Generate exact chronological compiler library tables with product aggregation and explicit binary and tape cost bounds

research/quantitative-rank-library/NOTICE.md

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+# Attribution and license notice
+
+New material is prepared for CubeJerry with substantial OpenAI assistance
+under the repository's Apache-2.0 license. It is a scoped proof, an exact
+metadata reference and a bounded literal-word checker.
+
+The unchanged reference texts preserve their own authorship and assistance
+notices. SOURCES.json pins their exact canonical commits, paths and bytes.
+The principal premises are Jacob Alan Sussman's integer compiler, zxv's
+chronological construction, Mihir Srivastava's batch/growth work,
+codyw912's plateau divisor, Nick Petalas's rank/homogeneous bounds and
+#5071's symbolic recurrence. None is claimed as new here.
+
+The tape worker independently supplied and checked the n=135 exit-pooling
+control. Root and peer reviews describe their own methods and snapshots.
+No independent human or proof-kernel acceptance is implied.

research/quantitative-rank-library/PR-TITLE.txt

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+Generate exact chronological compiler library tables with product aggregation and explicit binary and tape cost bounds

research/quantitative-rank-library/PR.md

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+## Change and mathematical scope
+
+The retained compiler proofs bound finite widths but leave numerical library
+generation and full native-word generation as different obligations. This
+package supplies an exact evaluator for all smaller-rank metadata under the
+fixed separated default-height, least-chronological batching policy. It
+constructs evaluated integer replication, productive width, expanded
+rank-one leaf count and expanded mixed-unit count at every rank through N.
+
+Ordered target-role and paid-position product tables recover the source
+census without enumerating paid paths or individual unit slots. Every
+source-complement divisor and every original one-job exit divisor remains
+present. Repeated exits may aggregate additive cost, but their counts may
+not cancel individual invocation denominators.
+
+The written theorem gives explicit parameter-dependent K/Z bounds. For
+each fixed rule, the indexed metadata computation takes N times a fixed
+power of log N in bit work. A separately specified fixed-tape scan
+construction takes N squared times a fixed power of log N, with library
+access, arithmetic, sorting, copies, resets, erasure and historical backing
+charged. This outputs N rows; it is not polynomial in the input length log N.
+
+## Exact result and novelty
+
+The gcd/LCM law is inherited from #4507 and #5071. The width divisor comes
+from #4638, with #5962's sharper multiplicative-rank refinement credited.
+The new result is compressed exact all-rank metadata generation and its
+complete bit-cost accounting. A normalized contracting-chain argument
+bounds fully expanded leaf and mixed-unit counts without assuming positive
+rank surplus. No factorization or unevaluated arithmetic-expression oracle
+is used. Old nested widths are a different policy and are not substituted.
+
+This complements the source-occurrence and complement-port codecs at
+[CubeJerry commit bd63147](https://github.com/CubeJerry/integer-mult-bounds/tree/bd63147b1a193f68b5713e5814ac3b2c743beff8/research/source-complement-port-index).
+It supplies their numerical smaller-library data, not the validity or
+physical implementation of the smaller native programs.
+
+## Sources and reproduction
+
+Canonical base: `e54523517d0f03e58352e647c403a5af3e525a57`.
+`SOURCES.json` authenticates eight unchanged theorem/context texts by exact
+commit, path, Git blob and SHA-256. There are no imported predecessor
+executables. From the package directory, Python 3.12 and standard library:
+
+```sh
+python -I -W error -B verify.py
+python -I -O -W error -B verify.py
+```
+
+Expected status: `PASS_QUANTITATIVE_RANK_LIBRARY`. Normal and optimized
+receipts agree. An independent literal role-word/path oracle checks all
+four library integers via prime deficits and normalized Fraction recurrences:
+35 fixtures, 1,061 library rows, 24,586 units, 51,727 cuts and 14,278 sources.
+Fifteen rejection controls include cut pooling, product overwrite, missing
+matched-job subtraction, fit equality, missing outer units and merged roles.
+Two fixtures have negative rank surplus.
+
+A larger 2,048-row negative-surplus case has maximum 336-bit output values.
+It inspects 85,044 product pairs while leaving 387,420,489 maximum-depth
+paid paths unexpanded. The #6612 homogeneous formula is checked on 1,023
+rows as credited calibration. Separate root and tape-worker reviews add
+their own literal constructions and complete-cost checks.
+
+## Limitations and kappa status
+
+**No new kappa.** The selected conditional `0.00363005817` is unchanged.
+No selected certificate is edited and no selected astronomical library or
+1920-fold word is emitted. Fully encoded native-word size still needs
+local scalar-word, coefficient and adapter production bounds. Native
+all-column semantics, whole-job adapters, ownership/erasure, physical
+stock/routing, precision/tapes, analytic recovery and all five foundational
+assumptions remain conditional. O_n counts expanded mixed-unit occurrences;
+it is not live memory. Python is not the separately priced tape procedure.
+
+## Credit and assistance
+
+Prepared for @CubeJerry with substantial OpenAI assistance in proof,
+implementation and verification. Credit Jacob Alan Sussman for the integer
+lockstep compiler; zxv for the retained flow; Mihir Srivastava (#4507/#4586),
+codyw912 (#4638), Nick Petalas (#5962/#6612), #5071's symbolic recurrence,
+the published source-row/port packages and all retained native/flow lineage.
+The separate tape worker supplied the strict-separation n=135 pooling
+control. Reference notices are unchanged. Independent human and formal
+proof-kernel acceptance are not claimed.
+
+## Independent acceptance checks
+
+[REVIEW.md](REVIEW.md) records the root's separate proof/code review and
+literal target-field/parent-edge oracle. That oracle checks every census and
+all four library outputs for seven fixed rules and 336 complete ranks, with
+zero/negative surplus and coincident products included. It rejects an actual
+exit-pooling mutant on the smaller n=12 witness, an exceeded rank budget and
+a nonseparated rule. [The complementary peer review](peer-review/REVIEW.md)
+independently authenticates the retained width/flow sources, audits all
+indexed and sequential costs, and verifies a different n=135 cut witness.
+
+```sh
+python3 -I -W error -B research/quantitative-rank-library/independent_check.py
+python3 -I -W error -B research/quantitative-rank-library/peer-review/exit_cut_control.py
+```
+
+Final packaged author normal and optimized runs agree. The independent
+scientific receipts pin the reviewed bytes. No human or proof-kernel
+acceptance is inferred. The complete proposed PR description is `PR.md`.
+
+## Open next questions
+
+Can the evaluated leaf/unit counts be bound to an actual emitted native
+scalar-word and owner manifest with a complete bit-output/production bound?
+This matters because numerical library generation does not by itself
+construct the smaller programs. The first step is to audit the retained
+#6878 occurrence adapters and the native word's constant encodings; the
+obligation is blocked by any missing uniform local-word/adapter producer.