Map paired-plane endpoint, rank and native cost contracts

docs/research/complex-decoder-scope-map.md

@@ -6,6 +6,10 @@ leave every retained obstruction. Conversely, a masked identity is outside these
 all-pairs theorems. Check [live overlap](../../autoresearch.md#1-orient-briefly-then-choose-a-distinct-task)
 before calling a class outside these hypotheses an open problem.
 
+For the fixed paired-plane masked endpoint, use the
+[paired-plane contract map](paired-plane-contract-map.md) to distinguish binary
+label identities, scalar/vector fitting rank and native payload costs.
+
 ## Shared model and the three boundaries
 
 The roots have squared norm two. If `R` contains the live E8 root-line

docs/research/paired-plane-contract-map.md

@@ -0,0 +1,100 @@
+# Which paired-plane quantity is being optimized?
+
+For the fixed 56 matched planes on 112 selected ports, **126, 112, 49 and
+224 measure different things**. A scalar fitting rank of 49 does not replace
+the 224 native copy mass of an independent-block implementation. Use this map
+when leaving the [all-pairs decoder bounds](complex-decoder-scope-map.md) for
+a masked paired-plane decoder.
+
+## Fix the endpoint first
+
+Write `E_i` for the plane of port `i`. For source `E_j -> FULL` and target
+`0 -> E_i^perp`, a normalized scalar decoder must satisfy
+
+```text
+K_ii = 1;
+K_ij = 0 when i != j and E_i is not orthogonal to E_j.
+```
+
+The diagonal block on the two ports of each plane is therefore `I_2`, not an
+all-ones block. Entries on orthogonal-plane pairs are free. The permission
+relation is symmetric; the values of the free entries need not be symmetric.
+These are ordinary scalar equations, even when the planes are labelled over
+`F_2`. PR1889's [two-port obstruction](../../research/paired-plane-scalar-mask-obstruction/README.md)
+explains why a binary label identity does not supply this endpoint.
+
+## Contract map
+
+| Result and credit | Exact object and quantity | What must still be supplied |
+| --- | --- | --- |
+| [PR1825](../../research/paired-plane-port-matching-seed6c563a/README.md), Cinna Davis / 1337isnot1337 | Binary factorization of the selected label-pairing matrix, with 56 matched planes and 16 nonzero query matrices. Its B14 support-pairing invoice is **126**. | This binary identity is not the displayed scalar fitting identity. PR1889 rules out its parity-preserving integral lifts, including free endpoint corrections; a new scalar construction is needed before using the optimistic moment. |
+| [PR2126](https://github.com/CrocSwap/integer-mult-bounds/blob/06be72298adf84f3eef0e36f54ac31c357956417/research/paired-plane-identity-fit-seed21ef98/README.md), Cinna Davis / 1337isnot1337 | `K=I_112`, factored into 56 rank-two coefficient blocks. The exact B14 support-pairing invoice is **112**. The scalar endpoint is valid. | The coefficient-block bill does not account for native payload multiplicity. It is neither scalar rank 49 nor a complete physical copy invoice. |
+| [PR2203](https://github.com/CrocSwap/integer-mult-bounds/blob/c3c85ea8c226640334b1d2246071f230d81cc137/research/paired-plane-native-payload/README.md), Jeremy Diviney | Under the independent matched-block / one-array-per-copy contract, each plane needs two independent payload arrays. There are **112 rank-two copy occurrences**, copy mass **224**, and full native profile `{7:224, 2:112}` of rank mass **1792**. | This is a bill for that implementation contract. Separate block floors do not automatically add for a jointly mixed multi-plane realization. Low simultaneous storage does not reduce the number of copy lifetimes. |
+| [PR2484](https://github.com/CrocSwap/integer-mult-bounds/blob/4823273c8163e4c72472bdf7d42202e2c12d2e46/research/paired-plane-minrank-bracket-audit/README.md), thakrarsagar | Minimum ordinary scalar fitting rank is **49 over every field**, for this exact mask. A partition gives the upper bound; an isolated `I_44` plus a ten-port C5 core gives the lower bound. | Algebraic query dimension is not the sum of binary support-pairing ranks or legal native COPY charges. A realization must price its supports, payloads, transports and restoration. |
