Bound all-cut precision for the completed P104 identity word

research/p104-delayed-precision/NOTICE.md

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+# Source notice
+
+New precision replay, stream exporter, tests and proof are Apache-2.0 under the
+repository LICENSE.
+
+`producer.py` is retained byte-for-byte from Jose Manuel / jmbarrancoml's
+PR2139, commit `1df674ca8e9d9e0fb98ba4df402b648e9b3be0a4`, at
+`research/p104-delayed-query-side/verify.py`. The original README and source
+manifest are preserved under `predecessor/`, including their original notices
+and disclosures. The exporter and literal stream are not a newly claimed
+P104 construction.
+
+The producer consumes Ali Romman's `research/native-source-codes/source_data.py`
+and its immutable selected archive. Its original source-word, Hamming packet,
+mutable-source/target, native compiler and hosting credits remain authoritative.
+The native fixture and compiler/interpreter are inherited through Rohan Arun /
+PR1972 and Chafik Boukhalfa / PR1991. Adam Gall / PR1940 and Josie Elliston /
+PR1071 supply the preceding delivery geometry. Compiler credit remains with
+icekylinx and the retained native lineage; the independent Gaussian interpreter
+is Ali Romman's PR1862/PR1931 lineage.
+
+Relevant unchanged notice files remain at:
+
+- `research/native-source-codes/README.md` and its source manifest.
+- `research/p104-native-channel/notices/`.
+- `research/gauge44-slots-t16/NOTICE.md` and `UPSTREAM-NOTICE.md`.
+- The selected archive's pinned source credits, listed by
+  `research/native-source-codes/source_data.py` in `CREDIT_PINS`.
+
+Adam Gall / PR2096, exact head `f22626f334a06f6e842766e4a6647419e6821d2d`,
+supplies the Hilbert-norm independent-defect and state-relative feedback method
+on the different G/2 channel. No code or numerical constant from that package
+is copied here. Its combined-word precision handoff motivated this check.

research/p104-delayed-precision/README.md

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+# Precision of the completed delayed-query P104 word
+
+This supplies a finite local precision implication for Jose Manuel's
+[PR2139](https://github.com/CrocSwap/integer-mult-bounds/pull/2139), exact head
+`1df674ca8e9d9e0fb98ba4df402b648e9b3be0a4`. It does not supply a rounded
+recursive implementation, an admitted supplier or a new exponent. The
+predecessor's unfavorable fixed-profile cost screen remains unchanged.
+
+Adam Gall's [PR2096](https://github.com/CrocSwap/integer-mult-bounds/pull/2096)
+checks precision for the different `G/2` channel. Its next question 2 asks for
+combined prefix/error maps once a corrected chronological word is available.
+This result checks that implication on PR2139's completed forward identity
+word, rather than transferring the old channel's constants.
+
+## Exact result
+
+The norm is the maximum of individual register Hilbert norms. It is not the
+addresswise maximum norm. Let every independent initial register have norm
+at most `B`.
+
+| All-cut quantity | Exact coefficient |
+| --- | ---: |
+| Ideal input-to-register row norm `P` | 131072 |
+| Accumulation of independent unit absolute defects `A` | 1394705 |
+| Accumulation of independent weighted defects `K` | 2134050 |
+
+All three first attain their maxima after combined event **33373**, in source
+register **93**. Events are zero-based: 7686 initial compensation additions,
+then the predecessor's 26647 actions. The attaining instruction is
+`source93 -= 8*source103`. Its ideal row is
+
+```
+-65536 * input86 - 65536 * input93.
+```
+
+Input86 is one of the omitted source ports and is an arbitrary dirty helper.
+The final source row is just input93. The final target rows are `Y_t + X_t`,
+and all 628 dirty helpers restore their own inputs. Thus the ideal endpoint
+maximum of two cannot replace the all-cut coefficient 131072.
+
+[RESULT.json](RESULT.json) contains the complete 2-input and 29-defect
+attaining rows, all-cut norm-stream hash and endpoint error maxima. The
+checker visits every changed register after every instruction; untouched
+registers retain their preceding norm. Exact adapters preserve Hilbert norm,
+and exact resets cannot increase it. This covers the initial boundary and
+all 34333 subsequent instruction boundaries, not sampled cuts.
+
+There are 32722 defect sites: 28108 additions, 707 scales and 3907 positive
+native transports. There are also 32 exact private resets and 1579 exact
+phase/adapter annotations. The eight private copies are additions following
+owned initialization, not eight uncharged extra operations. Their later
+reset does not erase defects already propagated to another register.
+
+The full paid profile stays
+`2564 H1 + 547 H2 + 432 H3 + 142 H4 + 83 H5 + 128 H6 + 11 H7`,
+with rank mass 6782. No precision or recursive charge is removed.
