Audit P104 private-copy lifetimes and price a copy-free query route

research/p104-copy-retirement/PROOF.md

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+# Literal private-copy lifetimes and a paid replacement
+
+All indices below are zero-based in the pinned 4,058-event PR1972 word retained
+by PR1991. This is a fixed-word ownership and changed-local-route result.
+It is not a universal lower bound on P104 copies, encoders or suppliers.
+
+## The actual eight lifetimes
+
+Let q_j be the exact normalized row in Q_j when it is copied. Sparse rational
+induction from all 280 independent inputs gives
+
+    q_j = h_Qj + sum_i a_ji x_i,
+
+with coefficient 1 on h_Qj, coefficient 0 on all other dirty inputs, and the
+source coefficients recorded in RESULT.json. No zero-input assumption is used.
+The original source gather produces these rows; they are not an assumed query.
+
+| Query | C initialization | Copy | Rank-seven descent | Last C read | C erase | Delivery helpers |
+|---|---:|---:|---:|---:|---:|---|
+| Q0 | 2461 | 2462 | 2463 | 2468 | 2469 | D0–D4 |
+| Q1 | 2470 | 2471 | 2472 | 2475 | 2476 | D5–D7 |
+| Q2 | 2477 | 2478 | 2479 | 2483 | 2484 | D8–D11 |
+| Q3 | 2485 | 2486 | 2487 | 2491 | 2492 | D12–D15 |
+| Q4 | 2493 | 2494 | 2495 | 2499 | 2500 | D16–D19 |
+| Q5 | 2501 | 2502 | 2503 | 2506 | 2507 | D20–D22 |
+| Q6 | 2508 | 2509 | 2510 | 2514 | 2515 | D23–D26 |
+| Q7 | 2516 | 2517 | 2518 | 2523 | 2524 | D27–D31 |
+
+Each private C starts at zero in the same eight-dimensional chart W_j as Q_j.
+Copying sets its normalized row to q_j. The literal transport takes C to a
+one-dimensional chart L_j contained in W_j; every reader is an addition
+D_k += C in that L_j chart. The private row remains q_j until erase. Since its
+h_Qj coefficient is 1, it is not zero. The inherited owned-private erase
+semantics permit discarding C; this does not permit discarding a public dirty
+Q_j or D_k. Only one C is live at a time, and none is live after event 2524.
+There is therefore no surviving C role at the completed #3882 boundary whose
+future lifetime can be silently credited as retirement of the paid descent.
+
+The 32 D helpers are actual consumers, not hypothetical available banks.
+RESULT.json records their first downstream reads and their cleanup events
+3579, 3581, ..., 3641. The cleanup subtracts the corresponding q_j after both
+roles reach FULL. Q_j itself remains unchanged from copying until its FULL
+transport at 3570+j, and is restored by the final source cleanup.
+
+## Removing delivery is observable downstream
+
+Remove all eight private intervals while retaining every public event.
+At each D_k in the j-th group, the missing addition leaves normalized defect
+−q_j. The later public program is linear. The exact complete replay shows:
+
+* X, Q and G final rows are unchanged;
+* all 32 D returns have defect −q_j;
+* the target defect and the complete public defect each have rational rank 8.
+
+The eight independent h_Qj columns already attain rank 8. In particular, take
+one h_Qj arbitrary and every other logical input zero. This is an explicit
+permitted dirty input, not a probability or generic-rank argument.
+
+Continue both original and mutilated words through the actual pinned #3882
+schedule. That schedule acts only on X/Y and is invertible in normalized rows.
+Our new evaluator uses its unchanged geometry/program builders but not its
+arithmetic evaluator. The 104 physical sum slots (Y_J, X_N) still have defect
+rank 8. All 32 D defects survive unchanged because the tail never touches D.
+Thus correct sums and dirty returns cannot be obtained by simply deleting the
+copies or their 32 uses. This is not a proof against changing the producer,
+consumer, other delivery operations or output contract.
+
+## A concrete copy-free local replacement
+
+Write T_j = Gamma_Lj Gamma_Wj^{-1}. Replace each private interval by:
+
+1. apply T_j directly to Q_j;
+2. perform the same D_k += Q_j additions in L_j;
+3. apply T_j^{-1} to Q_j.
