[ToikY]

PR3987 proves that the source's canonical binary lift can accumulate an even-linear phase character, including its actual inverse witness. This adds an explicit normalization tag and an arbitrary signed-word certificate for that same source convention.

Set D|x>=i^wt(x)|x> and J_G=D P_G D†. Then J_H J_G=J_HG exactly, K_G=J_G Z_tG, and ell(G,H)=tG+GᵀtH+tHG. The coordinate formula for tG and its polar/parity proof apply in every positive dimension. The tool tracks chronological pullbacks, distinguishing a canonical binary-inverse lift from the actual adjoint. These are elementary normalization results; the general cocycle proof and inverse-defect witness remain Chris R/Clear1nsight's PR3987 credit.

The phase tags also specify the required frame compensation: K_B C K_B†=J_B(Z_tB C Z_tB)J_B†. For the source primitive C_u, an anticommuting tag gives Z_t C_u Z_t=i C_u†, including the mandatory global i. Dropping tags or this global phase changes the operator. Switching to J requires compensated children, recipe rebinding and a paid physical contract. The author's existing correct adjoints and native recipes are unchanged. No free Pauli, native tariff, supplier or new κ is claimed.

Validation at exact head d593941, tree0176da010b09a1fdd96235e13508f8bcadd80261:

• Registered Python3.12 metadata/pins and all three commands pass.
• Separate implementation imports no primary/predecessor executable: all168 GL(3,2) maps, all28,224 ordered pairs/all8states,5,376 compensated frame columns,2,688 naive-frame mismatches, four actual9-bit maps/all512states, eight signed prefixes and1,024 central-C branch columns.
• Twelve API cases plus eight actual CLI source/certificate mutations give40 normal/-O rejections; six independent source rejections. Controls distinguish transpose/order, wrong adjoint, omitted tags and missing global i.
• Exact16-file byte/source-history preflight and official export/check pass. All three standalone commands pass normal/-O under isolated Python, empty PATH, noGit, all17files0444/all directories0555; hashes, modes and inodes unchanged. Export SHA256:69a0abd39c86e51b846c8e39502141ae1a521ef84d16529f7d95354a0e61e560.
• Hosted run39225559003 passes at this exact head:265 onboarding tests, only this package selected, all three commands onCPython3.12.15 and unchanged committed inputs. Finite checks corroborate the written general lemma; no human/kernel acceptance or complete native/selected-cold replay is claimed.

Scope:16new files only under research/native-lift-phase-tags/, one canonical-main parent20ecf2891d80b5acf18d980b2164fb44ea7faa90. Six exact PR3987 exports at fc53620 are retained locally, including original line endings/notices. No unmerged Git object or external input is needed at runtime. The four G maps are only its changed-interface subset, not the full PR3945 inventory. Reproduce: python3.12 -B scripts/research_package.py --package research/native-lift-phase-tags.

Handoff-first follow-up, changed scope of independent-moment / scope_key c191650c0fa8d2fa514e. Claim: #3987 (comment) . Main/priority6 refreshed unchanged at entry and prepublication. Complete702-open-PR-body coverage plus newest100-body delta through4000 and live1166/current-source comments; broader Discussion/closed/code coverage partial. No matching explicit normalization follow-up identified, without an exhaustive novelty claim.

Next: pin one actual physical interface and price its compensated tags/central children and every owner/helper/routing/precision charge before expansion. A wider alphabet with translations or nonmonomial children requires extra signed relations; this certificate covers K_G and its adjoint only. Physical/full-bill and all-size obligations remain open.

Credit Chris R/Clear1nsight3987, Dugongue3945/3929, dataisfire3734, Cinna Davis2226, Tekalign, icekylinx, DreamingOfClouds, Sagar Thakrar, roger-sato, Arham Tahir and the retained native/compiler/phase/owner lineage. New proof/tool/tests by ToikY with substantial OpenAI Codex assistance and separate AI math/test contexts. Apache-2.0. Maintainer edits disabled; no merge or selected-frontier change.

Discussion handoff. Claim released; no continuing reservation.

[Clear1nsight]

CLAIM — paid physical interface follow-up to ToikY's PR4002, pinned at d593941ea0a4926021cba9d01fe60500579e464f, using PR3987's exact signed recipes (fc536202fdaa924158789a5ef59ac079bbe21922) and PR3945's actual words (91f81d131252db704f945891da1ea54e29d46b8b).

I am testing warp5 on lender333, its three read-only uses B1081–1083, and its next frame climb before B1097. The existing physical monomial includes affine translation458. The proposed compilation retains that translation, every phase tag and compensated central child, while fusing the warp into the three consumer gathers and the following child boundary.

Success means a measured exact primitive-circuit saving on this actual512-coordinate f=1 interface, with reads, writes, signs, scratch, address preparation and dirty-state behavior explicit. The comparison is between two constructed circuits; the source emitter leaves the warp primitive tariff unpriced. Recursive/owner delta is0, and no all-size physical admission or κ follows. Stop if the complete bounded bill is unfavorable.

Local-only work until linked. Scope released by11:46UTC. Credit ToikY, the credited PR3987/3945/3929 lineage and original native/compiler/owner authors; substantial OpenAI Codex assistance.

[Clear1nsight]

FINDING / CLAIM RELEASED — actual lender333 finite physical comparison completed.

The released package follows PR4002's phase-tag handoff into PR3945's fifth native event and PR3987's exact signed recipe. Its lazy interface retains the actual affine offset 458 and global i³, feeds the three immediate −/−/+ consumers, and composes the next child's right monomial with the pending warp.

The robust result is 1024 fewer caller-real writes at f=1 against a stronger materialized comparator that already shares source loads and phase negations. Both use 7166 real reads, 3072 NEG, 5120 ADD, 1024 exact halves and 1536 routing-entry reads; writes fall 7166→6142. Recursive child and owner-width deltas are zero. The original stage-separated baseline overstated the read/NEG benefit; the released result uses the stronger comparator.

All 2048 complex basis columns of the four-array map agree; the independent sparse checks retain actual canonical-frame compensation/global phase. Eight semantic controls reject, and a constructive eight-word private schedule explicitly clears entry/return scratch. Normal and optimized registered verification pass. Routing setup and address/control cost are disclosed separately, so this is not a total native tariff, general-f implementation, supplier admission or new κ.

Open work is to price the actual general-f owner-compatible physical interface, including setup and stronger downstream fusion, before replaying the full native/owner/parent chain. The claimed lender333 source slice is now released. Thanks to ToikY's PR4002 handoff and the credited PR3987/PR3945 and retained earlier authors. Substantial OpenAI Codex assistance; same-session AI review, no independent human approval claimed.

Published as PR4049, exact head 4406317ff99ddef1d3c69ce42eef0c6bbddf64c4. All 25 public file bytes match the verified package; read-only Git-free normal/optimized export checks pass. Hosted CI is separately pending.