Certify active-mode restoration at a native paid-query cut

research/active-mode-restoration/PROOF.md

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+# A late active injection: restoration obstruction and conditional repair
+
+This checkpoint gives an exact scalar information test for a specified active
+injection. It does not rule out active feedback in general, implement a new
+physical transfer, or improve the multiplication bound.
+
+## Frozen interface
+
+Use the retained `F9-SOURCE-DAG-ALL8-WORD.json.gz`, SHA256
+`934fea11e51f674ce2031b7d3127b994a921a9d83317b00359292752563a1775`,
+backward direction, omitting its unimplemented `physical_add` events exactly
+as the retained observer probe does. The independent inputs are 112 X fields,
+112 Y fields, and 408 arbitrary helper fields H. All owned scratch is separate
+from this 632-dimensional input inventory.
+
+The test cut is immediately before word event 17978, original source event
+17155:
+
+```
+['climb', 'scalar_refactor', 240, 280, 1, 1]
+```
+
+L240 is then in rank-eight frame 280 and climbs to the unique full frame 1.
+Evaluate address operators on their common fixed vector. This retains every
+original input coefficient while giving a necessary scalar observer quotient;
+it is not a phase-aware physical replay.
+
+Write R for the retained 8 by 112 mode matrix, with `R R^T = 56 I`, and
+`A = I - R^T R/4`. The exact scalar baseline endpoint is
+
+```
+X -> X - A Y,       Y -> Y,       H -> H.
+```
+
+## 1. An active injection does not supply a clean extra observation
+
+Let M consist of all chronological full-frame snapshot rows on the 632
+original inputs. Let v record each snapshot's response to a unit injection
+into L240 at the stated cut. Grant a missing mode m at that cut without
+claiming that it can physically be supplied there. The changed snapshots
+are `M' = M + v m`, not a collection containing both original and modified
+versions of each affected snapshot.
+
+For m outside `row(M)`, pure m is in `row(M')` exactly when some q satisfies
+`qM = 0` and `qv != 0`. Such q extracts m, after which every original snapshot
+can also be recovered. Conversely, any extraction must satisfy these two
+conditions because m is outside the original row space. Equivalently,
+`rank([M|v]) > rank(M)` is necessary and sufficient.
+
+The exact replay finds 4868 distinct full snapshots and
+
+```
+rank(M) = rank([M|v]) = 482.
+```
+
+Every one of the eight RY modes lies outside `row(M)`. The saved certificate
+provides a 104-term z and checks `Mz = v` directly on all 4868 rows. Therefore
+the changed row space is the graph `r -> r + (rz)m` over the old row space;
+it contains no pure m. The coefficient of the original helper endpoint e240
+is `e240 z = 1`, so that original independent helper is not restored by
+declaring the changed value a clean mode observation.
+
+For `m5 = R5 Y`, a second directly checked certificate has
+
+```
+Mu = 0,   m5 u = 1,   m5 z = 0,
+a = u-z,
+(M+v m5)a = 0,   m5 a = 1,   e240 a = -1.
+```
+
+This separates both the pure mode and the original helper240 target from
+all allowed changed observations. It is an exact certificate, not a modular
+no-hit or a failed coefficient search. An invertible change of independent
+helper coordinates preserves this information test.
+
+## 2. Why the fixed full-frame sink gives a larger scoped obstruction
+
+Metadata verifies that exactly 482 persistent roles enter the full frame,
+each once; none leaves it. No owned scratch reaches the full frame. After
+entry, full-frame updates are nonaliasing ADDs and nonzero SCALEs, with no
+copy, clear, or non-full scalar source. The 72 full-frame warps act as the
+identity in this fixed-vector quotient.
+
+Consequently every recorded full snapshot is a fixed linear combination of
+the 482 final full coordinates: `M = S F`. Reverse the invertible full-frame
+updates to obtain S, leaving newly arriving coordinates unused until their
+arrival. Final observations show that S has full column rank. The same S
+applies if only lower-frame histories before first full arrival change.
