, ordered, disjoint and lie in (0,T); +2. U_epsilon^max is disjoint from F_epsilon; +3. every one of the nine A7 graphing maps sends F_epsilon∩domain into + F_epsilon; since inverse generators are present, K_epsilon is invariant; +4. the six physical Hub source maps from K_epsilon avoid 14 explicit + positive-Annulus intervals B_epsilon; +5. the 14 intervals are disjoint, lie in (epsilon,T), and have total measure + 14(h-2 epsilon) + = 7/2 (T-10 Delta-8 epsilon) > 0. + +This script proves the new finite geometric premises. The functional-analytic +kernel conclusion uses the already promoted IMG4 reducing/Hub/KNF mechanism +and is recorded separately in the candidate audit. +""" + +import sympy as sp + +print("SW1 M1-ND SALVAGE-A1/A2 UNIFORM BLIND WEDGE CERTIFICATE") + +L2,L3=sp.log(2),sp.log(3) +a=L2/2 +b=L3/2 +T=L2 +d=b-a +Delta=sp.expand(L3-sp.Rational(3,2)*L2) +h=sp.expand((T-10*Delta)/4) +eps_c=sp.expand(h/2) +eps=sp.symbols("eps", real=True) +T0=T+eps + +# ---------- exact sign engine for affine-in-epsilon log forms ---------- + +def linlog_coeff(expr): + z=sp.expand(expr) + A=sp.simplify(z.coeff(L2)) + B=sp.simplify(z.coeff(L3)) + rest=sp.simplify(z-A*L2-B*L3) + assert rest==0,(expr,A,B,rest) + assert A.is_Rational and B.is_Rational,(expr,A,B) + return sp.Rational(A),sp.Rational(B) + +def sign_log(expr): + A,B=linlog_coeff(sp.expand(expr)) + if A==0 and B==0: + return 0 + if A>=0 and B>=0: + return 1 + if A<=0 and B<=0: + return -1 + den=sp.ilcm(int(A.q),int(B.q)) + ai=int(A*den) + bi=int(B*den) + if ai>0 and bi<0: + lhs=2**ai + rhs=3**(-bi) + return (lhs>rhs)-(lhs0: + lhs=3**bi + rhs=2**(-ai) + return (lhs>rhs)-(lhs0: + return 1 + if c<0: + return -1 + return 0 + if s1==0: + return s0 + assert s0==s1,("epsilon crossing inside salvage wedge",expr,s0,s1) + return s0 + +def cmpu(x,y): + return sign_uniform(sp.expand(x-y)) + +def maxu(x,y): + return x if cmpu(x,y)>=0 else y + +def minu(x,y): + return x if cmpu(x,y)<=0 else y + +def inter(I,J): + lo=maxu(I[0],J[0]) + hi=minu(I[1],J[1]) + s=cmpu(hi,lo) + return (sp.expand(lo),sp.expand(hi)) if s==1 else None + +def image(I,s,c): + lo,hi=I + if s==1: + return (sp.expand(lo+c),sp.expand(hi+c)) + assert s==-1 + return (sp.expand(c-hi),sp.expand(c-lo)) + +# ---------- structural constants ---------- + +assert sp.simplify(h-(d-3*Delta))==0 +assert sp.simplify(h-(a-(d+2*Delta)))==0 +assert sp.simplify(h-(b-(a+3*Delta)))==0 +assert sp.simplify(h-(T-(b+2*Delta)))==0 +assert sp.simplify(h-(sp.simplify((a-Delta)/2)-2*Delta))==0 + +# h>0 is exactly 8 log2 > 5 log3, i.e. 2^8 > 3^5. +assert 2**8 > 3**5 +assert sign_log(h)==1 +assert sign_log(eps_c)==1 +assert sign_uniform(eps)==1 +assert sign_uniform(eps_c-eps)==1 +assert sign_uniform(h-2*eps)==1 + +# ---------- 24 forbidden Horizon gaps ---------- + +F=[] +for shift in (sp.Integer(0),a): + for k in range(6): + base=sp.expand(shift+k*Delta) + for j in (0,1): + lo=sp.expand(base+j*h+eps) + hi=sp.expand(base+(j+1)*h-eps) + F.append((lo,hi,(shift,k,j))) + +# Sort by one exact interior representative; all pairwise ordering checks below +# prove that the ordering is uniform on the full open epsilon wedge. +rep=sp.expand(eps_c/2) +F.sort(key=lambda z: float(sp.N(z[0].subs(eps,rep),50))) +assert len(F)==24 + +for i,(lo,hi,tag) in enumerate(F): + assert sign_uniform(hi-lo)==1,("gap width",tag) + assert sign_uniform(lo)==1,("gap lower",tag) + assert sign_uniform(T-hi)==1,("gap upper",tag) + if i+10: + cur=hi + assert cmpu(cur,I[1])>=0 + return True + +mapped_F_pieces=0 +for name,(s,c,doms) in domains.items(): + for lo,hi,tag in F: + for D in doms: + K=inter((lo,hi),D) + if K is None: + continue + covered_by_F(image(K,s,c)) + mapped_F_pieces += 1 + +assert mapped_F_pieces==70 + +# Inverse-domain facts needed to pass from F-invariance to K=F^c invariance. +def eq_int(I,J): + return sp.simplify(I[0]-J[0])==0 and sp.simplify(I[1]-J[1])==0 + +def image_full(s,c,I): + return image(I,s,c) + +assert eq_int(image_full(1,a,domains["+a"][2][0]),domains["-a"][2][0]) +assert eq_int(image_full(1,-a,domains["-a"][2][0]),domains["+a"][2][0]) +assert eq_int(image_full(1,T,domains["+T"][2][0]),domains["-T"][2][0]) +assert eq_int(image_full(1,-T,domains["-T"][2][0]),domains["+T"][2][0]) +for name in ("r_T","r_3a","r_4a","r_2b"): + s,c,Ds=domains[name] + assert eq_int(image_full(s,c,Ds[0]),Ds[0]) +ra0,ra1=domains["r_a"][2] +assert eq_int(image_full(-1,a,ra0),ra1) +assert eq_int(image_full(-1,a,ra1),ra0) + +# ---------- complement K and 14 blind Annulus gaps ---------- + +K=[] +cur=sp.Integer(0) +for lo,hi,_ in F: + if sign_uniform(lo-cur)==1: + K.append((sp.expand(cur),sp.expand(lo))) + cur=hi +if sign_uniform(T0-cur)==1: + K.append((sp.expand(cur),sp.expand(T0))) +assert len(K)==25 + +C=[ + sp.Integer(0),Delta,2*Delta,3*Delta, + d,d+Delta,d+2*Delta, + a,a+Delta,a+2*Delta,a+3*Delta, + b,b+Delta,b+2*Delta, +] +assert len(C)==14 + +B=[(sp.expand(c+eps),sp.expand(c+h-eps)) for c in C] +for i,(lo,hi) in enumerate(B): + assert sign_uniform(hi-lo)==1 + assert cmpu(lo,eps)>=0 + assert cmpu(T,hi)>=0 + if i+1 0: PASS") +print("epsilon_c=(T-10 Delta)/8: PASS") +print("24 forbidden Horizon gaps: ordered/disjoint/uniform PASS") +print("maximal KNF sampling set U_epsilon^max avoids F_epsilon: PASS") +print("70 active forbidden-gap FREE images remain in F_epsilon: PASS") +print("all nine A7 inverse-domain/involution relations: PASS") +print("therefore K_epsilon=F_epsilon^c is graph-invariant: ANALYTIC CONSEQUENCE") +print("25 K_epsilon cells assembled: PASS") +print("14 candidate Annulus blind gaps: ordered/disjoint/in (epsilon,T): PASS") +print("153 Hub image pieces from K_epsilon avoid all 14 blind gaps: PASS") +print("blind measure = 14(h-2 epsilon) = 7/2(T-10Delta-8epsilon) > 0: PASS") +print("FIREWALL: kernel conclusion imports promoted IMG4 reducing/Hub/KNF mechanism") +print("SW1 M1-ND SALVAGE-A1/A2 UNIFORM BLIND WEDGE CERTIFICATE: PASS") From fbbe3024f9610264000f4a57fe395e00a69f34d6 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:03:53 +0200 Subject: [PATCH 06/20] Document uniform blind wedge candidate --- ...AGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md | 591 ++++++++++++++++++ 1 file changed, 591 insertions(+) create mode 100644 audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md new file mode 100644 index 00000000..66d1f00a --- /dev/null +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md @@ -0,0 +1,591 @@ +# P11/R32 — SW1 M1-ND SALVAGE-A1/A2 Uniform Blind Wedge Candidate + +> **Stand:** 1. September 2026 +> **Branch:** `research/sw1-m1-nd-salvage-phase-diagram` +> **Status:** AI-GREEN candidate + exact finite/algebraic certificate for the +> new geometry; **no promotion yet**. +> **Certificate:** `scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py`. + +--- + +## 1. Statement + +Set + +[ +h:=d-3Delta. +] + +Using the physical constants one has + +[ +oxed{ +h += + rac{T-10Delta}{4} += + rac{8log2-5log3}{2} +>0, +} + ag{A12.1} +] + +because + +[ +2^8=256>243=3^5. +] + +Define + +[ +oxed{ + arepsilon_c +:= + rac h2 += + rac{T-10Delta}{8}. +} + ag{A12.2} +] + +Candidate theorem: + +> For every +> [ +> 0< arepsilon< arepsilon_c, +> qquad +> 0 qquad +> 0 ] +> the current effective SW1 M1-ND operator satisfies +> [ +> oxed{ +> kermathscr N_R +e{0}. +> } +> ag{A12.3} +> ] + +This