+
+At the entrance let the physical query be Gamma_Wj q_j and each D value be
+Gamma_Lj d_k. The exact endpoint is
+
+    Q_j -> Gamma_Wj q_j,
+    D_k -> Gamma_Lj (d_k + q_j).
+
+Every other role is untouched. This equals the original private-copy block on
+all arbitrary inputs. Eight block substitutions consequently preserve the full
+280-row channel endpoint and the actual #3882 continuation. There are no
+private zero/copy/erase events, and no dirty role is erased. The maximum local
+register count drops from 281 to 280; this is a local workspace observation,
+not a global width or recursive saving.
+
+The source certificate supplies the forward native recipes. RETURN-RECIPES.json
+contains eight newly lowered reverse recipes. native.py independently checks
+the physical label mapping at each literal event, exact signed Clifford action,
+global phase, both rank-seven child charges, 8,192 Gaussian columns (512 in each
+direction for each block), and the identity T_j^{-1} T_j. It rejects a changed
+global phase. It reuses the credited exact compiler/interpreter and does not
+repeat the complete inherited channel's native proof.
+
+## The price and its scope
+
+The original eight private descents cost 8*7 = 56 rank mass. The replacement
+uses eight descents and eight returns, costing 112. The query-freeing saving
+is eight zero operations, eight copies, eight private erases and one peak
+local array; the positive recursive-child bill increases by 56.
+
+For the restricted direct-Q route, this rank cost is sharp under the retained
+nested transport tariff. A path from dimension 8 through dimension 1 and back
+to dimension 8 has sum of absolute dimension jumps at least 7+7. The two direct
+transports attain that bound. If restoration is delayed until the existing
+FULL consumer, the 8 -> 1 -> 9 path costs at least 15, versus the original
+private drop 7 plus Q's existing 8 -> 9 lift 1, again seven extra. This bound
+fixes the same delivery chart, same Q owner and same later public consumers.
+It excludes replacement encodings, coupled roles, altered production or new
+non-nested/native primitives.
+
+| Complete local bill | Original channel | Copy-free replacement |
+|---|---:|---:|
+| Native profile, ranks 1 through 8 | 1074,58,86,104,48,24,8,8 | 1074,58,86,104,48,24,16,8 |
+| Rank mass | 2368 | 2424 |
+| Scalar array additions | 2624 | 2624 |
+| Native transport occurrences | 1410 | 1418 |
+| zero / copy / erase | 8 / 8 / 8 | 0 / 0 / 0 |
+| Total events | 4058 | 4042 |
+| With the unchanged #3882 208-H1 tail | 2576 | 2632 |
+
+The positive-child counts include all eight returns. Their actual Gaussian
+monomial wrappers are retained in the recipe file, not treated as positive
+recursive children. We do not claim a runtime saving: wrapper execution,
+precision, signed-floor behavior, memory/routing/control and all-size admission
+remain separate obligations. Unknown physical costs are not assigned zero.
+
+As a conditional substitution into #3954's stated 208-call, m=81, W=36608
+scaffold and the same persistent-progress allowance, its already failing
+M_0 numerator excess grows from 44096 to 55744. Granting all 208 correction
+rank units per local call for free would leave 832 excess for the original
+COPY56 channel and 12480 for this replacement. These are scoped favorable
+relaxations, not an actual two-axis construction or a general P104 barrier.
+For 0 <= a < 1, (r/81)^(1-a) >= r/81, so failure at zero also fails every such
+moment under those same hypotheses. The replacement does not justify another
+dependent construction round. A new route must eliminate real work with a
+changed producer/consumer or coverage contract and price every obligation.

research/p104-copy-retirement/README.md

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+# P104 private-copy lifetime and retirement audit
+
+The eight inherited COPY lifetimes are live deliveries of arbitrary dirty
+queries. Deleting them breaks all 32 delivery-helper returns and leaves a
+rank-eight defect in the actual #3882 sum outputs. A concrete copy-free
+replacement restores every public input/output and removes one peak local
+private array, but costs **56 extra native rank units**. It cannot repair the
+failed #3954 two-axis budget.
