QQ16: add an F0-B1 selected-state shear

docs/ci-verification.md

@@ -2,6 +2,18 @@
 
 ## Current selected-family replay
 
+Resolve the [selected record](../certificates/selected-result.json) before
+running a historical checkpoint. The current cold replay is
+`make frontier4359-verify`, using the
+[proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md),
+[validation](research/pr-intake-evidence/pr4359/VALIDATION.json) and
+[source manifest](../certificates/frontier4359-source.json).
+The [frontier4359 workflow](../.github/workflows/frontier4359.yml) provides
+hosted replay evidence. Metadata and source-pin checks are separate from
+operator replay and do not discharge the inherited theorem assumptions.
+
+## Historical frontier1094 replay
+
 Start with the [selected record](../certificates/selected-result.json). Its
 `reproduce`, `review`, `source_manifest` and `validation` fields identify the
 replay command, scoped assessment, source bindings and integration evidence.

docs/research/current-status.md

@@ -1,12 +1,14 @@
 # Current reviewed status
 
-Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage.
+Selected conditional κ: **0.0023** (= 23/10000), zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage.
 
 [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md).
 
 Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope.
 
-## Historical selected status through #1094
+All sections below are a historical snapshot; the selected-result.json record above is authoritative.
+
+## Historical checkpoint through #1094
 
 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555.
 

research/d8-mixed-target-seeda97c8e/SOURCES.json

@@ -4,25 +4,25 @@
   "files": [
     {
       "path": "autoresearch.md",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "8d5403e0f10f68a61d0cb9294fa2e83e872d1d82",
       "sha256": "215b3222f6a943edc69422a28ac21ea1f397ddf54770f1d87ac4195385d73699"
     },
     {
       "path": "certificates/selected-result.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
       "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
     },
     {
       "path": "docs/research/agent-task-catalog.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
       "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
     },
     {
       "path": "docs/research/current-status.md",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "d73b4ff9da41f044e793422db4318be17e234a6c",
       "sha256": "adb54af005eb11edaf84d782fe729338680ff908f6d4fbf39ba1062d2e7d8a77"
     },

research/d8-mixed-target-seeda97c8e/VERIFY.json

@@ -4,10 +4,6 @@
   "python": "3.12",
   "requirements": [],
   "inputs": [
-    "autoresearch.md",
-    "certificates/selected-result.json",
-    "docs/research/agent-task-catalog.json",
-    "docs/research/current-status.md",
     "research/bit-three-register-lower-bound/README.md",
     "research/d8-mixed-target-seeda97c8e/verify.py"
   ],

research/historical-1042-link/RESULT.json

@@ -2,8 +2,9 @@
   "historical_href": "../../certificates/selected-result.json",
   "checkpoint": "certificates/checkpoints/frontier1042.json",
   "historical_kappa": "1672188119205421/1000000000000000000",
-  "live_kappa": "836330098538459/500000000000000000",
+  "live_kappa": "23/10000",
   "same_href": true,
   "kappas_differ": true,
-  "no_new_kappa": true
+  "no_new_kappa": true,
+  "intermediate_checkpoint": "certificates/checkpoints/frontier1094.json"
 }

research/historical-1042-link/SOURCES.json

@@ -11,20 +11,29 @@
     {
       "path": "docs/research/current-status.md",
       "usage": "input",
-      "git_blob": "4e0a8b7cdacc1d9680f7f81d03624118bb20416d",
-      "sha256": "00a08925c51b26d168b8099ddeed659ac4381f7e04f3c7fd0e9de8e71f206823"
+      "git_blob": "532af84312cbfeb39a1e4659d8398deb560f1e4a",
+      "sha256": "54c843968d0b178369a7e56161be44c4692935c3f46ce261678aeedadb309891",
+      "pin": "head:f167c47c5e316d530bcc1d48164684bdd407dc75:docs/research/current-status.md"
     },
     {
       "path": "certificates/selected-result.json",
       "usage": "input",
-      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
-      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40",
+      "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9",
+      "pin": "head:f167c47c5e316d530bcc1d48164684bdd407dc75:certificates/selected-result.json"
     },
     {
       "path": "certificates/checkpoints/frontier1042.json",
       "usage": "input",
       "git_blob": "f451ced6626a1f03aba6915ce23a136b01ebe51d",
       "sha256": "207d1f49f113c585024b9d3c17eadbb8b1be17c1321e3d190aabe2f18ce1c5b7"
+    },
+    {
+      "path": "certificates/checkpoints/frontier1094.json",
+      "usage": "input",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+      "pin": "head:f167c47c5e316d530bcc1d48164684bdd407dc75:certificates/checkpoints/frontier1094.json"
     }
   ]
 }