is strictly stronger than the previously promoted single Small-(R) +witness: (R) may now range over the **entire** admissible interval +((0, arepsilon)). + +--- + +## 2. The 24-gap Horizon barrier + +Let + +[ +X_ arepsilon=(0,T+ arepsilon). +] + +For + +[ +sin{0,a}, +qquad +k=0,ldots,5, +qquad +jin{0,1}, +] + +define + +[ +F_{s,k,j} += +left( +s+kDelta+jh+ arepsilon,, +s+kDelta+(j+1)h- arepsilon + ight). + ag{A12.4} +] + +Because + +[ +0< arepsilon0. +] + +Let + +[ +oxed{ +F_ arepsilon += +igcup_{s,k,j} +F_{s,k,j}. +} + ag{A12.5} +] + +There are exactly (24) such gaps. + +The exact identities + +[ +h=d-3Delta, +] + +[ +h=a-(d+2Delta), +] + +[ +h=b-(a+3Delta), +] + +[ +h=T-(b+2Delta) + ag{A12.6} +] + +show why the barrier fits the physical centers. + +The certificate proves uniformly on the entire open +( arepsilon)-interval that all 24 gaps are ordered, pairwise disjoint and +contained in ((0,T)). + +Set + +[ +K_ arepsilon +:= +X_ arepsilonsetminus F_ arepsilon +] + +up to the null boundary points. + +--- + +## 3. Maximal KNF sampling lies in (K_ arepsilon) + +Define the boundary-majorant sampling set + +[ +U_ arepsilon^{max} += +(a- arepsilon,a+ arepsilon) +cup +(b- arepsilon,b+ arepsilon) +cup +(T- arepsilon,T+ arepsilon). + ag{A12.7} +] + +For every actual + +[ +0T), + +[ +B_ arepsilon +subset +( arepsilon,T) +subset +(R,S). + ag{A12.18} +] + +Thus (B_ arepsilon) is a genuine positive Annulus blind set for **every** +admissible (R,sigma) in the wedge. + +--- + +## 6. Uniform blind measure + +Every blind interval has width + +[ +h-2 arepsilon. +] + +Hence + +[ +egin{aligned} +|B_ arepsilon| +&= +14(h-2 arepsilon)\ +&= +14left( + rac{T-10Delta}{4} +- +2 arepsilon + ight)\ +&= +oxed{ + rac72 +(T-10Delta-8 arepsilon) +}. +end{aligned} + ag{A12.19} +] + +For + +[ +0< arepsilon< arepsilon_c +] + +this is strictly positive. + +Crucially, + +[ +oxed{ +|B_ arepsilon| + ext{ has no }R ext{-decay.} +} + ag{A12.20} +] + +This answers the strongest question raised on the new SALVAGE front: +the current geometry has an (R)-independent blind defect on an open +lower-( arepsilon) wedge. + +--- + +## 7. Kernel construction + +Choose + +[ +0 +e w_+in L^2(B_ arepsilon). +] + +By IMG0 obtain the corresponding + +[ +0 +e ginmathscr B_W. +] + +Because the six Hub source maps from (V_{ arepsilon,R}) avoid +(B_ arepsilon), + +[ +Pi_{V_{ arepsilon,R}}mathcal H_Rg=0. + ag{A12.21} +] + +The promoted IMG4 reducing-subspace mechanism gives + +[ +Pi_{V_{ arepsilon,R}} +mathscr T_B^{-1} += +mathscr T_B^{-1} +Pi_{V_{ arepsilon,R}}. + ag{A12.22} +] + +Define + +[ +f += +-mathscr T_B^{-1}mathcal H_Rg. +] + +Then + +[ +Pi_{V_{ arepsilon,R}}f=0. +] + +Since + +[ +U_Rsubset V_{ arepsilon,R}, +] + +all six KNF samples vanish, hence + +[ +finmathscr B_K. +] + +Finally + +[ +mathscr N_R(f,g) += +mathscr T_Bf+mathcal H_Rg += +0. +] + +Since (g +e0), + +[ +oxed{ +kermathscr N_R +e{0}. +} + ag{A12.23} +] + +No Mass-Transport theorem and no finite-component bound enters this proof. + +--- + +## 8. Interpretation + +The earlier possibility that Small-(R) degeneracy might merely be a +thin boundary phenomenon is now strongly disfavored. + +If A12.23 survives final audit, the current finite-level geometry is +degenerate on the open wedge + +[ +oxed{ +0< arepsilon< + rac{T-10Delta}{8}, +qquad +0 arepsilon_c), but this is exploratory only. + +--- + +## 10. Promotion gate + +Before any (checkmark[M]_{ m neg}) booking for A12.24: + +1. run the exact certificate on the committed blob; +2. adversarially inspect the sign engine and the inference + (F)-invariant + inverse graphing (Rightarrow K)-invariant; +3. verify the 153-piece Hub exclusion is on the actual IMG4 physical + Hub-source list; +4. verify the imported IMG4 reducing/KNF mechanism is parameter-uniform in + the entire lower chamber, not only at the old explicit witness. + +Until these are checked, status remains candidate. From 2a4182b2a4b54fe60d540eba54d48606b130a7b9 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:04:08 +0200 Subject: [PATCH 07/20] Run exact salvage uniform blind wedge certificate --- .github/workflows/sw1-m1-nd-salvage-phase-diagram.yml | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml index 9ebd4aaf..e552db47 100644 --- a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml +++ b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml @@ -8,6 +8,8 @@ on: - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md' - 'scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py' - 'scripts/probe_sw1_m1_nd_salvage_phase_diagram.py' + - 'scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py' + - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md' - '.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml' workflow_dispatch: @@ -34,9 +36,14 @@ jobs: git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md git hash-object scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py git hash-object scripts/probe_sw1_m1_nd_salvage_phase_diagram.py + git hash-object scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py + git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md - name: Run counting firewall certificate run: python scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py - name: Run full-saturation phase diagram probe run: python scripts/probe_sw1_m1_nd_salvage_phase_diagram.py + + - name: Run exact uniform blind wedge certificate + run: python scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py From 75befbc322945c13110e7f02ff195467ffe44270 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:05:36 +0200 Subject: [PATCH 08/20] Add uniform blind wedge review packet --- ...2_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md | 263 ++++++++++++++++++ 1 file changed, 263 insertions(+) create mode 100644 audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md new file mode 100644 index 00000000..f22f5167 --- /dev/null +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md @@ -0,0 +1,263 @@ +# P11/R32 — SALVAGE-A1/A2 Uniform Blind Wedge Review Packet + +**Date:** 1 September 2026 +**Branch:** `research/sw1-m1-nd-salvage-phase-diagram` +**Current status:** AI-GREEN candidate + exact finite/algebraic certificate; no promotion. + +## Claim under review + +Let + +[ + arepsilon_c= rac{T-10Delta}{8}. +] + +For every + +[ +0< arepsilon< arepsilon_c, +qquad +00, +] + +and + +[ +0< arepsilon0. +] + +Confirm that no comparison marked uniform can cross zero inside the open +wedge. + +**Verdict:** GREEN / PARTIAL / FAIL + +--- + +## Gate B — graph-invariant Horizon complement + +The 24 forbidden gaps are + +[ +F_{s,k,j} += +(s+kDelta+jh+ arepsilon,, + s+kDelta+(j+1)h- arepsilon) +] + +for + +[ +sin{0,a},quad +k=0,ldots,5,quad +j=0,1. +] + +Check: + +1. all 24 gaps are ordered/disjoint and lie in ((0,T)); +2. the maximal sampling majorant + [ + U_ arepsilon^{max} + = + (a- arepsilon,a+ arepsilon) + cup + (b- arepsilon,b+ arepsilon) + cup + (T- arepsilon,T+ arepsilon) + ] + avoids them; +3. every active image of (F_ arepsilon) under all nine A7 maps lies back + in (F_ arepsilon); +4. the inverse-domain facts are sufficient to conclude that + (K_ arepsilon=F_ arepsilon^c) is invariant a.e.; +5. hence for every (R< arepsilon), + [ + V_{ arepsilon,R} + = + operatorname{Sat}_{mathcal