certify R5 Hessian Krawczyk gates on all frozen leaves

SHA256SUMS.txt

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audit/artifact_manifest.json

@@ -340,7 +340,7 @@
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       "scientific_scope": "documentation for an isolated model-level Principle R test protocol; no R6 search or result",
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@@ -930,6 +930,94 @@
       "status": "prospective_r5_b1e_first_leaf_certified_only",
       "type": "script"
     },
+    {
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+        "principle_r_r1_r7_protocol",
+        "principle_r_r5_full_tube_protocol"
+      ],
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+        "principle_r_r5_full_tube_protocol",
+        "principle_r_r7_positive_control_certificate_v1_1"
+      ],
+      "path": "research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md",
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+        "principle_r_r5_first_leaf_hessian_krawczyk_certificate",
+        "principle_r_r5_full_tube_protocol",
+        "principle_r_r5_full_tube_auxiliary_data"
+      ],
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+        "principle_r_r5_first_leaf_hessian_krawczyk_certificate",
+        "principle_r_r5_first_leaf_affine_diagnostic_record",
+        "principle_r_r5_static_arb_gates_certificate",
+        "principle_r_r5_full_tube_protocol",
+        "principle_r_r5_full_tube_auxiliary_data"
+      ],
+      "path": "research/realizability_r1_r7/certify_r5_all_leaves_hessian_krawczyk.py",
+      "producer": "prospective R5-B2 all-leaves affine-Hessian Krawczyk driver",
+      "scientific_scope": "checks each of the 16 frozen leaves independently using the same frozen affine-Hessian Krawczyk construction",
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+      "type": "script"
+    },
+    {
+      "id": "principle_r_r5_all_leaves_hessian_krawczyk_certificate",
+      "inputs": [
+        "principle_r_r5_all_leaves_hessian_krawczyk_script",
+        "principle_r_r5_first_leaf_hessian_krawczyk_certificate",
+        "principle_r_r5_full_tube_protocol",
+        "principle_r_r5_full_tube_auxiliary_data"
+      ],
+      "path": "research/realizability_r1_r7/certificates/r5_all_leaves_hessian_krawczyk_v1_0.json",
+      "producer": "principle_r_r5_all_leaves_hessian_krawczyk_script",
+      "scientific_scope": "all 16 frozen leaves locally certified for normal-root existence/uniqueness; not adjacent-leaf gluing, not full-path continuity, not full R5, not PR-R6, and not normal K=1 recovery",
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+      "status": "prospective_r5_b2_all_leaves_local_only",
+      "type": "certificate"
+    },
+    {
+      "id": "principle_r_r5_all_leaves_hessian_krawczyk_verifier",
+      "inputs": [
+        "principle_r_r5_all_leaves_hessian_krawczyk_certificate",
+        "principle_r_r5_full_tube_protocol",
+        "principle_r_r5_full_tube_auxiliary_data"
+      ],
+      "path": "research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py",
+      "producer": "prospective R5-B2 all-leaves Hessian Krawczyk verifier",
+      "scientific_scope": "read-only verifier and mutation tests for the all-leaves local-only B2 record; rejects R5/PR-R6/global-flow claim inflation and arithmetic/hash tampering",
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+      "type": "script"
+    },
     {
       "allow_absolute_runtime_paths": true,
       "id": "v0_9_2_krawczyk_design_reference_script",

research/realizability_r1_r7/GF_PR_STAGE_NAMING_BOUNDARY.md

@@ -0,0 +1,27 @@
+# GF/PR Stage Naming Boundary
+
+This repository uses two separate naming layers.
+
+`PR-R1` through `PR-R7` denote the prospective Principle R interface:
+state-space declarations, response protocol, protocol-relative cost, admissible
+processes, shrinking-family requirements, future R6 gates, and the R7 positive
+control.
+
+`GF-R5`, `R5-A`, `R5-B0`, `R5-B1e`, `R5-B2`, and later `R5-B3`--`R5-B6`
+denote Geometric-Flow repository engineering stages for a possible R5 witness.
+These stages are evidence-producing or diagnostic substeps. They do not by
+themselves modify the published Geometric-Flow theorem boundary.
+
+In particular:
+
+```text
+GF-R5 local leaf success != PR-R5 certified.
+GF-R5 all-leaf local success != PR-R6 supplied.
+R5-B2 success != full R5 tube certificate.
+```
+
+R5-B2 checks only whether the same frozen affine-Hessian Krawczyk construction
+certifies one local normal root on each of the 16 frozen tube leaves. It does not
+certify adjacent-leaf gluing, full-path continuity, exact zero cost on the full
+path, positive-measure nonconstancy, R6, a global ODE flow, or normal K=1
+residual recovery.

research/realizability_r1_r7/PRINCIPLE_R_COMPLIANCE_MATRIX.md

@@ -0,0 +1,22 @@
+# Principle R Compliance Matrix
+
+This table records current repository evidence for the prospective model-level
+Principle R interface. It does not change the published Geometric-Flow theorem
+boundary.
+
+| Interface | Current evidence | Status |
+|---|---|---|
+| PR-R1 | Frozen fourteen-phase state space and phase-gauge handling | model-level |
+| PR-R2 | Frozen protocol, inputs, hashes, and 192-bit precision declarations | model-level |
+| PR-R3 | Response-induced protocol-relative cost using the declared `R3/W_Pi` meter | model-level, not fundamental vacuum cost |
+| PR-R4 | Allowed absolutely continuous nonconstant process class | local/partial |
+| PR-R5 | Shrinking family protocol plus static gates and local leaf diagnostics | not separately certified |
+| PR-R6 | Published local ODE result and prospective future gates; no complete 16-leaf path result | local only |
+| PR-R7 | Same-meter positive control certificate | explicit binding verified |
+| Full interface | No complete R1--R7 model-level witness | not certified |
+
+`R5-B2` success would strengthen only the local normal-root evidence for the
+frozen 16 leaves. It would not imply `PR-R6` success. R5-B3--R5-B5 are still
+needed for gluing, full-path coverage/continuity, exact response preservation,
+and positive-measure nonconstancy before any complete GF-R5 certificate can be
+considered.