research/historical-1042-link/VERIFY.json

@@ -6,16 +6,25 @@
   "inputs": [
     "docs/research/current-status.md",
     "certificates/selected-result.json",
-    "certificates/checkpoints/frontier1042.json"
+    "certificates/checkpoints/frontier1042.json",
+    "certificates/checkpoints/frontier1094.json"
   ],
   "commands": [
     {
-      "argv": ["{python}", "-B", "{package}/verify.py"],
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
       "timeout_seconds": 30,
       "checks": "Compare the #1042 status link with the live record and the frontier1042 checkpoint."
     },
     {
-      "argv": ["{python}", "-B", "{package}/test_verify.py"],
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/test_verify.py"
+      ],
       "timeout_seconds": 30,
       "checks": "Check the printed decimal and the historical section cut."
     }

research/historical-1042-link/verify.py

@@ -2,7 +2,8 @@
 """Separate the #1042 status link from the live selected record.
 
 The historical section states the #1042 kappa and links to the live record.
-The matching checkpoint is the selected record's previous_record field.
+The matching checkpoint is reached through the selected record's historical
+previous_record chain (currently via frontier1094).
 """
 
 import hashlib
@@ -16,6 +17,7 @@
 MARKER = "PASS_HISTORICAL_1042_LINK kappas_differ=true no_new_kappa"
 HREF = "../../certificates/selected-result.json"
 CHECKPOINT = "certificates/checkpoints/frontier1042.json"
+INTERMEDIATE = "certificates/checkpoints/frontier1094.json"
 SHOWN = "0.001672188119205421"
 
 
@@ -43,6 +45,7 @@ def authenticate():
         "docs/research/current-status.md",
         "certificates/selected-result.json",
         "certificates/checkpoints/frontier1042.json",
+        "certificates/checkpoints/frontier1094.json",
     }
     require(set(pinned) == expected, "input inventory changed")
     for path, row in pinned.items():
@@ -64,12 +67,15 @@ def evaluate():
     require(HREF in section, "the historical section lost the live-record link")
     require(SHOWN in section, "the historical kappa sentence moved")
     require(Fraction(SHOWN) == Fraction(old["kappa"]), "the checkpoint kappa left the printed decimal")
-    require(live["previous_record"] == CHECKPOINT, "the previous-record pointer moved")
+    require(live["previous_record"] == INTERMEDIATE, "the live previous-record pointer moved")
+    intermediate = json.loads((ROOT / INTERMEDIATE).read_text(encoding="utf-8"))
+    require(intermediate["previous_record"] == CHECKPOINT, "the checkpoint ancestry link moved")
     require(Fraction(live["kappa"]) != Fraction(old["kappa"]), "the live and historical kappas agree")
     require(text.index(HREF) < text.index("# Historical status through #1042"), "the live section lost its record link")
     return {
         "historical_href": HREF,
         "checkpoint": CHECKPOINT,
+        "intermediate_checkpoint": INTERMEDIATE,
         "historical_kappa": old["kappa"],
         "live_kappa": live["kappa"],
         "same_href": True,