+
+## Error contract and proof
+
+### Literal scalar reduction
+
+Use the predecessor's actual common unitary charts. A physical register at a
+cut is `Gamma_W z`. Each exact native transport is
+`Gamma_new Gamma_old^-1`; additions and scales have their literal rational
+coefficients in logical coordinates. Boundary monomial factors are exact.
+The inherited normalized Clifford factors are unitary in Hilbert norm; this
+is not a claim of addresswise contraction.
+
+An additive physical output defect at site `j` becomes
+`eta_j = Gamma_after_j^-1 e_j`, with the same Hilbert norm. Therefore every
+cut row has the exact form
+
+```
+z_r = sum_s a[r,s] * input_s + sum_j c[r,j] * eta_j.
+```
+
+The implementation retains signed dyadic coefficients until it takes the
+row's absolute sum. At every updated row it checks cached input, absolute and
+weighted norms against direct reductions of the complete coefficient maps.
+It does not multiply positive majorants throughout the word. A separate
+reverse-adjoint recurrence uses `Fraction` arithmetic and
+agrees on the attaining rows. Sign-aligned forward executions attain `P`,
+`A` and `K`. For arbitrary independent vectors, choose one unit vector and
+align each input or logical defect with the sign of its row coefficient.
+Unitary charts convert those logical defects to physical defects with the
+same norm. This proves sharpness for **independent additive vector defects**,
+not for correlated rounding errors.
+
+Exact private reset replaces only its current row by zero. Existing error
+symbols in other registers survive. Each later instruction has a fresh
+error symbol, so reusing the private field cannot alias different lifetimes.
+The replay independently checks all 844 initial columns, including the eight
+private columns, against the completed endpoint and full frame contract.
+
+### Absolute defects
+
+If every defect has norm at most `delta`, every cut has error at most
+`1394705 * delta`. This finite independent-defect coefficient is sharp.
+For example, `delta <= B * 2^(-b-21)` suffices for all-role error at most
+`B * 2^-b` for any integer `b >= 0`.
+
+### State-relative feedback
+
+Assume exact dyadic coefficients and a common `u >= 0` satisfying these
+completed-instruction output-defect bounds on the actual perturbed operands:
+
+- Native transport: `u * ||input||`.
+- Addition `dst += a*src`: `u * (||dst_before|| + |a|*||src_before||)`.
+- Scale `dst *= a`: `u * |a| * ||dst_before||`.
+
+Resets and monomial factors are exact. A recursively implemented transport
+must first meet this completed-output contract; its internal errors are not
+analyzed here. For a copy expressed as an addition after exact reset, the
+addition hypothesis is sufficient, but may overestimate its actual error.
+
+Put `w_j=1`, `1+|a|`, or `|a|` respectively at those sites. The sharp weighted
+independent-defect coefficient is `K=2134050`. If `M` is the maximum actual
+register norm over the finite execution, then
+
+```
+M <= 131072*B + 2134050*u*M.
+```
+
+When `2134050*u < 1`, rearranging gives
+
+```
+M <= 131072*B / (1 - 2134050*u),
+max_boundary_error <= 131072*2134050*u*B / (1 - 2134050*u).
+```
+
+For every integer `b >= 0`, **`u <= 2^(-b-39)` suffices** for all-cut error at
+most `B*2^-b`. Indeed,
+
+```
+K*(P+1) = 279716335650 < 2^39,
+P*K = 279714201600 > 2^38.
+```
+
+For `b >= 0`, `K*(P*2^b+1) <= K*(P+1)*2^b < 2^(b+39)`, which proves the
+claim for all `b`, not only the tested examples. The second inequality means
+38 uniform guard bits fail this particular sufficient feedback estimate.
+It does not prove a minimal numerical precision requirement. This estimate also does not justify subtracting 39
+bits from, or replacing, the selected production precision bill.
+
+## Source binding and replay
+
+[producer.py](producer.py) is byte-for-byte PR2139's original `verify.py`.
+Its original README and source manifest are under [predecessor/](predecessor/).
+`export_word.py` authenticates inputs before importing that producer, observes
+only the return of its `main` function, and exports its actual initial frames,
+final frames, every compensation coefficient, every action and frame basis.
+It does not alter the producer's operations or checks. The registered replay
+reconstructs and compares **every** exported field, not just a profile or hash
+from a submitted receipt. Native mode also runs the predecessor's 241 new
+recipe checks, all 421 bindings and its global-phase rejection control.
+Original selected native recipes retain their inherited proof and pins; this
+is not a fresh audit of every retained Clifford recipe.
