Mister-Meeseeks · Oct 15, 2026 · Oct 15, 2026
diff --git a/docs/research/bottleneck-brief.md b/docs/research/bottleneck-brief.md
@@ -39,7 +39,11 @@ The [review through #2027](community-efficient1000-review.md) leaves the selecte
 - **Joint-query controller:** [#1969's local words](../../research/joint-query/README.md)
   are checked, but the fixed-first-pair selected-only controller has an explicit
   lost-query witness. Test one changed first pair or paid extra observation
-  against that witness before designing a full schedule.
+  against that witness before designing a full schedule. The
+  [QQ16 observation-contract map](qq16-controller-scope-map.md) indexes later
+  pending and fork evidence to check first: a 252-pair first-pair catalogue,
+  witness detection versus full recovery, and recorded-cut versus final-only
+  recovery.
 - **Selected proof obligation:** [#1990's stock audit](../../research/selected-bootstrap-stock-audit/README.md)
   leaves the actual selected reserve coefficient unknown. Derive one source-bound
   stage envelope rather than recomputing the already checked headrooms.

diff --git a/docs/research/qq16-controller-scope-map.md b/docs/research/qq16-controller-scope-map.md
@@ -0,0 +1,165 @@
+# Which QQ16 observation contract has been checked?
+
+Use this map before changing a QQ16 first pair or adding a query. The
+[retained local words](../../research/joint-query/README.md) do not by
+themselves close a controller. Later evidence separates three questions:
+whether a read detects one witness, whether it recovers the original selected
+inputs given an intermediate cut, and whether the final records supply that
+cut. A positive answer to the first or second question does not answer the next.
+
+This is a bounded navigation audit, not a new obstruction or supplier. The
+selected result remains governed by
+[selected-result.json](../../certificates/selected-result.json). At the source
+checkpoint below, PR1969 is retained on main; the other numbered results are
+open submissions and the first-pair catalogue is a public fork artifact.
+Replaying a submission is not maintainer acceptance. Check
+[Discussion #2074](https://github.com/CrocSwap/integer-mult-bounds/discussions/2074)
+and [live overlap](../../autoresearch.md#1-orient-briefly-then-choose-a-distinct-task)
+before treating a surviving hypothesis as unclaimed work.
+
+## Common notation and the observation cut
+
+The selected sets `A,T` have eight ports each; `U` has 96. Write
+`B_s = R_s iota_U` for the ordinary-source query in chart `s`. Each query
+returns eight coordinates per owner. These are logical observations, not a
+paid recursive-child rank or a native implementation.
+
+The fixed first pair is `F0` followed by `B_(1,2)` on bank pair 0. The retained
+local-call pairs, at stages 0 through 8, are `0,0,0,1,1,2,2,3,3`.
+An ordinary bridge acts on `U` by
+`X_dst += c X_src; Y_src -= c Y_dst`. The terminal is
+`(X_U,Y_U) -> (Y_U,-X_U)`. Thus the **named final Y** is the completed-X
+descendant; named final X carries the former-Y field. Its name alone does not
+make it an allowed completed-X observation.
+
+The distinction between the selected state **immediately after B1** and the
+selected state **at the end** is essential. If a construction promises only
+the latter, a decoder using the former needs a separate retention or
+reconstruction argument, with its physical cost.
+
+## Six source contracts
+
+| Source and evidence status | Fixed or changed hypothesis | Established statement | Boundary that must be preserved |
+| --- | --- | --- | --- |
+| **PR1969, retained**: [selected witness][witness] and [rational review][rational] | Fixed `F0/B_(1,2)` and ordinary schedule; selected outputs, completed-X descendants and all five forward histories are observed. | The family `h_k=(48I-B1*B1)B2*e_k` is invisible although the original selected T input is nonzero. The identity coefficient of `B2 h_k` is `2112 e_k`. Later homogeneous selected-only linear maps do not repair it. | This proof alone does not cover changed first maps or ordinary-to-selected reads. The retained package's local-word replay does not rerun the global witness. |
+| **Philippe Van Velzen, public fork**: [first-pair catalogue][pairs] | Keep the same logical maps, A/T/U partition, ordinary tail and observation set; choose any `F_a/B_(s,t)` with `0<=a<=8`, `1<=s<t<=8`. | All **252** choices have a transported lost witness. For each of the 28 `(s,t)`, `B_s h=0` and the identity coefficient of `B_t h` is `2112 I`. Saving the original `h_(1,2)` by moving the pair does not remove the new pair's kernel. | This covers the 9-by-28 catalogue, not changed logger/response maps, new reads, arbitrary first maps or native frame legality. The trajectory fixtures use permutation stand-ins; the actual-route checks and written transport argument carry distinct parts of the evidence. |