+
+This source-bound result adds the exact lifetime/consumer map, deletion
+counterexamples, a fully priced direct-query replacement, and eight phase-exact
+native return recipes. It does not rediscover or generalize the old COPY56
+floor. The lower bound is restricted to taking the same Q role through the
+same delivery chart and returning it to its fixed later consumer.
+
+See [PROOF.md](PROOF.md), [RESULT.json](RESULT.json) and
+[RETURN-RECIPES.json](RETURN-RECIPES.json). All 280 independent logical rows and
+72 arbitrary dirty helpers are explicit. The normal and optimized Python
+checks require only Python 3.12's standard library:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-copy-retirement
+python3.12 -B scripts/check_research_commit.py --package research/p104-copy-retirement --check-source-history
+```
+
+The first command checks exact scalar/frame composition, the unchanged actual
+#3882 tail, and the eight local native reverses on all 512 Gaussian columns in
+each direction, with ownership/frame/rank/global-phase controls and seven actual optimized CLI
+rejection fixtures for malformed receipts and changed/missing sources. It does not
+repeat the full inherited native channel, signed-floor or supplier proof.
+RETURN-RECIPES.json can be independently regenerated with
+`python3.12 -B research/p104-copy-retirement/native.py --generate`; ordinary
+verification is read-only. The compiler and independent native interpreter
+remain separate retained predecessor implementations; they are not new here.
+
+`SOURCES.json` pins canonical inputs at main
+`20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority revision 6. The exact PR3882
+schedule builder is a self-contained unchanged source export with its original
+head/path/hash; cold replay does not require an unmerged Git object. Its builder
+is reused, while the row evaluator and ownership audit are new. Original task
+card and bounded changed scope are retained in `TASK.json`.
+
+## Scope and remaining obligations
+
+The replacement is a finite local native rewrite with the inherited endpoint
+contract. No new kappa, source-preserving correction improvement, scalar
+optimum, universal copy lower bound, actual global owner map, opposite-orientation
+supplier or selected-frontier change is claimed. General resynthesis may change
+these conclusions by changing their stated contract. The conditional #3954
+arithmetic is a losing complete-cost relaxation, not supplier admission.
+
+Entry overlap used all 662 open PR bodies including drafts over seven pages,
+a bounded read of current Discussions by the coordinating agent, and the
+repository helper. The helper had no Discussion cache and sparse local notes;
+this is not proof of novelty. PR3956 already completes the 960-versus-1152 ADD
+comparison, which this package does not repeat. Sibling adjacent-encoding and
+coverage audits are separate scopes.
+
+## Open next questions
+
+Can one concrete changed delivery consumer avoid the Q descent/return pair
+while still restoring every actual dirty D helper? This matters because the
+source-bound copy-free replacement worsens the recursive invoice. First derive
+one replacement block on all Q/D inputs and its physical charts, then test a
+complete cost gate before expanding it. Fixed lifetime deletion and direct-Q
+retiming are closed only within the restricted contracts above. A changed
+encoding, producer or coverage obligation is required to reopen this route.
+
+## Credit
+
+Rohan Arun / PR1972 owns the complete dirty-restored gather, query production,
+COPY56 word and cleanup. Chafik Boukhalfa / PR1991 owns its concrete finite
+native realization and complete channel induction. Adam Gall / PR1940 supplies
+the retained 32-chain delivery schedule. Chris R / Clear1nsight owns PR3882's
+source-consuming correction and PR3940/PR3943/PR3954 caller work; PR3956's
+matched return comparison is credited to ToikY. Josie Elliston's E8 fixture,
+Sagar Thakrar, Douglas Colkitt, Dominik Scholz, the retained Clifford compiler
+(icekylinx PR531 and its lineage), and PR1862's independent interpreter retain
+their source attribution. Existing notices in p104-native-channel are unchanged.
+
+New lifetime audit, local rewrite, eight return recipes and tests prepared for
+Chris R / Clear1nsight with substantial OpenAI Codex assistance, including a
+separate coordinating-agent dirty-column check. No independent human or formal
+proof-assistant review is claimed. Apache-2.0.