+| [PR2541](https://github.com/CrocSwap/integer-mult-bounds/blob/cfe0f7f450cca3b8490ea8073a0e585bdf174e22/research/paired-plane-block-rank/README.md), ywz65 | For `d` coordinates per port, diagonal `I_d`, and the same forbidden blocks, minimum rank is **49d**, allowing arbitrary nonsymmetric, noncommuting free blocks. Thus linear queries of capacity `d` need at least 49 channels. | This is a linear query-dimension theorem. It does not impose a native bill of49 or224. Changed masks, side information, unequal port dimensions or nonlinear mechanisms need their own statements. |
+
+For PR2203 the distinction is already visible on one plane: broadcasting one
+payload produces the all-ones `2 x 2` matrix, of rank one; two independent
+outputs require `I_2`, of rank two. Its positive broadcast example is legal
+for the broadcast contract and fails the identity contract. Conversely,
+PR2484's rank 49 construction mixes the fixed mask globally; PR2203 does not
+exclude that construction by summing independent-block floors.
+
+For vector queries, the C5 block bound in PR2541 is `ceil(5L/2)` for block
+dimension `L`. Substituting `L=2d` in the isolated core yields `5d`, then adding
+`44d` gives `49d`. The argument is not the invalid rule that every scalar
+minrank bound tensorizes: PR2541 includes a scalar-C5 rank3 versus block-size2
+rank5 control.
+
+## Choose the next check
+
+For a proposed binary decoder, check the scalar endpoint before pricing it.
+For a scalar or vector fitting matrix, give its factors and specify whether
+the quoted number is query dimension, support-pairing rank, or native copy
+mass. For a native realization, enumerate independent payload arrays and
+every COPY lifetime, then include legal level transitions and restoration.
+Only a complete charged implementation can be compared with the selected
+supplier's budget. None of the rows above establishes a new selected kappa.
+
+The unresolved joint implementation question is concrete: can a realization
+of the rank 49 fitting matrix share work across planes while meeting the
+physical endpoint and paying a favorable complete invoice? First expand one
+global factor into actual payloads and legal native operations. PR2203's
+independent-block bill is a baseline, not a theorem for every such expansion.
+Check [live overlap](../../autoresearch.md#1-orient-briefly-then-choose-a-distinct-task)
+before taking this handoff; this map does not certify that a question is unclaimed.
+
+## Sources, validation and scope
+
+This is a navigation contribution, not a new proof or maintainer disposition.
+At canonical main `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, PR1825 and PR1889
+are merged; PR2126, PR2203, PR2484 and PR2541 remain open. Their linked full
+commit IDs pin the inspected versions, regardless of later PR updates.
+The merged source heads are respectively
+`d16fb8936795ff101e4d2f63cfdc6a25066ebabf` and
+`5f05652c7dc7f51555ddb59b716000199a72c0ff`.
+
+Validation checks the source heads, quoted contracts and local link targets,
+plus `scripts/research_baseline.py` for selected-record bindings. It does not
+independently rerun all six research packages or the selected supplier's full
+cold replay. Follow each pinned README for its exact proof, checker and limits.
+PR1889 credits ctoth and collaborators in Discussion 1587 for the plane
+endpoint; PR2203 credits that thread for the earlier 224 baseline and
+PhilippeVV's stronger integral floor. Those attributions are preserved here.
+
+Task `scope-navigation`, priority revision 4, nonce
+`4843ad9aee96bd899b94e4d5e09c9359`, scope key `fff26335d457e528d9c4`.
+The card is refined to this fixed-mask family because the existing all-pairs
+map does not distinguish these pending masked endpoint and cost results.
+Coordination: [PR2484](https://github.com/CrocSwap/integer-mult-bounds/pull/2484).
+Prepared for ywz65 with substantial OpenAI Codex assistance and separate AI
+review; no independent human review is claimed. Apache-2.0.
+
+## Open next questions
+
+Can the rank 49 factors be compiled to a fully charged native implementation
+that improves on the independent-block baseline? Which query-factor supports
+permit sharing without changing the fitting mask or losing independent
+payloads? These questions require explicit operators and costs, not merely a
+smaller scalar matrix rank. Source interpretation, owner/hosting obligations
+and the all-size supplier interface remain separate checks.