+| **Cinna Davis, PR2079, pending**: [extra B2 read][extra] | Add a read-only pre-F0 record `B2 X_U` to the fixed-pair observation set. | It distinguishes the **eight displayed witness directions** of PR1969. A separate optimistic profile screen leaves only a small conditional margin. | Witness separation is not full selected-input recovery. The profile screen is not a legal read, retained record or complete supplier bill. |
+| **Adam Gall, PR2093, pending**: [expanded-observation kernel][nonzero] | The same fixed pair and ordinary tail, with all initial nonzero-chart ordinary reads `B_s X_U`, `1<=s<=8`, granted. | A different three-port witness has every `B_s h=0` for `s>=1`, but `B0 h!=0`; the original A input remains hidden. This answers the fixed-pair full-recovery question left by PR2079 negatively. | A `B0` record detects this witness but is not thereby proved sufficient. Rewriting the first pair, adding another kind of read, or granting a former-Y endpoint changes the contract. |
+| **commdata2338, PR2174, pending**: [two-query decoder][cut] | Add initial pair-0 records `q0=B0 X_U`, `q2=B2 X_U`; grant the post-B1 selected cut, histories `f0,f2`, and pair 0's final completed-X descendant. | An ordered decoder recovers **pair 0's four original A/T blocks for arbitrary inputs in all four bank pairs**. It uses cut values `p_A=X_A+Y_A`, `p_T=X_T+Y_T`, `d_A=Y_A`. | This does not recover every pair from two pair-0 records, replace the cut by final values, or implement the reads. Sixteen recorded coordinates are not sixteen paid rank units. |
+| **alephnan, PR2346, pending**: [final-record obstruction][final] | Ordinary-only bridges/terminal; no added selected intervention before completion of F2. Grant final selected values, completed-X descendants, all five forward histories and the **specified** 64 initial coordinates listed below. | On the actual regular owner cover `G`, the original pair-0 selected defect has dimension at least `ceil(8|G|/7)`. These records cannot replace PR2174's cut premise. | This does not exclude all choices of 64 coordinates, interventions before F2, or the separate first-six-selected-swap program. The family has nonzero selected values after B1 and becomes selected-zero only after F2. |
+
+For PR2346 the eight initial queries, each with eight coordinates per owner,
+are exactly:
+
+| Bank pair | Initial ordinary X records |
+| --- | --- |
+| 0 | `B0 X_(0,U)`, `B2 X_(0,U)` |
+| 1 | `B3 X_(1,U)`, `B4 X_(1,U)` |
+| 2 | `B5 X_(2,U)`, `B6 X_(2,U)` |
+| 3 | `B7 X_(3,U)`, `B8 X_(3,U)` |
+
+The reported failure concerns this list and these dynamics. It is not a
+transcript-width lower bound for arbitrary observations.
+
+## How the positive and negative results fit together
+
+PR2174 reconstructs the initial ordinary Y input through the ordered identity
+`Y_(0,U)^initial = Y_(0,U)^final - K_(2,U) f2`. It then uses `q0,q2` and
+`p_A,p_T,d_A` at B1 to recover the original selected inputs. The B1 record
+`d_A` is an explicit input to that decoder, not a consequence of the two
+initial reads.
+
+PR2346 supplies a family where every allowed final record is zero but the
+post-B1 `d_A` is nonzero. Its proof obtains compatible ordinary inputs from an
+intersection of two constrained query images. Each image has dimension at
+least `ceil(32|G|/7)` in an `8|G|`-dimensional space; after the required
+invertible selected transport, their intersection has dimension at least
+`ceil(8|G|/7)`. The written proof supplies the regular-cover existence
+argument; its finite fixtures alone do not establish that quantifier.
+
+There is therefore no conflict between the two results. Adding records while
+removing a previously granted observation cut is not a monotone enlargement
+of the observation set. Likewise, PR2079's detection of one family and
+PR2093's different invisible family can both hold.
+
+## Open next questions
+
+For one proposed successor, first state its first maps, every ordinary read,
+the exact time each record is taken, subsequent selected interventions, and
+which native endpoint types are observable. Then compare its complete
+selected-input kernel with the required output, rather than testing only a
+known witness. This is a task-definition step, not a claim that the resulting
+question is unclaimed.
+
+* **A changed first pair:** identify a hypothesis outside the 252-pair
+  catalogue, such as a changed logger or response. This avoids repeating a
+  covered route choice. The smallest test is the ordered first-pair map with
+  its compensated witness; a native boundary and full cost remain blockers.
+* **A final-only successor to PR2174:** show that its actual available records
+  recover `p_A,p_T,d_A`, or specify paid retention of those values. Compare the
+  early dynamics with PR2346 before using its obstruction. Full recovery and
+  legal native access are separate requirements; detecting that one family
+  is only the first test.