E_ arepsilon}(U_R) + subset K_ arepsilon. + ] + +The certificate reports exactly 70 nonempty forbidden-gap/map-domain pieces. + +Relevant upstream: +- `audits/P11_R32_SW1_A7_FINITE_STATE_COCYCLE_CANDIDATE.md` +- `scripts/certify_sw1_m1_nd_img4_gateB_pmp_graphing.py` + +**Verdict:** GREEN / PARTIAL / FAIL + +--- + +## Gate C — 14-gap Hub exclusion + +The candidate positive Annulus blind set is + +[ +B_ arepsilon += +igcup_{cinmathcal C} +(c+ arepsilon,c+h- arepsilon) +] + +with + +[ +mathcal C= +{ +0,Delta,2Delta,3Delta, +d,d+Delta,d+2Delta, +a,a+Delta,a+2Delta,a+3Delta, +b,b+Delta,b+2Delta +}. +] + +Check: + +1. the 14 intervals are pairwise disjoint and contained in + (( arepsilon,T)); +2. the 24-gap complement has exactly 25 interval cells; +3. after splitting the three absolute-value maps at (a,b,T), every physical + Hub source piece + [ + |x-a|, x+a, |x-b|, x+b, |x-T|, x+T + ] + from every (K_ arepsilon)-cell avoids every interval of + (B_ arepsilon); +4. the reported 153 nonempty image pieces are exhaustive; +5. therefore + [ + H(V_{ arepsilon,R})cap B_ arepsilon= arnothing. + ] + +Check the exact measure identity + +[ +|B_ arepsilon| += +14(h-2 arepsilon) += + rac72(T-10Delta-8 arepsilon)>0. +] + +**Verdict:** GREEN / PARTIAL / FAIL + +--- + +## Gate D — parameter-uniform analytic kernel handoff + +This is the only non-finite gate. + +Check that the already audited/promoted IMG4 mechanism used here does not rely +on the old special value ( arepsilon=Delta/4) except in the discarded +Mass-Transport/780 estimate. + +Needed statements: + +1. for the lower chamber the actual FREE offdiagonal graph is contained in the + nine A7 maps; +2. for any measurable A7-saturated (V), + [ + Pi_Vmathscr T_B=mathscr T_BPi_V, + qquad + Pi_Vmathscr T_B^{-1}=mathscr T_B^{-1}Pi_V; + ] +3. the unitary Annulus transport gives + [ + mathcal H_R=V^*HW + ] + for all SW1 parameters; +4. if (ginmathscr B_W) is supported in (B_ arepsilon), then + [ + Pi_{V_{ arepsilon,R}}mathcal H_Rg=0; + ] +5. with + [ + f=-mathscr T_B^{-1}mathcal H_Rg, + ] + one gets (f=0) on (U_R), hence (finmathscr B_K); +6. therefore + [ + mathscr N_R(f,g)=0, + qquad + (f,g) +e0. + ] + +Important: no 780 component bound, no Mass Transport, and no finite-component +theorem is needed in this new proof. + +Relevant files: +- `audits/P11_R32_SW1_M1_ND_IMG4_ANALYTIC_GATES_CANDIDATE.md` +- `audits/P11_R32_SW1_M1_ND_IMAGE_SPACE_CANDIDATE.md` +- `audits/P11_R32_SW1_M1_ND_IMG4_SMALLR_NEG_PROMOTION.md` + +**Verdict:** GREEN / PARTIAL / FAIL + +--- + +## Promotion criterion + +Promote the wedge only if Gates A–D are all GREEN. + +If promoted, the exact scope would be + +[ +oxed{ +0< arepsilon< rac{T-10Delta}{8}, +quad +00. +} +] + +No claim that ( arepsilon_c) is the exact global phase transition. +No injectivity claim for ( arepsilonge arepsilon_c). +No Object-X or RH conclusion. From a1cd7befbee3f7d50a2800ae98a1e0d65452c2ac Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:06:12 +0200 Subject: [PATCH 09/20] Close salvage uniform-wedge analytic handoff candidate --- ...ALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md | 401 ++++++++++++++++++ 1 file changed, 401 insertions(+) create mode 100644 audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md new file mode 100644 index 00000000..f45679fc --- /dev/null +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md @@ -0,0 +1,401 @@ +# P11/R32 — SALVAGE-A1/A2 Analytic Handoff Candidate + +> **Stand:** 1. September 2026 +> **Status:** interner analytischer Handoff für Gate D; keine eigenständige Promotion. +> **Zweck:** zeigen, dass der neue uniform-blind-Wedge nur parameteruniforme +> IMG0/IMG3/IMG4-Bausteine benutzt und nicht den alten speziellen +> ( arepsilon_0=Delta/4)-Mass-Transport-Teil. + +--- + +## 1. Scope + +Fixiere + +[ +0< arepsilon< arepsilon_c +:= + rac{T-10Delta}{8}. +] + +Da + +[ + arepsilon_cT, +] + +gilt + +[ +B_ arepsilon +subset +( arepsilon,T) +subset +(R,S). + ag{HOF.9} +] + +Wähle + +[ +0 +e w_+in L^2(B_ arepsilon). +] + +IMG0 liefert einen eindeutigen + +[ +0 +e ginmathscr B_W. +] + +Aus HOF.7–HOF.9: + +[ +oxed{ +Pi_{ arepsilon,R}mathcal H_Rg=0. +} + ag{HOF.10} +] + +--- + +## 6. KNF-Handoff + +Setze + +[ +f += +-mathscr T_B^{-1}mathcal H_Rg. +] + +Mit HOF.6 und HOF.10: + +[ +Pi_{ arepsilon,R}f=0. +] + +Damit verschwindet die positive physische Horizonrekonstruktion von (f) +auf + +[ +V_{ arepsilon,R}, +] + +also insbesondere auf + +[ +U_R. +] + +IMG2/KNF charakterisiert den zulässigen Horizonraum durch die einzige Row + +[ +p[f(a-u)-f(a+u)] ++r[f(b-u)-f(b+u)] ++q[f(T-u)-f(T+u)] +=0 +] + +für fast jedes (0 Date: Tue, 1 Sep 2026 18:06:25 +0200 Subject: [PATCH 10/20] Track salvage uniform-wedge audit packet in CI provenance --- .github/workflows/sw1-m1-nd-salvage-phase-diagram.yml | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml index e552db47..84611594 100644 --- a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml +++ b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml @@ -10,6 +10,8 @@ on: - 'scripts/probe_sw1_m1_nd_salvage_phase_diagram.py' - 'scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md' + - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md' + - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md' - '.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml' workflow_dispatch: @@ -36,6 +38,8 @@ jobs: git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A0_PHASE_DIAGRAM_FIREWALL.md git hash-object scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py git hash-object scripts/probe_sw1_m1_nd_salvage_phase_diagram.py + git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md + git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md git hash-object scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md From 21aa4e185e2e2c36c771d4c7ce86dc0175e89d8c Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:25:16 +0200 Subject: [PATCH 11/20] Harden salvage wedge lower-chamber scope --- ..._sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py b/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py index b8142435..4c0805b2 100644 --- a/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py +++ b/scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py @@ -129,9 +129,21 @@ def image(I,s,c): assert 2**8 > 3**5 assert sign_log(h)==1 assert sign_log(eps_c)==1 + +# The entire new wedge must remain inside the lower A7 chamber. +# eps_c < Delta/2 is equivalent to 11*log(2) < 7*log(3), +# hence to the exact integer inequality 2^11 < 3^7. +assert 2**11 < 3**7 +assert sign_log(sp.expand(Delta/2-eps_c))==1 + assert sign_uniform(eps)==1 assert sign_uniform(eps_c-eps)==1 assert sign_uniform(h-2*eps)==1 +assert sign_uniform(Delta-2*eps)==1 + +# Maximal KNF centers remain inside the positive Horizon. +assert sign_uniform(a-eps)==1 +assert sign_uniform(b-eps)==1 # ---------- 24 forbidden Horizon gaps ---------- @@ -286,7 +298,7 @@ def avoids_B(I): assert sign_uniform(expected)==1 print("h=(T-10 Delta)/4=d-3 Delta > 0: PASS") -print("epsilon_c=(T-10 Delta)/8: PASS") +print("epsilon_c=(T-10 Delta)/8 and epsilon_c Date: Tue, 1 Sep 2026 18:26:15 +0200 Subject: [PATCH 12/20] Repair and harden uniform blind wedge candidate audit --- ...AGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md | 