[Dugongue]

Add fifteen target-preserving G20 helper fusions and conditionally admit ordinary BIT saving 0.003496. The construction retains every surviving arbitrary original input and its actual physical endpoint. It does not prove kappa >= 0.0035 or a new best whole multiplication coefficient.

Seven new upper-snapshot windows include six exact cancellations of a protected helper read against its earlier cold contribution. Eight more windows explicitly refine an existing SOURCE H3 into H1 followed by H2 through the helper's required rank-two frame. Two snapshots expose the actual intermediate and upper values. The refinement is paid, recipients retain their independent injections, and no unavailable same-frame SOURCE value is assumed.

Together with the retained four partial-helper retirements and two earlier fusions, the eighteen-call controller has delta P=-378H1-378H3+306H4 and delta T=-72H4 against ai-nanachi PR5512. Its exact moment gain is 378(1+3^(1-C)-4^(1-C))>0. Seventeen fused full helpers retain their arbitrary H8 jobs; only the four genuinely retired H4 inputs lose productive credit. Forty owned arrays are reserved for each simultaneously live compiled instance. All copies, clears, positive fees, matching and routing remain charged.

A rank-mass tail dominance argument proves convexity of the predecessor's full moment and a useful secant derivative bound. Rational logarithm inequalities give a strict test at C=0.003497 without a price engine. The complete changed paid second moment decreases at the old test, both tails remain contracted, and fresh compiler, coefficient, prime, cover, forty-array stock and at most six acyclic ordinary backends yield B=0.003496. The native/all-column, ROW/spectator, constructive mixed-target compiler, ordinary cover/backends, precision, fixed-tape and analytic framework hypotheses remain inherited premises, not independently verified here.

Gaussian companions give an explicit ordinary metric transport nullifying one actual H5 edge under a matched right-frame flip and an exact Pauli-corrected occurrence compiler. Their universal constant-endpoint premise belongs to the original unrestricted full source, not automatically to the newer coupled-provider profile. No complete profitable gauge assignment is claimed.

The completed D25 omitted-mode service is also improved: a lossless section borrows sixteen existing arbitrary selected receiver carriers, whose already paid H8 advances transport the modes. A second section restores SOURCE and selected baselines after the complete-cover barrier; a paid 96H1 hole correction and original late query restore the exact original joined endpoint. This costs p8+96H1, avoiding sixteen extra H8 carries compared with the separate-owned-centre completion. The original unprojected service costs p8, so this is not a profitable complete Gaussian supplier.

Adds ten mathematical Markdown documents, including the two predecessor proof notes so the source construction chain can be reviewed in one place. All proofs are informal and separately reviewed by workers. No mathematical computation, numerical pricing, source replay, solver, Lean run, web search or remote PR refresh was performed. Source pin: 5e0052c. Stored old intervals and guards are predecessor evidence. Publication byte checks are separate from mathematical evidence. No selected-frontier change is proposed.

Start with bit.md and bit-refinement.md, then analytic-funding.md and assembly.md. The resulting ordinary BIT component remains below 0.0035, and Gaussian funding at the target is still unproved. Isolated local savings are not inserted into a whole multiplication claim.

Credit ai-nanachi PR5512; Ali Romman PR5421; compact436/PR4326 and PR4760/PR4814; DreamingOfClouds PR589; 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; the original G20 helper-464 shadow; and the retained four-retirement/two-snapshot proofs. Gaussian/centre credit retains Cao Yifan PR4610; Cinna Davis PR4690/PR4672 and PR4694/PR4698; phase PR4710; caller PR4713 with PR4630/PR4635; Dillon Amburgey PR5402; Chris R / Clear1nsight PR5407/PR5413; Ali Romman PR5383/PR5398; DaysSky; Nick Petalas; Ryanson Jonathan; zxv; Jacob Alan Sussman; Dugongue; source lane authors and PR3133/PR3148/PR2588/PR2226; and all native Clifford, scalar, stock, precision and analytic source notices. No owning PR or worldwide novelty is inferred where retained sources do not establish it.

Substantial OpenAI Codex assistance from one coordinator and three workers. New text is Apache-2.0. Only research/g20-refined-source-snapshots is added.