+
+Only after recovery survives should a candidate price all reads, retention,
+frame/cover maps, restoration, hosting, address work and precision. None of
+the six entries supplies a completed QQ16 supplier or changes the selected
+exponent. The related shear, tap, native-line and transcript-minimum work is
+outside this small index; consult the live board before choosing a mechanism.
+
+## Exact sources, reproduction and credit
+
+Scientific and guidance base: `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`,
+priority revision 4. The frozen heads are:
+
+| Source | Exact head | Package |
+| --- | --- | --- |
+| Ali Romman, PR1969 | `a6e6ad3936f67b8f63b5b68c5e75d540610a65e7` | `research/joint-query` (retained on the base) |
+| Philippe Van Velzen, first-pair catalogue | `261eb732c229cf523304e1c3cf7123251260c992` | `research/joint-query-first-pair-catalogue` in `philippeVV/integer-mult-bounds` |
+| Cinna Davis, PR2079 | `49df8190b158e3028e702b2c6b798117006f7249` | `research/joint-query-extra-b2-observation-seed3e62` |
+| Adam Gall, PR2093 | `8b21a900eb520e4f11ea177b310f66316f8e8983` | `research/qq16-b2-observation-kernel` |
+| commdata2338, PR2174 | `f79470a7931f3943360c10d15b428e0e4e479c22` | `research/qq16-two-query-kernel` |
+| alephnan, PR2346 | `653520d7f18f686ea3a274b4963981f5be563477` | `research/qq16-final-record-obstruction` |
+
+In an isolated checkout of each exact numbered head, use Python 3.12 and run
+`python3 -I -B scripts/research_package.py --package PACKAGE`, substituting
+the package path from the table. The registered commands include the
+predecessors' own controls; this is reproduction, not a code-disjoint proof
+audit. For the fork catalogue, at its exact head run
+`sh research/joint-query-first-pair-catalogue/reproduce.sh` without Python
+optimization: its trajectory and two mutation controls use assertions.
+These packages are pending evidence; the commands do not require adopting
+them into the selected construction or changing frozen source files.
+
+On 2026-10-15, all four registered PR packages above passed on CPython
+3.12.3, including their declared controls. The fork replay matched its complete
+committed JSON receipt, checked all 252 trajectories, and rejected both
+mutations. Local links and immutable Git targets were resolved. Main and all
+four PR heads were fetched again at 06:44 UTC and were unchanged. These are
+source inspection and predecessor replays, not new independent checkers.
+No full native supplier replay,
+formal proof, new compact regular-cover witness, global all-size admission,
+precision theorem or complete paid invoice is claimed. The source packages
+retain their own, narrower descriptions of what each executable checks.
+
+Task `scope-navigation`, scope key `b18e0e173a4430a9564b`, nonce
+`bafb6bd89e7033358716a71143cc59c7`, consolidation track. Scope is refined to
+this six-contract family: the onboarding first-pair suggestion lacked the
+later catalogue and did not distinguish recorded-cut recovery from final-only
+recovery. The claim is in discussion #2074. This map preserves the authors'
+results and their pending status; it does not repeat them as new theorems.
+
+Credit also belongs to Ross Richardson for the three-query rank method,
+Philippe Van Velzen for the four-bank final-record lead
+(`680d0997621a2cecfef2186ab143377658687825`), and the retained supplier,
+geometry and compiler lineage in the [QQ16 notice](../../research/joint-query/NOTICE.md).
+Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.
+No independent human review is claimed. Apache-2.0.
+
+[witness]: ../../research/joint-query/evidence/QQ16-SELECTED-WITNESS.md
+[rational]: ../../research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md
+[pairs]: https://github.com/philippeVV/integer-mult-bounds/blob/261eb732c229cf523304e1c3cf7123251260c992/research/joint-query-first-pair-catalogue/README.md
+[extra]: https://github.com/CrocSwap/integer-mult-bounds/blob/49df8190b158e3028e702b2c6b798117006f7249/research/joint-query-extra-b2-observation-seed3e62/README.md
+[nonzero]: https://github.com/CrocSwap/integer-mult-bounds/blob/8b21a900eb520e4f11ea177b310f66316f8e8983/research/qq16-b2-observation-kernel/README.md
+[cut]: https://github.com/CrocSwap/integer-mult-bounds/blob/f79470a7931f3943360c10d15b428e0e4e479c22/research/qq16-two-query-kernel/PROOF.md
+[final]: https://github.com/CrocSwap/integer-mult-bounds/blob/653520d7f18f686ea3a274b4963981f5be563477/research/qq16-final-record-obstruction/PROOF.md