M1-ND salvage phase diagram and uniform blind wedge candidate - #49
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Leitfaden für ReviewerDieser PR ersetzt die frühere Heuristik zur Sichtbarkeitszählung durch einen exakten A7/A8-Intervallgeometrie-Kandidaten: Er etabliert eine Horizon-Komplementinvariante mit 24 Lücken sowie einen R-unabhängigen, 14 Lücken umfassenden blinden Annulus-Keil für 0<epsilon<(T-10Delta)/8, liefert explorative und symbolische Zertifikate sowie eine parameter-uniforme analytische Kernel-Übergabe und bindet die Prüfungen in CI ein, wobei der Status „nur Kandidat/keine Beförderung“ beibehalten wird. Sequenzdiagramm für die parameter-uniforme Kernel-ÜbergabesequenceDiagram
participant W as AnnulusData
participant H as HubMap
participant V as SaturatedHorizon
participant TB as HorizonOperator
participant K as KNFSampling
participant N as EffectiveOperator
W->>H: H_R(g)
H->>V: Pi_V H_R(g) = 0
V->>TB: Pi_V T_B_inverse = T_B_inverse Pi_V
TB->>K: f = -T_B_inverse H_R(g)
K->>N: f vanishes on U_R
N->>N: N_R(f,g) = T_B f + H_R(g)
N-->>W: N_R(f,g) = 0 with g nonzero
Flussdiagramm für das Zertifikat des uniformen blinden Keilsflowchart TD
P["Parameters: 0 < epsilon < epsilon_c, 0 < R < epsilon, 0 < sigma < R"] --> U["Maximal KNF sampling majorant U_epsilon^max"]
U --> F["24 forbidden Horizon gaps F_epsilon"]
F --> K["25-cell invariant complement K_epsilon"]
K --> V["FREE saturation V_epsilon_R subset K_epsilon"]
K --> B["14 Annulus blind gaps B_epsilon"]
B --> M["Blind measure: 14(h - 2 epsilon) > 0"]
V --> H["Six Hub source maps avoid B_epsilon"]
H --> C["Nontrivial kernel via uniform IMG4 handoff"]
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Original review guide in EnglishReviewer's GuideThis PR replaces the former visibility-count heuristic with an exact A7/A8 interval-geometry candidate: it establishes a 24-gap invariant Horizon complement and 14-gap, R-independent Annulus blind wedge for 0<epsilon<(T-10Delta)/8, supplies exploratory and symbolic certificates plus a parameter-uniform analytic kernel handoff, and wires the checks into CI while retaining candidate-only/no-promotion status. Sequence diagram for the parameter-uniform kernel handoffsequenceDiagram
participant W as AnnulusData
participant H as HubMap
participant V as SaturatedHorizon
participant TB as HorizonOperator
participant K as KNFSampling
participant N as EffectiveOperator
W->>H: H_R(g)
H->>V: Pi_V H_R(g) = 0
V->>TB: Pi_V T_B_inverse = T_B_inverse Pi_V
TB->>K: f = -T_B_inverse H_R(g)
K->>N: f vanishes on U_R
N->>N: N_R(f,g) = T_B f + H_R(g)
N-->>W: N_R(f,g) = 0 with g nonzero
Flow diagram for the uniform blind wedge certificateflowchart TD
P["Parameters: 0 < epsilon < epsilon_c, 0 < R < epsilon, 0 < sigma < R"] --> U["Maximal KNF sampling majorant U_epsilon^max"]
U --> F["24 forbidden Horizon gaps F_epsilon"]
F --> K["25-cell invariant complement K_epsilon"]
K --> V["FREE saturation V_epsilon_R subset K_epsilon"]
K --> B["14 Annulus blind gaps B_epsilon"]
B --> M["Blind measure: 14(h - 2 epsilon) > 0"]
V --> H["Six Hub source maps avoid B_epsilon"]
H --> C["Nontrivial kernel via uniform IMG4 handoff"]
File-Level Changes
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Summary
Post-promotion M1-ND-SALVAGE branch. This PR remains a candidate-only review package; no promotion and no merge are requested yet.
SALVAGE-A0 firewall
beta(epsilon,R,sigma)=|(R,S)\W_vis|;M_N <= 288N+144alone gives onlyN=Omega(1/R), not an R-independent blind fraction.SALVAGE-A1/A2 uniform blind-wedge candidate
Let
[
h=(T-10\Delta)/4=d-3\Delta,qquad
\varepsilon_c=(T-10\Delta)/8.
]
The exact scope check now includes
[
\varepsilon_c<\Delta/2
iff 2^{11}<3^7.
]
Candidate statement:
[
0<\varepsilon<\varepsilon_c,quad
0<R<\varepsilon,quad
0<\sigma<R
\Longrightarrow
\ker\mathscr N_R\neq{0}.
]
Primary exact geometry certificate
scripts/certify_sw1_m1_nd_salvage_a1_a2_uniform_blind_wedge.pyChecks uniformly in epsilon:
(epsilon,T);[
|B_\varepsilon|
=14(h-2\varepsilon)
=\frac72(T-10\Delta-8\varepsilon)>0.
]
Adversarial cross-check 1: direct complement invariance
scripts/certify_sw1_m1_nd_salvage_direct_complement_crosscheck.pyDoes not infer K-invariance from F-invariance. It checks
K∩D_phi -> Kdirectly for all nine maps:Adversarial cross-check 2: epsilon-uniform raw words
scripts/certify_sw1_m1_nd_salvage_uniform_raw_word_graph.pyCloses the upstream A7-transfer question directly from the eleven A1 raw words:
a,T;Analytic handoff
audits/P11_R32_SW1_M1_ND_SALVAGE_A1_A2_ANALYTIC_HANDOFF_CANDIDATE.mdUses only parameter-uniform statements:
T_B=V^*(I+A)V >= I;H_R=V^*HW;B_K.No 780 bound, Mass Transport, ±14 separator cover or special
epsilon=Delta/4value is imported.Measurability and null-boundary handling are now explicit: saturation is a countable union of partial-Borel word images, and the word-saturation of the finite boundary set remains null.
Defects found and repaired during adversarial review
epsilon_c<Delta/2scope check; this is now certified exactly.No mathematical counterexample to the 24-gap/14-gap construction was found.
Current reviewed head
2ed1583f074574c2fdb5a48203d63d520a86b5f6Final workflow run on that head:
33532345053— SUCCESSStatus firewall
✓[M]_negpromotion;epsilon_cis the exact global phase transition;epsilon>=epsilon_c;