research/realizability_r1_r7/R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md

@@ -0,0 +1,53 @@
+# R5-B2 All-Leaves Hessian Krawczyk Boundary
+
+R5-B2 freezes a first-pass all-leaves preflight for the 16 initial leaves in the
+subordinate R5 full-tube protocol. The leaf list, order, endpoint rule, centers,
+fixed slope, Arb precision, candidate eta radii, formal eta radius, and
+Krawczyk gates are declared before running the all-leaf check.
+
+The frozen tube is:
+
+```text
+t in [-1e-12, 1e-12]
+```
+
+with 16 ordered leaves of width `1.25e-13`. Endpoints are recorded as closed
+intervals for interval enclosure; later gluing work must treat adjacency and
+branch consistency separately.
+
+For leaf `i`, the center is:
+
+```text
+a_C,i = (left_i + right_i)/2
+b_C,i = -P F(a_C,i, 0)
+```
+
+The fixed affine slope `S` is the B1c/B1e slope and is not refit per leaf. The
+directional Hessian remainder is computed for:
+
+```text
+w = T*v + N*S
+Y2_i <= 1/2 sup ||P*B*D2R3(theta_C,i + w*alpha)[w,w]||_inf * alpha_radius^2
+```
+
+The Krawczyk forcing bound is:
+
+```text
+Y_total_i = Y0_i + Y1_i + Y2_i + Y_eta_cross_i
+```
+
+where eta variation is not interval-subtracted into the forcing term; it is
+handled by `Z_i*r_eta` over the full `(alpha, eta)` box.
+
+Allowed scientific statuses:
+
+```text
+R5_ALL_LEAVES_HESSIAN_KRAWCZYK_CERTIFIED
+R5_ALL_LEAVES_HESSIAN_KRAWCZYK_NOT_CERTIFIED
+R5_ALL_LEAVES_HESSIAN_KRAWCZYK_INCONCLUSIVE
+R5_B2_INPUT_BOUNDARY_MISMATCH
+R5_B2_IMPLEMENTATION_ERROR
+```
+
+Even if all 16 leaves pass their local gates, this is not a full R5 certificate,
+not PR-R5, not PR-R6, not a global flow result, and not normal K=1 recovery.

research/realizability_r1_r7/README.md

@@ -39,6 +39,9 @@ R5_FIRST_LEAF_CENTER_DIAGNOSTIC.md
 R5_FIRST_LEAF_AFFINE_DIAGNOSTIC.md
 R5_SECOND_ORDER_REMAINDER_DIAGNOSTIC.md
 R5_FIRST_LEAF_HESSIAN_KRAWCZYK_BOUNDARY.md
+GF_PR_STAGE_NAMING_BOUNDARY.md
+R5_ALL_LEAVES_HESSIAN_KRAWCZYK_BOUNDARY.md
+PRINCIPLE_R_COMPLIANCE_MATRIX.md
 r5_full_tube_protocol_v1_0.json
 prepare_r5_full_tube_auxiliary.py
 verify_r5_full_tube_auxiliary.py
@@ -62,6 +65,9 @@ diagnostics/r5_second_order_remainder_diagnostic_v1_0.json
 certify_r5_first_leaf_hessian_krawczyk.py
 verify_r5_first_leaf_hessian_krawczyk.py
 certificates/r5_first_leaf_hessian_krawczyk_v1_0.json
+certify_r5_all_leaves_hessian_krawczyk.py
+verify_r5_all_leaves_hessian_krawczyk.py
+certificates/r5_all_leaves_hessian_krawczyk_v1_0.json
 certificates/r7_positive_control_v1_0.json  # superseded
 certificates/r7_positive_control_v1_1.json  # current R7 positive control
 ```
@@ -82,6 +88,7 @@ python research/realizability_r1_r7/verify_r5_first_leaf_center_diagnostic.py --
 python research/realizability_r1_r7/verify_r5_first_leaf_affine_diagnostic.py --mutation-tests
 python research/realizability_r1_r7/verify_r5_second_order_remainder_diagnostic.py --mutation-tests
 python research/realizability_r1_r7/verify_r5_first_leaf_hessian_krawczyk.py --mutation-tests
+python research/realizability_r1_r7/verify_r5_all_leaves_hessian_krawczyk.py --mutation-tests
 ```
 
 The verifier checks schema, required fields, declared file hashes, R1--R5/R7
@@ -166,6 +173,16 @@ self-map margins. This certifies only first-leaf graph root
 existence/uniqueness; it is not a full R5 tube certificate, not R6, and not
 normal K=1 recovery.
 
+`certificates/r5_all_leaves_hessian_krawczyk_v1_0.json` records the R5-B2
+all-leaves affine-Hessian Krawczyk preflight over the 16 frozen initial tube
+leaves. Its status is `R5_ALL_LEAVES_HESSIAN_KRAWCZYK_CERTIFIED`: every leaf
+has a strict local normal-root existence/uniqueness gate at the formal eta
+radius `1e-23` under the same predeclared formula, radius set, and 192-bit Arb
+precision. This remains local leaf evidence only. It does not certify adjacent
+leaf gluing, full-path continuity, exact response preservation, zero total
+cost, positive-measure nonconstancy, PR-R6, full R5, a global ODE flow, or
+normal K=1 recovery.
+
 ## Scope
 
 The published Geometric-Flow theorem remains the v1.2.13 local quantum-control