+
+The 482 baseline final rows F have distinct X/helper pivots. The eight RY
+rows have only Y coordinates and rank eight. Thus their row spaces intersect
+trivially and `rank([F; RY]) = 490`.
+
+Suppose a family of added controls changes the full endpoint only by fixed
+missing modes, so `F' = F + V(RY)`, while the full sink interface remains
+unchanged. If `aF' = b(RY)`, independence gives `aF = 0`, hence a=0 and b=0.
+No nonzero pure missing mode can then be extracted from any number of these
+modified full-frame snapshots. This covers multiple fixed-mode injections
+inside that interface, not arbitrary feedback words or changed source
+alphabets. Feedback carrying other original input combinations, new full
+ingress, saved independent owned data, new address maps, or changed target
+inventory is not covered.
+
+Most importantly, this theorem does not prohibit direct repair of the main
+endpoint. A successful construction can change F to the desired target
+without ever exposing a separate pure missing-mode observation.
+
+## 3. A direct one-mode repair is algebraically consistent
+
+The unit L240 impulse has final main coefficient `+R5^T` and helper
+coefficient `+S5`, with 56 and 48 nonzero entries respectively. This agrees
+with the retained center5 suffix data; that helper cleanup was already known.
+
+The source already captures `c = R5 Y/4` in ground-frame owned C6 at events
+511--567. At events 568--615 it applies `H -= S5 c`. C6 is unchanged through
+the tested cut. Conditional on an oracle injection `L240 -= c`, omit those
+48 existing helper precompensation ADDs. The resulting effects are
+
+```
+main:    -R5^T c,
+helpers: -S5 c + S5 c = 0.
+```
+
+An independent direct replay verifies every coefficient in all 632 endpoint
+rows, all 408 helper identities, all final charts, and every owned zero:
+
+```
+X -> X - A Y - R5^T R5 Y/4,       Y -> Y,       H -> H.
+```
+
+There are no downstream warp events after the named climb. Once the
+required field reaches full frame 1, its remaining propagation is therefore
+the displayed scalar suffix impulse. The payload supplied in frame 280
+must transport through the selected climb to that required field. The
+fixed-vector calculation does not establish this physical availability.
+
+Indeed C6 is in frame 0 while L240 is in frame 280. The literal ADD between
+them fails the ordinary coframing validator. The conditional identity is
+therefore a target for a new routing or dependency construction, not an
+unpaid legal edit or a claimed improvement.
+
+## Distinction from retained passive exclusions
+
+The retained `CORRECTIONS` and observer work study corrections built from
+the unchanged history. Here the snapshots themselves change: the extra
+response column v and all helper targets are tracked after a granted active
+injection. The result adds an exact restoration certificate for this cut and
+a fixed-mode extension under the verified full-sink interface. It does not
+reprove the source-DAG helper compensation, supersede broader physical
+semantics, or turn either the old passive exclusions or this scoped theorem
+into a prohibition of active feedback.

research/active-mode-restoration/README.md

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+# Active-mode restoration at a native paid-query cut
+
+This package certifies why a granted mode injection into the retained L240
+query does not provide a clean extra observation while preserving the original
+helper. It also proves a broader limitation for the same monotone full-frame
+observer interface and records a conditional direct endpoint repair whose
+physical payload transport remains open. **No new bound, supplier or legal
+center replacement is claimed.**
+
+## Result and evidence
+
+The frozen source is the backward `F9-SOURCE-DAG-ALL8` program from
+[filtered-native-kappa004](../filtered-native-kappa004/README.md), with its
+`physical_add` tails omitted. The observer calculation evaluates native address
+operators on their common fixed vector and retains all 632 arbitrary original
+input amplitudes, including all 408 helpers. It is a scalar necessary interface,
+not a complete phase-aware physical replay.