699 +++++++----------- 1 file changed, 270 insertions(+), 429 deletions(-) diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md index 66d1f00a..707a6a2a 100644 --- a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md @@ -1,559 +1,404 @@ # P11/R32 — SW1 M1-ND SALVAGE-A1/A2 Uniform Blind Wedge Candidate > **Stand:** 1. September 2026 -> **Branch:** `research/sw1-m1-nd-salvage-phase-diagram` -> **Status:** AI-GREEN candidate + exact finite/algebraic certificate for the -> new geometry; **no promotion yet**. -> **Certificate:** `scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py`. +> **Branch:** \`research/sw1-m1-nd-salvage-phase-diagram\` +> **Status:** AI-GREEN candidate + exact finite/algebraic certificate for the new geometry; **no promotion yet**. +> **Certificate:** \`scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py\`. --- -## 1. Statement +## 1. Statement and scope Set -[ -h:=d-3Delta. -] +\[ +h:=d-3\Delta. +\] -Using the physical constants one has +Using the physical constants, -[ -oxed{ -h -= - rac{T-10Delta}{4} -= - rac{8log2-5log3}{2} ->0, +\[ +\boxed{ +h=\frac{T-10\Delta}{4} +=\frac{8\log2-5\log3}{2}>0 } - ag{A12.1} -] +\tag{A12.1} +\] -because - -[ -2^8=256>243=3^5. -] +because \(2^8>3^5\). Define -[ -oxed{ - arepsilon_c -:= - rac h2 -= - rac{T-10Delta}{8}. +\[ +\boxed{ +\varepsilon_c:=\frac h2=\frac{T-10\Delta}{8}. } - ag{A12.2} -] +\tag{A12.2} +\] + +Moreover + +\[ +\boxed{ +\varepsilon_c<\frac{\Delta}{2} +} +\tag{A12.3} +\] + +because this is equivalent to \(11\log2<7\log3\), hence to +\(2^{11}<3^7\). Candidate theorem: > For every -> [ -> 0< arepsilon< arepsilon_c, -> qquad -> 0 qquad -> 0 ] -> the current effective SW1 M1-ND operator satisfies -> [ -> oxed{ -> kermathscr N_R -e{0}. -> } -> ag{A12.3} -> ] - -This is strictly stronger than the previously promoted single Small-(R) -witness: (R) may now range over the **entire** admissible interval -((0, arepsilon)). +> \[ +> 0<\varepsilon<\varepsilon_c,\qquad +> 0 0<\sigma \] +> the current effective SW1 operator satisfies +> \[ +> \boxed{\ker\mathscr N_R\ne\{0\}.} +> \tag{A12.4} +> \] + +Since \(\varepsilon<\Delta/2\) and \(R<\varepsilon\), one has +\(R+\varepsilon<2\varepsilon<\Delta\), so the whole wedge lies in the +lower SW1 chamber where A7 applies. --- ## 2. The 24-gap Horizon barrier -Let - -[ -X_ arepsilon=(0,T+ arepsilon). -] - For -[ -sin{0,a}, -qquad -k=0,ldots,5, -qquad -jin{0,1}, -] +\[ +s\in\{0,a\},\qquad k=0,\ldots,5,\qquad j\in\{0,1\}, +\] define -[ +\[ F_{s,k,j} = -left( -s+kDelta+jh+ arepsilon,, -s+kDelta+(j+1)h- arepsilon - ight). - ag{A12.4} -] - -Because +\left( +s+k\Delta+jh+\varepsilon,\, +s+k\Delta+(j+1)h-\varepsilon +\right). +\tag{A12.5} +\] -[ -0< arepsilon0. -] +\[ +h-2\varepsilon>0. +\] Let -[ -oxed{ -F_ arepsilon -= -igcup_{s,k,j} -F_{s,k,j}. +\[ +\boxed{ +F_\varepsilon=\bigcup_{s,k,j}F_{s,k,j}. } - ag{A12.5} -] - -There are exactly (24) such gaps. - -The exact identities +\tag{A12.6} +\] -[ -h=d-3Delta, -] +The exact certificate proves uniformly on the full open +\(0<\varepsilon<\varepsilon_c\) interval: -[ -h=a-(d+2Delta), -] - -[ -h=b-(a+3Delta), -] - -[ -h=T-(b+2Delta) - ag{A12.6} -] - -show why the barrier fits the physical centers. - -The certificate proves uniformly on the entire open -( arepsilon)-interval that all 24 gaps are ordered, pairwise disjoint and -contained in ((0,T)). +- all 24 gaps are nonempty; +- they are strictly ordered and pairwise disjoint; +- they lie in \((0,T)\). Set -[ -K_ arepsilon -:= -X_ arepsilonsetminus F_ arepsilon -] +\[ +K_\varepsilon:=(0,T+\varepsilon)\setminus F_\varepsilon +\] -up to the null boundary points. +up to the finite boundary set. --- -## 3. Maximal KNF sampling lies in (K_ arepsilon) +## 3. Maximal KNF sampling lies in \(K_\varepsilon\) Define the boundary-majorant sampling set -[ -U_ arepsilon^{max} +\[ +U_\varepsilon^{\max} = -(a- arepsilon,a+ arepsilon) -cup -(b- arepsilon,b+ arepsilon) -cup -(T- arepsilon,T+ arepsilon). - ag{A12.7} -] - -For every actual - -[ -0T), +Because \(R<\varepsilon\) and \(S=T+\sigma>T\), -[ -B_ arepsilon -subset -( arepsilon,T) -subset -(R,S). - ag{A12.18} -] +\[ +B_\varepsilon\subset(\varepsilon,T)\subset(R,S). +\tag{A12.19} +\] -Thus (B_ arepsilon) is a genuine positive Annulus blind set for **every** -admissible (R,sigma) in the wedge. +So \(B_\varepsilon\) is a genuine positive Annulus blind set for every +admissible \(R,\sigma\) in the wedge. --- ## 6. Uniform blind measure -Every blind interval has width - -[ -h-2 arepsilon. -] +Each blind interval has width \(h-2\varepsilon\), hence -Hence - -[ -egin{aligned} -|B_ arepsilon| -&= -14(h-2 arepsilon)\ +\[ +\begin{aligned} +|B_\varepsilon| +&=14(h-2\varepsilon)\\ &= -14left( - rac{T-10Delta}{4} -- -2 arepsilon - ight)\ -&= -oxed{ - rac72 -(T-10Delta-8 arepsilon) +\boxed{ +\frac72(T-10\Delta-8\varepsilon) }. -end{aligned} - ag{A12.19} -] - -For - -[ -0< arepsilon< arepsilon_c -] +\end{aligned} +\tag{A12.20} +\] -this is strictly positive. +For \(0<\varepsilon<\varepsilon_c\), this is strictly positive. Crucially, -[ -oxed{ -|B_ arepsilon| - ext{ has no }R ext{-decay.} +\[ +\boxed{ +|B_\varepsilon| +\text{ has no }R\text{-decay.} } - ag{A12.20} -] - -This answers the strongest question raised on the new SALVAGE front: -the current geometry has an (R)-independent blind defect on an open -lower-( arepsilon) wedge. +\tag{A12.21} +\] --- -## 7. Kernel construction +## 7. Kernel handoff Choose -[ -0 -e w_+in L^2(B_ arepsilon). -] - -By IMG0 obtain the corresponding - -[ -0 -e ginmathscr B_W. -] - -Because the six Hub source maps from (V_{ arepsilon,R}) avoid -(B_ arepsilon), +\[ +0\ne w_+\in L^2(B_\varepsilon) +\] -[ -Pi_{V_{ arepsilon,R}}mathcal H_Rg=0. - ag{A12.21} -] +and let \(0\ne g\in\mathscr B_W\) be its IMG0 basislift reconstruction. -The promoted IMG4 reducing-subspace mechanism gives +The parameter-uniform analytic handoff is recorded separately in -[ -Pi_{V_{ arepsilon,R}} -mathscr T_B^{-1} -= -mathscr T_B^{-1} -Pi_{V_{ arepsilon,R}}. - ag{A12.22} -] - -Define +\`audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md\`. -[ -f -= --mathscr T_B^{-1}mathcal H_Rg. -] +It gives -Then +\[ +\Pi_{V_{\varepsilon,R}}\mathcal H_Rg=0, +\] -[ -Pi_{V_{ arepsilon,R}}f=0. -] +and for -Since +\[ +f=-\mathscr T_B^{-1}\mathcal H_Rg +\] -[ -U_Rsubset V_{ arepsilon,R}, -] +one obtains -all six KNF samples vanish, hence +\[ +\Pi_{V_{\varepsilon,R}}f=0. +\] -[ -finmathscr B_K. -] +Since \(U_R\subset V_{\varepsilon,R}\), all six KNF sample values vanish, so -Finally +\[ +f\in\mathscr B_K. +\] -[ -mathscr N_R(f,g) -= -mathscr T_Bf+mathcal H_Rg -= -0. -] +Therefore -Since (g -e0), +\[ +\mathscr N_R(f,g)=0 +\] -[ -oxed{ -kermathscr N_R -e{0}. -} - ag{A12.23} -] - -No Mass-Transport theorem and no finite-component bound enters this proof. +with \(g\ne0\). Hence the candidate conclusion is A12.4. --- ## 8. Interpretation -The earlier possibility that Small-(R) degeneracy might merely be a -thin boundary phenomenon is now strongly disfavored. - -If A12.23 survives final audit, the current finite-level geometry is +If A12.4 survives adversarial review, the current finite-level geometry is degenerate on the open wedge -[ -oxed{ -0< arepsilon< - rac{T-10Delta}{8}, -qquad -0 arepsilon_c), but this is exploratory only. +The