+
+The default precision replay reads only `WORD.json.gz` and `RESULT.json`,
+needs neither Git nor network and writes nothing. It verifies the complete
+uncompressed word SHA256 before parsing. Full producer rebinding requires
+Git history for the original selected archive. Compressed bytes are not the
+mathematical regeneration comparison.
+
+From the repository root, standard-library CPython 3.12:
+
+```sh
+python3.12 -I -O -W error -B research/p104-delayed-precision/verify.py
+python3.12 -I -O -W error -B research/p104-delayed-precision/test_verify.py
+python3.12 scripts/research_package.py --package research/p104-delayed-precision --check-only
+python3.12 scripts/research_package.py --package research/p104-delayed-precision
+```
+
+`verify.py --write NEW_PATH` and `export_word.py --write NEW_PATH` create new
+files exclusively. The behavior suite checks seven separate endpoint adjoints,
+dyadic coefficient extremes, private-defect survival after discard, missing
+clear and baseline compensation, illegal charts, receipt/word corruption,
+changed-producer rejection before import, no overwrite, capacity limits and
+relocated read-only normal/optimized execution.
+
+Observed locally on Linux x86_64 with CPython 3.12.15: the complete registered
+replay passes, including new native phase checks and all nine behavior tests
+in normal and optimized modes. The 65 repository research-workflow tests and
+`python3 -B scripts/research_baseline.py` also pass. The latter checks selected
+source bindings only, not the selected cold replay. No hosted CI pass,
+proof-assistant run or independent human review is claimed.
+
+### Implementation bounds
+
+New replay loops have fixed stream bounds: 844 roles, 1008 frames of at most
+nine generators, 34333 events and at most one defect symbol per event. Input
+files are capped at 4 MiB compressed and decompressed. Receipt generation
+observed at most 671250 live error coefficients and a maximum row denominator
+of 54 bits. The optimized direct replay took 3.27 seconds with 114768 KiB peak
+RSS on the stated Linux/Python environment. These are local measurements,
+not portable resource guarantees. The registered commands have explicit
+120/240-second limits.
+
+Python requires dynamic allocation and dictionary dispatch. These are
+managed-runtime deviations from Power of Ten rules 3 and 9, bounded by the
+fixed domain above; there is no ambient registry or unbounded queue. Rule 8
+also has a narrow replay-only deviation for importing the authenticated
+producer and a return-profile callback with one known target, restored in
+`finally`. The independent precision verifier does neither. All new functions
+fit within 60 lines; Python warnings are errors in the registered checks.
+No separate type checker or linter was available locally; strict compilation
+and execution are the available diagnostics, not a substitute for type analysis.
+The preserved producer and loader contain long functions and historical
+library/control-flow patterns. They remain immutable predecessor inputs,
+not refactored code. Their compensating controls are source authentication,
+fixed input geometry, exact regeneration and bounded replay. A future
+predecessor API change would require a separately source-bound successor.
+
+## Open next questions
+
+1. Bind an actual rounded rank-1 through rank-7 child to the completed-output
+   Hilbert defect hypothesis. First test the exact rounding convention at
+   `u <= 2^(-b-39)`. The missing implementation/interface, not native unitarity,
+   blocks recursive precision admission.
+2. Reduce the source93 transient while retaining the full dirty boundary and
+   bill. First inspect the gauge/scalar cleanup interval around event33373,
+   propose one exact resynthesis, and replay all columns and paid operations.
+   Common-chart legality and arbitrary dirty restoration are required.
+
+Global owners, the dual word, tape/all-size lifting and supplier admission
+remain open. PR2139's fixed-profile cost obstruction still applies. Neither
+finite precision implication nor automated verification is a complete
+multiplication theorem or independent human review.
+
+## Credit and freshness
+
+Jose Manuel / PR2139 supplies the entire corrected construction. Adam Gall /
+PR2096 supplies the Hilbert-defect and feedback method on the older channel;
+no constants or code from that package are imported. Rohan Arun / PR1972,
+Chafik Boukhalfa / PR1991, Ali Romman's source reconstruction and Gaussian
+interpreter, Adam Gall / PR1940, Josie Elliston / PR1071, icekylinx's Clifford
+lineage and the selected Hamming/dirty-helper contributors retain their
+original attribution. See [NOTICE.md](NOTICE.md) and the retained source
+manifest. New material is Apache-2.0.
+
+The scientific base is canonical main
+`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, priority revision 4. The sole chooser
+nonce is `159427fb87da401855d7b74679378fb5`. [TASK.json](TASK.json) records the
+changed scope and overlap limits. The canonical coordination claim is in
+[Discussion2121](https://github.com/CrocSwap/integer-mult-bounds/discussions/2121#discussioncomment-18934115).
+No selected record, frozen predecessor or review disposition is changed.