+
+* **Granted L240 injection.** Immediately before source event 17155 (word event
+  17978), grant an additive mode at L240's rank-8 frame 280, just before its
+  rank-1 climb to full frame 1. The 4,868 distinct full-frame observations have
+  rank 482 both before and after adjoining the injection-response column.
+  Explicit rational witnesses check `Mz=v` and separate both the missing mode5
+  and the original helper240 output from the changed observation span. This
+  includes dirty-helper restoration; fitting only a desired main coefficient
+  would miss the obstruction. See [l240-extra-column-gate.json](l240-extra-column-gate.json)
+  and [the complete observation data](l240-full-observations.json.gz).
+* **Monotone full-frame observer limitation.** The source has 482 persistent
+  full-frame arrivals, no full-frame departures or new owned full-frame fields,
+  and only invertible scalar updates within the full-frame subsystem. Its
+  history is therefore spanned by its 482 final full rows. For the stated
+  fixed-mode changes `F'=F+VR`, the eight missing R modes cannot become separate
+  pure observations while preserving the original full targets. This is the
+  exact interface in [full-sink-gate.json](full-sink-gate.json), not an exclusion
+  of arbitrary active feedback or new physical observations.
+* **Conditional direct repair.** Omitting the 48 helper-precompensation updates
+  at word events 568–615 and granting `L240 -= C6`, where `C6=R5Y/4`, gives the
+  scalar endpoint `X-AY-R5^T R5Y/4`, with Y and all helpers unchanged and owned
+  scratch returned to zero. Here A is the retained center-free owner matrix.
+  The literal ADD is **illegal**: C6 is at frame 0 while L240 is at frame 280.
+  The checker rejects that operation under actual coframing. The result in
+  [direct-l240-repair.json](direct-l240-repair.json) is conditional on supplying
+  the required transported payload at frame 280, with its entire cost charged.
+
+[PROOF.md](PROOF.md) states the hypotheses and witness identities. Direct repair
+of the prescribed endpoint without exposing a separate pure mode, new full-frame
+ingress, changed source dependencies,
+additional paid jobs and broader address operations are outside the observer
+limitation. No native, caller, compiler, precision or outer-bound certificate
+for a successful repair is supplied.
+
+## Reproduce
+
+From the repository root, using Python 3.12 and only its standard library:
+
+```sh
+python3 scripts/research_package.py --package research/active-mode-restoration --check-only
+python3.12 scripts/research_package.py --package research/active-mode-restoration
+```
+
+The two registered commands run `verify.py` normally and with `-O`; each has a
+120-second timeout. Direct replay is also available:
+
+```sh
+python3 -B research/active-mode-restoration/verify.py
+python3 -O -B research/active-mode-restoration/verify.py
+```
+
+The verifier authenticates the unchanged predecessor archive and four member
+hashes, materializes only those regular data members in a temporary directory,
+and regenerates the three gates. It compares semantic evidence, excluding
+elapsed time, and separately checks the saved witness pairings against every
+observation. It imports no scientific source code from the archive. Controls
+cover a corrupted witness, useful before/after side information, forbidden
+full-frame lifecycle changes, incorrect compensation/sign, and the illegal
+cross-frame ADD. No broad parameter search or heavy native suite is run.
+
+## Sources and relation to prior work
+
+[SOURCES.json](SOURCES.json) pins main
+`df0137efd35e11b4445734bf612bdd4c7ebc330c`, the original task catalogue and
+selected record, and the live archive
+`research/filtered-native-kappa004/inputs/original-packet.tar.gz` (SHA256
+`595f988e748b1f3b25e7525a226da173966e4278a70f511b2919245cec1b45f7`).
+The archive is the only external replay input; the four member paths, sizes
+and hashes are recorded too. No predecessor package or archive is copied into
+this directory. The declared archive is included by the repository's committed
+package exporter. Full Git history is required for registered provenance checks.