research/qq16-f0-b1-shear-seedccce426/CLAIM.md

@@ -0,0 +1,32 @@
+CLAIM — QQ16 F0-to-B1 selected A/T shear using existing query width (Cycle 38; recursive-interfaces, priority revision 4)
+
+**Assignment pins:** selector seed `ccce426f938ce02908e39f554d0187b2`; task `joint-query-controller`, key `0e34adbc1dd119161c3a`; exact base `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`; catalogue SHA-256 `d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7`; selected-record SHA-256 `10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`.
+
+**Object / question:** Insert the reversible selected-state shear immediately after F0 and before B1: `X_T <- X_T + X_A`, `Y_T <- Y_T - X_A`, with all other fields fixed. Does this make the actual post-B1 selected output injective on the eight-dimensional selected-input defect from the fixed QQ16 witness, while using the existing query and recursive-child counts?
+
+**Changed assumption and bounded method:** Permit one A-to-T shear on the already-produced selected fields, with identity coordinate map only. I will derive the exact 8-by-8 transfer on the pinned witness span using the actual QQ16 selected sections and ordered B1 maps, then compare identity shear, zero shear, and a sign-corrupted control. The experiment covers this witness span and this one shear; it does not claim a full controller or all-size supplier.
+
+**Optimistic full local charge:** 16 scalar additions per owner (eight to X_T and eight to Y_T), eight copied values hosted in existing selected fields, zero new helpers, zero added recursive children, and no new coefficient precision for C=I. The B1 and F0 children stay as before. Frame/address transitions and restoration are provisionally granted free for the initial screen; any exact map or hosting cost found in the route calculation will be added. The local source/F0/B1 invoice remains 211210/214986 scalar primitives with 8/24 added rank-one children before the shear. The favorable selected profile has only two rank-one-equivalent operations of slack after an ideal rank-eight output charge, so any added child is a stop condition. No supplier or κ gain is presumed.
+
+**Nearest work / distinct contribution:** PR #2086 treats arbitrary changes to the first A logger with the old T output fixed and names changed T records as open. PR #2093 and the completed B2-read work add ordinary-source observations. PR #2174 recovers pair 0 only with privileged post-B1 selected-cut values. PR #2189 gives a read-only transcript-width bound. This scope instead changes the selected state between the two calls by an invertible sum-preserving shear; no extra observation is added. The live exact-term scan at 23:47Z covered 445 open PRs and 892 Discussion records with complete pagination and no warnings, and returned no matches.
+
+**Expected result / stop:** an exact rank-eight transfer or a counterexample on the witness span, with a source-bound reproducible check and charged local operations. Stop if the map is not injective or if implementation needs any extra recursive child. Claim expires 2026-10-15T01:50Z.
+
+**Predecessor credit:** Ali Romman and the retained joint-query lineage (PR #1969) supply the local maps and witness; Cinna Davis (PR #2079) and Adam Gall (PR #2093) supply adjacent observation analyses. Substantial AI assistance from OpenAI Codex.
+
+## FINDING — exact witness repaired at the B1 cut
+
+The all-route group-algebra replay passes for all eight pinned `h_k`
+directions. It verifies `B1 h_k=0`, the `2112 I` identity coefficient of
+`B2 h_k`, rank eight in the post-F0 A field, rank zero in the zero-shear B1
+T output, and rank eight in the sheared B1 T output. An exact eight-row
+minor has determinant `-1/4096`; its group-map keys and rational
+coefficients are in `RESULT.json`.
+
+The shear costs 16 scalar additions per owner at the common `completed(0)`
+frame, uses existing A/T fields, preserves selected sums, and adds no
+helper, cover map, precision, or recursive child. This is a fixed-witness
+interface mechanism, not a full controller, supplier, or kappa result.
+Package and source pins pass; the final verifier passed locally on Python
+3.14.7. The registered package replay targets Python 3.12 and remains for
+hosted CI.

research/qq16-f0-b1-shear-seedccce426/NOTICE.md

@@ -0,0 +1,10 @@
+New work in this package is released under Apache-2.0.
+
+Predecessor credit: Ali Romman and the retained joint-query lineage supply
+the QQ16 maps, ordered local words, route model, and erased-input witness
+(merged PR #1969). Cinna Davis's PR #2079 and Adam Gall's PR #2093 study
+additional ordinary observations. PR #2086 studies changed A logging while
+leaving the T output fixed. Their code and frozen sources are not modified.
+
+Substantial AI assistance: OpenAI Codex derived, implemented, checked, and
+wrote this scoped result. No independent human review is claimed.

