[Dugongue]

Replace two actual G20 inverse helper-return windows by SOURCE snapshots. At helper 465/SOURCE 19 and helper 467/SOURCE 38, the exact identity G4^(-1)(h_U+x_U)=G1^(-1)(G3^(-1)h_U+x_L) removes H1+H3 and adds H4 while preserving the arbitrary full helper input and its productive endpoint. SOURCE follows its unchanged original trajectory. Both snapshots have actual version deadlines, overlapping lifetimes and separately paid owned storage.

Compose with the preceding four partial-helper retirements, retaining their complete target debit. Against ai-nanachi PR5512 the eighteen-call controller has delta P=-108H1-108H3+36H4, delta T=-72H4, and exact moment gain 108(1+3^(1-C)-4^(1-C))>108C. Seventeen owned arrays are reserved per live instance; no shadow earns a productive target. All ordinary copies, clears, routes, normalizers and positive native costs remain charged.

Using the stored predecessor interval and guards, elementary derivative and concavity bounds prove a strict test above its old raw crossing, preserve both tail contractions, and construct new finite compiler constants and at most six acyclic ordinary backends. This proves the conditional ordinary BIT component saving 0.0034839863305 under the retained native/all-column, ROW/spectator, compiler, precision, fixed-tape, backend and analytic hypotheses. It is a conservative analytical certificate, not a newly evaluated root or a new physical-interface verification.

Companion Gaussian results prove coherent complements for the actual greedy frame constructor, exact physical left-gauge ranks, phase-exact rank-one centre bridges and a distinct right-frame compiler with per-generator occurrence consistency. A source-bound projected-input D25 forward restores SOURCE and its owned centre at exact cost p8+kH8. Its coupling is A(I-JD), not A. None of these isolated possible savings is included in the BIT invoice.

Kappa >= 0.0035 and a new best whole multiplication kappa are NOT established. The new BIT component remains below 0.0035, and no complete funded Gaussian caller or globally profitable source-gauge assignment is supplied. No selected-frontier change is proposed.

Adds six mathematical Markdown documents with informal proofs and separate worker review. No numerical pricing, source replay, mathematical computation, solver, Lean run, web search or remote PR refresh was performed. The offline source pin is 5e0052c. Publication byte checks are separate from mathematical evidence. Start with snapshot-fusion.md, then bit-admission.md Theorems 3-5 and assembly.md.

Credit ai-nanachi PR5512; Ali Romman PR5421; compact436/PR4326 and PR4760/PR4814; DreamingOfClouds PR589 and eumemic PR555; Cinna Davis's SOURCE/ROW/controller/cover work; rohanarun PR185/PR199/PR204; zxv and Jacob Alan Sussman's mixed-target/compiler/precision lineage; and the direct g20-partial-helper-retirement predecessor. The earlier helper 464/SOURCE 0 shadow is predecessor work. Gaussian/centre credit retains Dillon Amburgey PR5402, Chris R / Clear1nsight PR5407/PR5413, Ali Romman PR5383/PR5398, Cinna Davis PR4694/PR4698, Cao Yifan, DaysSky, Nick Petalas, Ryanson Jonathan, zxv, Jacob Alan Sussman, Dugongue, centre-service PR3133/PR3148/PR2588/PR2226, gaussian-reader-recoding and all source notices. No owning PR or worldwide novelty is inferred where the retained source does not establish it.

Substantial OpenAI Codex assistance from one coordinator and three workers. New text is Apache-2.0. Only research/g20-snapshot-ordinary-admission is added.