+
+The source packet already implements dirty shared-query reuse and a later
+helper-clean source-DAG construction with a filtered main endpoint. Their
+helper compensation is not a new result here. The earlier
+[coded-active-feedback](../coded-active-feedback/README.md) investigation uses
+a different whole-bank feedback grammar. The new evidence is the explicit
+all-original-input restoration certificate at this native cut, its stated
+full-frame interface extension, and the conditional direct-repair identity.
+
+The original `joint-query-controller` card is retained verbatim in
+[TASK.json](TASK.json). Its scope is marked **changed**: this is a scoped native
+observer/endpoint checkpoint, rather than a completed QQ16 protocol or a
+favorable supplier invoice. The selected frontier is unchanged.
+
+## Open next questions
+
+[TASK.json](TASK.json) records a first test and blocker for each question:
+
+1. Supply the required payload at frame 280 with a legal, fully charged
+   schedule. This is the missing step in the conditional direct repair.
+2. Change one actual source dependency or full-frame ingress and recompute the
+   complete chronological observation and restoration maps. More coefficients
+   within the certified fixed observer interface do not provide new information.
+3. Repair the prescribed endpoint directly without requiring a separate pure-mode
+   observer, then verify every arbitrary input, physical phase and endpoint.
+
+## Credit
+
+Prepared for flyingviper with substantial OpenAI Codex assistance, including
+separate agent checks. This is not independent human peer review or
+proof-assistant formalization. New work is Apache-2.0. The recovered
+filtered-native packet retains the prior continuation work. Its source lineage
+includes Cao Yifan's 632-field native source and Cinna Davis's center-removal
+and cache-kernel work; the retained involutory-producer package was prepared
+by Dugongue and preserves the earlier mode and repair sources. All inherited
+attribution and notices remain in the unchanged archive. This package does not
+claim those predecessor constructions.

research/active-mode-restoration/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "df0137efd35e11b4445734bf612bdd4c7ebc330c",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "581f8d87008354eb5b869f7ed9de1317ad837ce8",
+      "sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+    },
+    {
+      "path": "research/filtered-native-kappa004/inputs/original-packet.tar.gz",
+      "usage": "input",
+      "git_blob": "7f904307bd99f2d778bc7b64e98e353715cbc041",
+      "sha256": "595f988e748b1f3b25e7525a226da173966e4278a70f511b2919245cec1b45f7"
+    }
+  ],
+  "archive_members": [
+    {
+      "path": "filtered_native_implementation/research/retained_state_next/F9-SOURCE-DAG-ALL8-WORD.json.gz",
+      "bytes": 428325,
+      "sha256": "934fea11e51f674ce2031b7d3127b994a921a9d83317b00359292752563a1775"
+    },
+    {
+      "path": "filtered_native_implementation/research/native_contact/SCALED-GLOBAL-CANCEL-WORD.json.gz",
+      "bytes": 206603,
+      "sha256": "de4b75c106f8a3ebe1ee68b53fe7e64bd218120526e726d9bdfd4dab711dd4b2"
+    },
+    {
+      "path": "filtered_native_implementation/upstream/research/involutory-producer-raw-dual/inputs/R/R.json",
+      "bytes": 4664,
+      "sha256": "7b33b6dfb494c6eafe6d87a08d6a2c2e0681e56429495b2b27949040f0f63cd1"
+    },
+    {
+      "path": "filtered_native_implementation/research/retained_state_next/CENTER5-SUFFIX.json",
+      "bytes": 102442,
+      "sha256": "5f2439d2f724f9f6fc6766bd74cd0885e923a0f8f3736d1eff6873c68d99279a"
+    }
+  ],
+  "archive_contract": "The verifier checks the exact archive and four member hashes, then materializes only these regular member files in a private temporary directory. No source code is imported from the archive; no predecessor bytes are duplicated or edited in this package.",
+  "predecessor_credit": "The retained filtered-native packet, its native/source-DAG/mode authors and pinned upstream notices retain their original attribution and licenses. This package adds scoped restoration certificates and a conditional endpoint identity."
+}