research/qq16-f0-b1-shear-seedccce426/PROOF.md

@@ -0,0 +1,91 @@
+# Exact witness calculation
+
+## Frozen object and witness
+
+The source and route model is the selected QQ16 package at the base pinned
+in `SOURCES.json`. The inherited witness uses the actual sets
+
+```text
+A = [0, 7, 20, 27, 36, 46, 57, 111]
+T = [21, 37, 47, 76, 81, 87, 92, 110]
+U = the other 96 ports.
+```
+
+For each centre basis vector `e_k` at the identity owner, the checker builds
+
+```text
+h_k = (48 I - B1* B1) B2* e_k,       k=0,...,7.
+```
+
+`B_s` is the actual stage-s query restricted to U, including each port's
+exact stage owner map. The checker works in the group algebra of the 73-bit
+owner linear maps and uses rational coefficients. Payload translations are
+omitted only because every payload block is held constant, as in the
+predecessor witness. The exact checks give `B1 h_k = 0` and identity
+coefficient `2112 e_k` in `B2 h_k` for all eight k. Applying the invertible
+stage-2 A section gives an eight-dimensional vector `a_k=P_(2,A)B2 h_k`.
+
+The ordered F0 witness state immediately before B1 is
+
+```text
+X_U = Y_U = h_k
+X_A = a_k,  Y_A = -a_k
+X_T = Y_T = 0.
+```
+
+At zero shear, the retained B1 word returns the erased selected output on
+this family; the checker verifies that its T output is the zero group-ring
+vector for every k.
+
+## The changed interface
+
+Insert the coordinatewise shear
+
+```text
+X_T <- X_T + X_A
+Y_T <- Y_T - X_A.
+```
+
+For each T coordinate the change in `X_T+Y_T` is zero. The full map is
+invertible, with inverse `X_T <- X_T-X_A`, `Y_T <- Y_T+X_A`; it uses no
+scratch field. After the shear the B1 inputs have
+
+```text
+X_T = a_k,  Y_T = -a_k.
+```
+
+In the ordered B word, write `u=E_2 Y`, `a=ell_1 X`, and `b=R_1 u`. Its T
+output is `P_(1,T)(b+12a)`. Thus the shear's exact effect is
+
+```text
+Delta X'_T = P_(1,T) (12 ell_1 - R_1 E_2) iota_T a_k,
+```
+
+where each term is evaluated with the pinned 73-bit owner routes. The
+verifier propagates all eight `a_k` as sparse rational group-algebra
+vectors. It finds 287,368 distinct owner-map labels in the T outputs and
+extracts eight rows, indexed by T port and exact owner map, whose coefficient
+matrix has determinant `-1/4096`. This proves the post-B1 T outputs are
+linearly independent on the eight-dimensional witness family. The sparse
+rows, route keys, and exact coefficients are in `RESULT.json`; the checker
+recomputes them from the pinned source.
+
+The zero-shear control has rank zero. The positive result is limited to this
+fixed erased family and this post-F0 state shear. It does not prove that
+subsequent events retain the output, restore every selected input, or form
+a complete controller.
+
+## Cost and remaining obligations
+
+At the F0/B1 boundary all data fields use the common `completed(0)` frame.
+The shear therefore uses same-owner scalar adds without changing an owner
+map or a frame. Its exact local cost is 16 scalar additions per owner, zero
+new helpers, zero new recursive children, zero new coefficient precision,
+and zero temporary storage. It reads the existing A fields, writes existing
+T fields, and preserves the logical selected sums. The ordinary helper
+restoration contract is unchanged.
+
+The route test establishes an exact interface effect, not a priced complete
+supplier. Any integration must still propagate the state through the
+remaining tail and prove final output/restoration for arbitrary inputs.
+There is no new κ claim.