[thakrarsagar]

Change and mathematical scope

For a rational matrix X, every complex fixed-reader single lift has a rational representative with identical support pairs in all rank-one terms. This extends @woklerx's #998 reciprocal-projection argument from complex-to-real descent to every infinite base field. The proof uses a linear functional on a finite span, avoiding finitely many polynomial roots. A 1 by 1 F4-to-F2 counterexample identifies a genuine boundary of the statement.

The P112 consequence is equality of the attainable ordered nine-term support-cost vectors over Q, R and C. Mihir Srivastava's #845 floor 64 remains inherited. There is no new kappa, physical supplier, coefficient-height bound, terminating rational search, or efficiency-preserving compiler claim. The proof allows arbitrary complex inputs, while the exact implementation demonstrates inputs with supplied quadratic-field coordinates. This differs from #998's already-effective Gaussian rational examples and #1098's Gram spectra.

Nine new files live only in research/rational-lift-descent-seed95/. Base: ba82555c64e1879e4b7decce28186f208fcb8262. SOURCES.json pins six predecessor files and records the historical selected context. The six dependencies are unchanged at refreshed main ce7ad1b6ab09452c3478723a2e96ed5ff212dc08. Existing sources, upstream/ and the selected frontier are unchanged. Seed 95 selected research consolidation; the local claim records the alternatives and overlap checks.

Credit: @woklerx for reciprocal support transfer, @mihir-s-05 for the real obstruction, DreamingOfClouds for P112 geometry and the copy interpretation, and GamingPuzzled / Joel Pulikkan for the coordinate cost. New work is Apache-2.0 with substantial OpenAI Codex assistance, disclosed in NOTICE.md. No independent human or proof-assistant review is claimed.

Validation

rtk proxy python3.11 -I -B research/rational-lift-descent-seed95/verify.py
rtk proxy python3.11 -I -O -B research/rational-lift-descent-seed95/test_verify.py

• CPython 3.11.15 and 3.14.8 on macOS arm64, normal and optimized verification: nine exact examples, all 162 declared scalar lifts, five mathematical controls, a degree-two avoidance example, and all four F2 candidates pass. The written proof establishes the uniform theorem; finite checks test its implementation and counterexample.
• Relocated minimal source closure passes. Four certificate mutations and one source mutation reject. Certificate regeneration is byte-identical, SHA256 1d4cd17ba4970a62624d378c402422c074e5d5dcc73a3700df10077bc618f0d7.
• The pinned geometry builder and its checks confirm the corollary's 112 by 8 rational matrix, with all 896 entries in {-1,0,1}. Whitespace and isolated-diff checks pass.

The predecessor's full support census, full make verify, selected-supplier cold replay, Linux and formalization were not run. The inherited physical and analytic assumptions remain. Search coverage and stopping rules are explicit in the package; no previous decoder search was repeated.

[Mister-Meeseeks]

100-PR batch review at 8301a4698152cf63d3b4992145ecc8621942a6cd.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Support-preserving reciprocal-projection descent over any infinite base field, with a finite-field counterexample; only fixed-reader single-lift support costs are preserved.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.