numerical phase-diagram probe is discovery evidence only. --- ## 10. Promotion gate -Before any (checkmark[M]_{ m neg}) booking for A12.24: +Before any \(\checkmark[M]_{\rm neg}\) booking for A12.22: -1. run the exact certificate on the committed blob; -2. adversarially inspect the sign engine and the inference - (F)-invariant + inverse graphing (Rightarrow K)-invariant; -3. verify the 153-piece Hub exclusion is on the actual IMG4 physical - Hub-source list; -4. verify the imported IMG4 reducing/KNF mechanism is parameter-uniform in - the entire lower chamber, not only at the old explicit witness. +1. verify the exact sign engine and \(\varepsilon_c<\Delta/2\); +2. verify that the 70 FREE pieces exhaust all A7 gap/domain intersections; +3. verify that forward+inverse \(F_\varepsilon\)-invariance implies + \(K_\varepsilon\)-invariance a.e.; +4. verify that the 153 Hub pieces exhaust the physical six-map list; +5. verify that the imported reducing/Hub/KNF handoff is parameter-uniform. -Until these are checked, status remains candidate. +Until then: **candidate only**. From dfa99b0eee948c0b59a6a82486e16b3af2b432a8 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:26:21 +0200 Subject: [PATCH 13/20] Repair uniform blind wedge review packet --- ...2_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md | 313 +++++++----------- 1 file changed, 115 insertions(+), 198 deletions(-) diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md index f22f5167..38b88f60 100644 --- a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md @@ -1,67 +1,61 @@ # P11/R32 — SALVAGE-A1/A2 Uniform Blind Wedge Review Packet **Date:** 1 September 2026 -**Branch:** `research/sw1-m1-nd-salvage-phase-diagram` -**Current status:** AI-GREEN candidate + exact finite/algebraic certificate; no promotion. +**Branch:** \`research/sw1-m1-nd-salvage-phase-diagram\` +**Status:** candidate only; no promotion. -## Claim under review +## Claim Let -[ - arepsilon_c= rac{T-10Delta}{8}. -] +\[ +\varepsilon_c=\frac{T-10\Delta}{8}. +\] -For every +Review whether -[ -0< arepsilon< arepsilon_c, -qquad -00, -] +\[ +h=\frac{T-10\Delta}{4}=d-3\Delta>0, +\qquad +\varepsilon_c=\frac h2, +\] and -[ -0< arepsilon0. -] +\[ +\boxed{\varepsilon_c<\Delta/2.} +\] + +The certificate reduces these signs to exact integer comparisons +\(2^m\) versus \(3^n\). -Confirm that no comparison marked uniform can cross zero inside the open -wedge. +For every affine-in-\(\varepsilon\) comparison, check that endpoint signs at +\(\varepsilon=0\) and \(\varepsilon=\varepsilon_c\) suffice to determine the +sign on the open interval and that endpoint zeros are handled correctly. **Verdict:** GREEN / PARTIAL / FAIL @@ -71,52 +65,29 @@ wedge. The 24 forbidden gaps are -[ +\[ F_{s,k,j} = -(s+kDelta+jh+ arepsilon,, - s+kDelta+(j+1)h- arepsilon) -] - -for +(s+k\Delta+jh+\varepsilon,\, +s+k\Delta+(j+1)h-\varepsilon) +\] -[ -sin{0,a},quad -k=0,ldots,5,quad -j=0,1. -] +for \(s\in\{0,a\}\), \(k=0,\ldots,5\), \(j=0,1\). Check: -1. all 24 gaps are ordered/disjoint and lie in ((0,T)); -2. the maximal sampling majorant - [ - U_ arepsilon^{max} - = - (a- arepsilon,a+ arepsilon) - cup - (b- arepsilon,b+ arepsilon) - cup - (T- arepsilon,T+ arepsilon) - ] - avoids them; -3. every active image of (F_ arepsilon) under all nine A7 maps lies back - in (F_ arepsilon); -4. the inverse-domain facts are sufficient to conclude that - (K_ arepsilon=F_ arepsilon^c) is invariant a.e.; -5. hence for every (R< arepsilon), - [ - V_{ arepsilon,R} - = - operatorname{Sat}_{mathcal E_ arepsilon}(U_R) - subset K_ arepsilon. - ] - -The certificate reports exactly 70 nonempty forbidden-gap/map-domain pieces. +1. all 24 gaps are nonempty, ordered, disjoint and lie in \((0,T)\); +2. \(U_\varepsilon^{\max}\) avoids them; +3. the loop over all 24 gaps and every A7 domain component is exhaustive; +4. each nonempty image is covered by \(F_\varepsilon\); +5. the reported count 70 is only a checksum, not the reason for exhaustivity; +6. the verified inverse graphing relations imply + \(K_\varepsilon=F_\varepsilon^c\) is invariant a.e.; +7. boundary points form only a finite null set. Relevant upstream: -- `audits/P11_R32_SW1_A7_FINITE_STATE_COCYCLE_CANDIDATE.md` -- `scripts/certify_sw1_m1_nd_img4_gateB_pmp_graphing.py` +- \`audits/P11_R32_SW1_A7_FINITE_STATE_COCYCLE_CANDIDATE.md\` +- \`scripts/certify_sw1_m1_nd_img4_gateB_pmp_graphing.py\` **Verdict:** GREEN / PARTIAL / FAIL @@ -124,106 +95,73 @@ Relevant upstream: ## Gate C — 14-gap Hub exclusion -The candidate positive Annulus blind set is +Check the 14 intervals -[ -B_ arepsilon -= -igcup_{cinmathcal C} -(c+ arepsilon,c+h- arepsilon) -] - -with - -[ -mathcal C= -{ -0,Delta,2Delta,3Delta, -d,d+Delta,d+2Delta, -a,a+Delta,a+2Delta,a+3Delta, -b,b+Delta,b+2Delta -}. -] +\[ +B_{\varepsilon,c}=(c+\varepsilon,c+h-\varepsilon) +\] -Check: +for -1. the 14 intervals are pairwise disjoint and contained in - (( arepsilon,T)); -2. the 24-gap complement has exactly 25 interval cells; -3. after splitting the three absolute-value maps at (a,b,T), every physical - Hub source piece - [ - |x-a|, x+a, |x-b|, x+b, |x-T|, x+T - ] - from every (K_ arepsilon)-cell avoids every interval of - (B_ arepsilon); -4. the reported 153 nonempty image pieces are exhaustive; -5. therefore - [ - H(V_{ arepsilon,R})cap B_ arepsilon= arnothing. - ] - -Check the exact measure identity - -[ -|B_ arepsilon| +\[ +\mathcal C= +\{ +0,\Delta,2\Delta,3\Delta, +d,d+\Delta,d+2\Delta, +a,a+\Delta,a+2\Delta,a+3\Delta, +b,b+\Delta,b+2\Delta +\}. +\] + +Verify: + +1. they are nonempty, ordered, disjoint and lie in \((\varepsilon,T)\); +2. the complement \(K_\varepsilon\) has exactly 25 cells; +3. for every cell and each \(\tau\in\{a,b,T\}\), the code includes: + - the left piece of \(|x-\tau|\), + - the right piece of \(|x-\tau|\), + - the full \(x+\tau\) piece; +4. these are exactly the six physical positive Hub source maps; +5. all 153 nonempty pieces avoid all 14 blind intervals; +6. 153 is again only a checksum after exhaustive looping. + +Verify also + +\[ +|B_\varepsilon| = -14(h-2 arepsilon) +14(h-2\varepsilon) = - rac72(T-10Delta-8 arepsilon)>0. -] +\frac72(T-10\Delta-8\varepsilon)>0. +\] **Verdict:** GREEN / PARTIAL / FAIL --- -## Gate D — parameter-uniform analytic kernel handoff - -This is the only non-finite gate. - -Check that the already audited/promoted IMG4 mechanism used here does not rely -on the old special value ( arepsilon=Delta/4) except in the discarded -Mass-Transport/780 estimate. - -Needed statements: - -1. for the lower chamber the actual FREE offdiagonal graph is contained in the - nine A7 maps; -2. for any measurable A7-saturated (V), - [ - Pi_Vmathscr T_B=mathscr T_BPi_V, - qquad - Pi_Vmathscr T_B^{-1}=mathscr T_B^{-1}Pi_V; - ] -3. the unitary Annulus transport gives - [ - mathcal H_R=V^*HW - ] - for all SW1 parameters; -4. if (ginmathscr B_W) is supported in (B_ arepsilon), then - [ - Pi_{V_{ arepsilon,R}}mathcal H_Rg=0; - ] -5. with - [ - f=-mathscr T_B^{-1}mathcal H_Rg, - ] - one gets (f=0) on (U_R), hence (finmathscr B_K); -6. therefore - [ - mathscr N_R(f,g)=0, - qquad - (f,g) -e0. - ] - -Important: no 780 component bound, no Mass Transport, and no finite-component -theorem is needed in this new proof. - -Relevant files: -- `audits/P11_R32_SW1_M1_ND_IMG4_ANALYTIC_GATES_CANDIDATE.md` -- `audits/P11_R32_SW1_M1_ND_IMAGE_SPACE_CANDIDATE.md` -- `audits/P11_R32_SW1_M1_ND_IMG4_SMALLR_NEG_PROMOTION.md` +## Gate D — parameter-uniform analytic handoff + +Use + +\`audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md\`. + +Check that the proof uses only parameter-uniform statements: + +\[ +\mathscr T_B=V^*(I+A)V,\qquad +\mathscr T_B\ge I, +\] + +the reducing projection for any A7-saturated measurable set, + +\[ +\mathcal H_R=V^*HW, +\] + +and the IMG2/KNF characterization of \(\mathscr B_K\). + +Confirm explicitly that no 780 bound, Mass Transport, \(\pm14\) separator +cover or special \(\varepsilon=\Delta/4\) value is imported. **Verdict:** GREEN / PARTIAL / FAIL @@ -231,33 +169,12 @@ Relevant files: ## Promotion criterion -Promote the wedge only if Gates A–D are all GREEN. - -If promoted, the exact scope would be - -[ -oxed{ -0< arepsilon< rac{T-10Delta}{8}, -quad -00. -} -] - -No claim that ( arepsilon_c) is the exact global phase transition. -No injectivity claim for ( arepsilonge arepsilon_c). +Only if A–D are GREEN may the wedge be considered for + +\[ +\checkmark[M]_{\rm neg}. +\] + +No claim that \(\varepsilon_c\) is the exact global phase transition. +No injectivity claim for \(\varepsilon\ge\varepsilon_c\). No Object-X or RH conclusion. From 812772383b2cfde698c01885325586175820de65 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:26:29 +0200 Subject: [PATCH 14/20] Repair and harden uniform wedge analytic handoff --- ...ALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md | 468 +++++++----------- 1 file changed, 182 insertions(+), 286 deletions(-) diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md index f45679fc..81b06b5c 100644 --- a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md @@ -1,401 +1,297 @@ # P11/R32 — SALVAGE-A1/A2 Analytic Handoff Candidate > **Stand:** 1. September 2026 -> **Status:** interner analytischer Handoff für Gate D; keine eigenständige Promotion. -> **Zweck:** zeigen, dass der neue uniform-blind-Wedge nur parameteruniforme -> IMG0/IMG3/IMG4-Bausteine benutzt und nicht den alten speziellen -> ( arepsilon_0=Delta/4)-Mass-Transport-Teil. +> **Status:** internal analytic handoff candidate; no independent promotion. +> **Purpose:** verify that the new uniform blind wedge uses only +> parameter-uniform IMG0/IMG2/IMG3/IMG4 identities and does not import the old +> \(\varepsilon_0=\Delta/4\) Mass-Transport argument. --- ## 1. Scope -Fixiere +Fix -[ -0< arepsilon< arepsilon_c +\[ +0<\varepsilon<\varepsilon_c := - rac{T-10Delta}{8}. -] +\frac{T-10\Delta}{8}. +\] -Da +The exact certificate proves -[ - arepsilon_cT, -] +## 5. Kernel handoff -gilt +Because -[ -B_ arepsilon -subset -( arepsilon,T) -subset -(R,S). - ag{HOF.9} -] +\[ +B_\varepsilon\subset(\varepsilon,T)\subset(R,S), +\qquad S=T+\sigma, +\] -Wähle +choose -[ -0 -e w_+in L^2(B_ arepsilon). -] +\[ +0\ne w_+\in L^2(B_\varepsilon). +\] -IMG0 liefert einen eindeutigen +IMG0 gives a unique nonzero \(g\in\mathscr B_W\) with that positive Annulus +reconstruction. By HOF.7–HOF.8 and the blind support, -[ -0 -e ginmathscr B_W. -] - -Aus HOF.7–HOF.9: - -[ -oxed{ -Pi_{ arepsilon,R}mathcal H_Rg=0. +\[ +\boxed{ +\Pi_{\varepsilon,R}\mathcal H_Rg=0. } - ag{HOF.10} -] +\tag{HOF.9} +\] ---- +Set -## 6. KNF-Handoff +\[ +f=-\mathscr T_B^{-1}\mathcal H_Rg. +\] -Setze - -[ -f -= --mathscr T_B^{-1}mathcal H_Rg. -] +Using HOF.6, -Mit HOF.6 und HOF.10: +\[ +\Pi_{\varepsilon,R}f=0. +\] -[ -Pi_{ arepsilon,R}f=0. -] +Thus the physical Horizon reconstruction of \(f\) vanishes on +\(V_{\varepsilon,R}\), hence on \(U_R\). -Damit verschwindet die positive physische Horizonrekonstruktion von (f) -auf +IMG2/KNF characterizes \(\mathscr B_K\) by -[ -V_{ arepsilon,R}, -] - -also insbesondere auf - -[ -U_R. -] - -IMG2/KNF charakterisiert den zulässigen Horizonraum durch die einzige Row - -[ +\[ p[f(a-u)-f(a+u)] +r[f(b-u)-f(b+u)] +q[f(T-u)-f(T+u)] =0 -] +\] -für fast jedes (0 Date: Tue, 1 Sep 2026 18:27:03 +0200 Subject: [PATCH 15/20] Add direct complement invariance cross-check --- ...nd_salvage_direct_complement_crosscheck.py | 176 ++++++++++++++++++ 1 file changed, 176 insertions(+) create mode 100644 scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py diff --git a/scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py b/scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py new file mode 100644 index 00000000..80ca06fa --- /dev/null +++ b/scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Direct-complement adversarial cross-check for SALVAGE-A1/A2. + +Unlike the primary certificate, this script does NOT infer K-invariance from +F-invariance plus inverse generators. It constructs the 25 complement cells +K_epsilon directly and checks every active K-cell/domain image under all nine +A7 maps is again covered by K_epsilon, uniformly for + 0 < epsilon < epsilon_c. + +It also independently re-enumerates the physical Hub pieces from K_epsilon +and checks direct avoidance of all 14 candidate blind intervals. + +This is a cross-check of Gates B/C only. No functional-analytic kernel claim. +""" + +import sympy as sp + +print("SW1 M1-ND SALVAGE DIRECT-COMPLEMENT CROSSCHECK") + +L2,L3=sp.log(2),sp.log(3) +a=L2/2 +b=L3/2 +T=L2 +d=b-a +Delta=sp.expand(L3-sp.Rational(3,2)*L2) +h=sp.expand((T-10*Delta)/4) +eps_c=sp.expand(h/2) +eps=sp.symbols("eps", real=True) +T0=T+eps + +def linlog_coeff(expr): + z=sp.expand(expr) + A=sp.simplify(z.coeff(L2)) + B=sp.simplify(z.coeff(L3)) + rest=sp.simplify(z-A*L2-B*L3) + assert rest==0,(expr,A,B,rest) + assert A.is_Rational and B.is_Rational + return sp.Rational(A),sp.Rational(B) + +def sign_log(expr): + A,B=linlog_coeff(expr) + if A==0 and B==0: return 0 + if A>=0 and B>=0: return 1 + if A<=0 and B<=0: return -1 + den=sp.ilcm(int(A.q),int(B.q)) + ai=int(A*den); bi=int(B*den) + if ai>0 and bi<0: + return (2**ai>3**(-bi))-(2**ai<3**(-bi)) + if ai<0 and bi>0: + return (3**bi>2**(-ai))-(3**bi<2**(-ai)) + raise AssertionError((expr,A,B)) + +def sign_uniform(expr): + z=sp.expand(expr) + ce=sp.simplify(z.coeff(eps)) + rest=sp.expand(z-ce*eps) + assert ce.is_Rational + s0=sign_log(rest) + s1=sign_log(sp.expand(rest+ce*eps_c)) + if s0==0: + return 1 if ce>0 else (-1 if ce<0 else 0) + if s1==0: + return s0 + assert s0==s1,("crossing",expr,s0,s1) + return s0 + +def cmpu(x,y): return sign_uniform(sp.expand(x-y)) +def maxu(x,y): return x if cmpu(x,y)>=0 else y +def minu(x,y): return x if cmpu(x,y)<=0 else y + +def inter(I,J): + lo=maxu(I[0],J[0]); hi=minu(I[1],J[1]) + return (sp.expand(lo),sp.expand(hi)) if cmpu(hi,lo)>0 else None + +def image(I,s,c): + lo,hi=I + return (sp.expand(lo+c),sp.expand(hi+c)) if s==1 else (sp.expand(c-hi),sp.expand(c-lo)) + +rep=sp.expand(eps_c/2) + +# Construct F only to determine the complement endpoints. +F=[] +for shift in (sp.Integer(0),a): + for k in range(6): + for j in (0,1): + base=sp.expand(shift+k*Delta+j*h) + F.append((sp.expand(base+eps),sp.expand(base+h-eps))) +F.sort(key=lambda z:float(sp.N(z[0].subs(eps,rep),50))) + +K=[] +cur=sp.Integer(0) +for lo,hi in F: + if cmpu(lo,cur)>0: + K.append((sp.expand(cur),sp.expand(lo))) + cur=hi +if cmpu(T0,cur)>0: + K.append((sp.expand(cur),sp.expand(T0))) +assert len(K)==25 + +def covered_by_K(I): + pieces=[J for G in K if (J:=inter(I,G)) is not None] + assert pieces,("no K cover",I) + pieces.sort(key=lambda z:float(sp.N(z[0].subs(eps,rep),50))) + assert cmpu(pieces[0][0],I[0])<=0 + cur=pieces[0][1] + for lo,hi in pieces[1:]: + assert cmpu(lo,cur)<=0,("K cover gap",I,cur,(lo,hi)) + if cmpu(hi,cur)>0: cur=hi + assert cmpu(cur,I[1])>=0 + +domains={ + "+a": ( 1, a, [(sp.Integer(0),a+eps)]), + "-a": ( 1,-a, [(a,T0)]), + "+T": ( 1, T, [(sp.Integer(0),eps)]), + "-T": ( 1,-T, [(T,T0)]), + "r_a":(-1, a, [(sp.Integer(0),eps),(a-eps,a)]), + "r_T":(-1, T, [(sp.Integer(0),T)]), + "r_3a":(-1,3*a,[(a-eps,T0)]), + "r_4a":(-1,4*a,[(T-eps,T0)]), + "r_2b":(-1,2*b,[(2*d-eps,T0)]), +} + +counts={} +total=0 +for name,(s,c,Ds) in domains.items(): + n=0 + for I in K: + for D in Ds: + J=inter(I,D) + if J is None: continue + covered_by_K(image(J,s,c)) + n+=1; total+=1 + counts[name]=n + +# The count is a checksum after exhaustive loops, not an assumption. +assert set(counts)==set(domains) + +C=[ + sp.Integer(0),Delta,2*Delta,3*Delta, + d,d+Delta,d+2*Delta, + a,a+Delta,a+2*Delta,a+3*Delta, + b,b+Delta,b+2*Delta, +] +B=[(sp.expand(c+eps),sp.expand(c+h-eps)) for c in C] + +def avoids_B(I): + assert all(inter(I,J) is None for J in B) + +hub_counts={} +hub_total=0 +for tau_name,tau in (("a",a),("b",b),("T",T)): + n=0 + for I in K: + left=inter(I,(sp.Integer(0),tau)) + if left is not None: + avoids_B((sp.expand(tau-left[1]),sp.expand(tau-left[0]))) + n+=1; hub_total+=1 + right=inter(I,(tau,T0)) + if right is not None: + avoids_B((sp.expand(right[0]-tau),sp.expand(right[1]-tau))) + n+=1; hub_total+=1 + avoids_B((sp.expand(I[0]+tau),sp.expand(I[1]+tau))) + n+=1; hub_total+=1 + hub_counts[tau_name]=n + +assert hub_total==153 + +print("25 complement cells reconstructed: PASS") +print("direct K-invariance under all nine A7 maps: PASS") +print("active K/domain image counts:",counts) +print("total active K/domain pieces:",total) +print("Hub piece counts by center:",hub_counts) +print("Hub total pieces:",hub_total) +print("all Hub pieces avoid all 14 blind intervals: PASS") +print("FIREWALL: Gate B/C direct cross-check only; no kernel promotion") +print("SW1 M1-ND SALVAGE DIRECT-COMPLEMENT CROSSCHECK: PASS") From 08f5285b727f8a4c1a097151b042fba8878e0c44 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:27:16 +0200 Subject: [PATCH 16/20] Run direct complement salvage cross-check --- .github/workflows/sw1-m1-nd-salvage-phase-diagram.yml | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml index 84611594..4831845a 100644 --- a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml +++ b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml @@ -9,6 +9,7 @@ on: - 'scripts/certify_sw1_m1_nd_salvage_a0_counting_firewall.py' - 'scripts/probe_sw1_m1_nd_salvage_phase_diagram.py' - 'scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py' + - 'scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md' @@ -41,6 +42,7 @@ jobs: git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md git hash-object scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py + git hash-object scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md - name: Run counting firewall certificate @@ -51,3 +53,6 @@ jobs: - name: Run exact uniform blind wedge certificate run: python scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py + + - name: Run direct complement invariance cross-check + run: python scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py From b91558e83bf13a3dc792aab6c6c852bf44d5cec0 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:29:28 +0200 Subject: [PATCH 17/20] Add epsilon-uniform raw-word graph cross-check --- ...w1_m1_nd_salvage_uniform_raw_word_graph.py | 237 ++++++++++++++++++ 1 file changed, 237 insertions(+) create mode 100644 scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py diff --git a/scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py b/scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py new file mode 100644 index 00000000..5056bab0 --- /dev/null +++ b/scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py @@ -0,0 +1,237 @@ +#!/usr/bin/env python3 +"""Uniform raw-word cross-check for the SALVAGE lower-epsilon wedge. + +This closes the upstream question left by the older A1 representative-point +certificate. It works symbolically for the full open interval + + 0 < epsilon < epsilon_c = (T-10*Delta)/8 + +and derives the A7 graph directly from the eleven raw four-echo A1 words. + +Certified: +1. all positive internal gate/source-horizon walls are exactly + epsilon, a-epsilon, a+epsilon, 2d-epsilon, T-epsilon; +2. all positive internal source-folding zeros are exactly a,T; +3. therefore the eight open lower-chamber row cells are exhaustive; +4. direct raw-word evaluation on those cells produces exactly the nine A7 + nonidentity maps, no tenth map; +5. the mapwise unions equal A7.1--A7.9 uniformly in epsilon. + +No reducing-subspace or kernel claim. +""" + +import sympy as sp +import certify_sw1_a1_raw_archetypes as a1 + +print("SW1 M1-ND SALVAGE UNIFORM RAW-WORD GRAPH CROSSCHECK") + +X=a1.X +L2,L3=sp.log(2),sp.log(3) +a,b,T,d,Delta=a1.a,a1.b,a1.T,a1.d,a1.Delta +eps=sp.symbols("eps", real=True) +eps_c=sp.expand((T-10*Delta)/8) +T0=T+eps + +# ---------- exact signs on 0=0 and B>=0: return 1 + if A<=0 and B<=0: return -1 + den=sp.ilcm(int(A.q),int(B.q)) + ai=int(A*den); bi=int(B*den) + if ai>0 and bi<0: + return (2**ai>3**(-bi))-(2**ai<3**(-bi)) + if ai<0 and bi>0: + return (3**bi>2**(-ai))-(3**bi<2**(-ai)) + raise AssertionError((expr,A,B)) + +def sign_uniform(expr): + z=sp.expand(expr) + ce=sp.simplify(z.coeff(eps)) + rest=sp.expand(z-ce*eps) + assert ce.is_Rational,(expr,ce) + s0=sign_log(rest) + s1=sign_log(sp.expand(rest+ce*eps_c)) + if s0==0: + return 1 if ce>0 else (-1 if ce<0 else 0) + if s1==0: + return s0 + assert s0==s1,("epsilon crossing",expr,s0,s1) + return s0 + +assert sign_log(sp.expand(Delta/2-eps_c))>0 +assert sign_uniform(eps)>0 +assert sign_uniform(eps_c-eps)>0 + +# ---------- exhaustive wall reconstruction ---------- + +walls=set() +foldzeros=set() + +for delta,eta,lam in a1.WORDS: + # Horizon gate equations |x +/- delta| = T0-lambda. + B=sp.expand(T0-lam) + for shift in (-delta,delta): + for s in (-1,1): + x=sp.expand(s*B-shift) + if sign_uniform(x)>0 and sign_uniform(T0-x)>0: + walls.add(sp.simplify(x)) + + # Source horizon equations |x+shift|=T0 and folding zeros x+shift=0. + shifts=(-delta-eta,-delta+eta,delta-eta,delta+eta) + for shift in shifts: + for s in (-1,1): + x=sp.expand(s*T0-shift) + if sign_uniform(x)>0 and sign_uniform(T0-x)>0: + walls.add(sp.simplify(x)) + x0=sp.expand(-shift) + if sign_uniform(x0)>0 and sign_uniform(T0-x0)>0: + foldzeros.add(sp.simplify(x0)) + +expected_walls={ + sp.simplify(eps), + sp.simplify(a-eps), + sp.simplify(a+eps), + sp.simplify(2*d-eps), + sp.simplify(T-eps), +} +assert walls==expected_walls,(walls,expected_walls) +assert foldzeros=={sp.simplify(a),sp.simplify(T)},foldzeros + +# ---------- direct raw-word evaluation on exhaustive open cells ---------- + +def inside_abs_uniform(q,bound): + return sign_uniform(sp.expand(bound-q))>=0 and sign_uniform(sp.expand(bound+q))>=0 + +def folded(src_sym,src_mid): + s=sign_uniform(src_mid) + assert s!=0,("fold zero at row midpoint",src_mid) + return sp.expand(src_sym if s>0 else -src_sym) + +def aggregate_direct(mid): + out={} + for j,(delta,eta,lam) in enumerate(a1.WORDS): + shifts=(-delta-eta,-delta+eta,delta-eta,delta+eta) + gates=(X-delta,X-delta,X+delta,X+delta) + for k,(gexpr,sh) in enumerate(zip(gates,shifts)): + gmid=sp.expand(gexpr.subs(X,mid)) + if not inside_abs_uniform(gmid,T0-lam): + continue + src=X+sh + smid=sp.expand(src.subs(X,mid)) + if not inside_abs_uniform(smid,T0): + continue + prof=folded(src,smid) + out[prof]=sp.simplify(out.get(prof,0)+a1.SIGNS[k]*a1.weights[j]) + return {sp.expand(k):sp.simplify(v) for k,v in out.items() if sp.simplify(v)!=0} + +regions=[ + ("R0",sp.Integer(0),eps), + ("R1",eps,a-eps), + ("R2",a-eps,a), + ("R3",a,a+eps), + ("R4I",a+eps,2*d-eps), + ("R5",2*d-eps,T-eps), + ("R6",T-eps,T), + ("R7",T,T+eps), +] +for row,lo,hi in regions: + assert sign_uniform(hi-lo)>0,(row,lo,hi) + +map_exprs={ + "+a":X+a, + "-a":X-a, + "+T":X+T, + "-T":X-T, + "r_a":a-X, + "r_T":T-X, + "r_3a":3*a-X, + "r_4a":4*a-X, + "r_2b":2*b-X, +} + +def classify(expr): + if sp.simplify(expr-X)==0: + return "I" + for name,ref in map_exprs.items(): + if sp.simplify(expr-ref)==0: + return name + raise AssertionError(("unexpected map",expr)) + +by_map={} +row_maps={} +for row,lo,hi in regions: + mid=sp.expand((lo+hi)/2) + got=aggregate_direct(mid) + names=[] + for expr,coeff in got.items(): + name=classify(expr) + if name=="I": + continue + names.append(name) + by_map.setdefault(name,[]).append((lo,hi)) + row_maps[row]=names + +assert set(by_map)==set(map_exprs),(set(by_map),set(map_exprs)) +assert set(row_maps["R6"])=={"r_T","r_3a","r_4a","-a","r_2b"} +assert set(row_maps["R7"])=={"-T","r_3a","r_4a","-a","r_2b"} + +# ---------- symbolic interval-union reconstruction ---------- + +rep=sp.expand(eps_c/2) + +def merge(intervals): + xs=sorted(intervals,key=lambda I:float(sp.N(I[0].subs(eps,rep),50))) + out=[] + for lo,hi in xs: + if not out: + out.append([lo,hi]); continue + gap=sign_uniform(sp.expand(lo-out[-1][1])) + if gap<=0: + if sign_uniform(sp.expand(hi-out[-1][1]))>0: + out[-1][1]=hi + else: + out.append([lo,hi]) + return [(sp.expand(lo),sp.expand(hi)) for lo,hi in out] + +got_domains={name:merge(iv) for name,iv in by_map.items()} +expected={ + "+a":[(sp.Integer(0),a+eps)], + "-a":[(a,T0)], + "+T":[(sp.Integer(0),eps)], + "-T":[(T,T0)], + "r_a":[(sp.Integer(0),eps),(a-eps,a)], + "r_T":[(sp.Integer(0),T)], + "r_3a":[(a-eps,T0)], + "r_4a":[(T-eps,T0)], + "r_2b":[(2*d-eps,T0)], +} + +assert set(got_domains)==set(expected) +for name in expected: + assert len(got_domains[name])==len(expected[name]),(name,got_domains[name],expected[name]) + for (glo,ghi),(elo,ehi) in zip(got_domains[name],expected[name]): + assert sp.simplify(glo-elo)==0,(name,"lo",glo,elo) + assert sp.simplify(ghi-ehi)==0,(name,"hi",ghi,ehi) + +print("eleven raw A1 words evaluated symbolically: PASS") +print("all positive internal horizon walls =",sorted(map(str,walls))) +print("all positive source-folding zeros =",sorted(map(str,foldzeros))) +print("eight lower-wedge row cells exhaustive: PASS") +print("derived nonidentity alphabet =",sorted(by_map)) +print("no tenth nonidentity map: PASS") +print("derived domains == A7.1--A7.9 uniformly in epsilon: PASS") +print("R6/R7 five-arm support uniform in epsilon: PASS") +print("FIREWALL: raw graph support only; no reducing/kernel verdict") +print("SW1 M1-ND SALVAGE UNIFORM RAW-WORD GRAPH CROSSCHECK: PASS") From 07074ad41c2d4d844f85a5fecf74d8c51ddc5904 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:29:39 +0200 Subject: [PATCH 18/20] Run epsilon-uniform raw-word graph cross-check --- .github/workflows/sw1-m1-nd-salvage-phase-diagram.yml | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml index 4831845a..3af6b287 100644 --- a/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml +++ b/.github/workflows/sw1-m1-nd-salvage-phase-diagram.yml @@ -10,6 +10,7 @@ on: - 'scripts/probe_sw1_m1_nd_salvage_phase_diagram.py' - 'scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py' - 'scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py' + - 'scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md' - 'audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md' @@ -43,6 +44,7 @@ jobs: git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md git hash-object scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.py git hash-object scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py + git hash-object scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py git hash-object audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_UNIFORM_BLIND_WEDGE_CANDIDATE.md - name: Run counting firewall certificate @@ -56,3 +58,6 @@ jobs: - name: Run direct complement invariance cross-check run: python scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.py + + - name: Run epsilon-uniform raw-word graph cross-check + run: python scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.py From 9e9451e619d7c437c14d80aee0bb6918eef4296d Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:31:52 +0200 Subject: [PATCH 19/20] Make salvage saturation measurability and null boundaries explicit --- ...ALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md | 20 ++++++++++++++++--- 1 file changed, 17 insertions(+), 3 deletions(-) diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md index 81b06b5c..97bde342 100644 --- a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.md @@ -61,19 +61,33 @@ For every \(R<\varepsilon\), U_R\subset U_\varepsilon^{\max}\subset K_\varepsilon. \] -Therefore +Therefore, up to the finite gap/domain boundary set, \[ \boxed{ V_{\varepsilon,R} := \operatorname{Sat}_{\mathcal E_\varepsilon}(U_R) -\subset K_\varepsilon. +\subset K_\varepsilon +\quad\text{a.e.} } \tag{HOF.2} \] -No component bound is used. +This saturation is measurable: the A7 relation is generated by finitely many +partial Borel isometries, hence +\[ +V_{\varepsilon,R} += +\bigcup_{w} +w\bigl(U_R\cap\operatorname{dom}w\bigr) +\] +over the countable set of finite graphing words. The finite endpoint set and +its word-saturation are null because every word is measure preserving on its +domain. Thus the boundary convention does not affect the \(L^2\) projection +or the reducing identity. + +No component bound and no Mass-Transport estimate is used. --- From 2ed1583f074574c2fdb5a48203d63d520a86b5f6 Mon Sep 17 00:00:00 2001 From: Waschtl904 Date: Tue, 1 Sep 2026 18:31:57 +0200 Subject: [PATCH 20/20] Add saturation measurability to salvage review gate --- audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md index 38b88f60..ed23eedf 100644 --- a/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md +++ b/audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_REVIEW_PACKET.md @@ -83,7 +83,9 @@ Check: 5. the reported count 70 is only a checksum, not the reason for exhaustivity; 6. the verified inverse graphing relations imply \(K_\varepsilon=F_\varepsilon^c\) is invariant a.e.; -7. boundary points form only a finite null set. +7. boundary points form only a finite null set; +8. the saturation is measurable as a countable union of partial-Borel word + images, and the word-saturation of the boundary null set remains null. Relevant upstream: - \`audits/P11_R32_SW1_A7_FINITE_STATE_COCYCLE_CANDIDATE.md\`