[DreamingOfClouds]

Result

No kappa claim above #6936. Package: research/p104-whitehead-native-objects. It records three exact objects for the Whitehead (t = -1, d = 0) hosted stage and the price a better native has to meet. Both words are priced below #6936.

• A hosted word on Conditional κ = .00362702 (+0.087% over #6934): seven main contacts on shared wires #6936's mixed word. The outer Whitehead stage (stages 1 and 18) on the 8 hosted ports. Their native adds one owned rank-1 UP carrier per port and computes X = x - 2y, Y = x/2. Exact kappa .0035927413806393823240, S = 1504, -0.9451% against Conditional κ = .00362702 (+0.087% over #6934): seven main contacts on shared wires #6936 (.0036270188296). Native, joint caller and invoice are in the package. The hub saving is +0.1167% and the 16 carriers cost -1.0605%.
• A helper-free d = 0 native on all 104 ports. One window swap removes y; the beta crossing costs 2 owned rank-1 moves per port. Exact in two engines, 100 single-edit mutants (97 rejected; the 3 accepted are one true equivalence). Public 1652.63 R0, 1.13 above the floor 1651.50; owned 208, over the replacement budget by 35.2 (outer) / 32.1 (rho = 1) per W call.
• The connected rho = 1 all-Whitehead root. 38 fields, 18 stages at t = -1, product -I, irreducible; passes every requirement of the root checker. Free-native ceiling +19.33%.

Targets

• Break-even per port-call: 0.110 (outer root), 0.1395 (rho = 1). The carrier here costs 1.00.
• A native replacing Conditional κ = .00362702 (+0.087% over #6934): seven main contacts on shared wires #6936's at each W call must satisfy owned <= 111.573 + T - dpub, with T = 11.426 (outer) or 14.513 (rho = 1) R0 per call and dpub the change in public bill against 1702.405.
• Pass line with the helper-free public layer: 1.66 owned per port (outer), 1.69 (rho = 1). The window native pays 2.0.

The package lists the routes closed against these targets, each with its scope, and the routes still open (Gamma coupling on the Y registers after the bounce; shared landings for the beta crossing and the hybrid with the window swap), with odds marked as judgement.

Declared assumption: owned ascent

Both words move owned registers up as well as down: the Whitehead native has 31 owned UP events (rank mass 64, #6936's 56 plus 8) and the window native 104. The verifiers accept an owned MOVE between nested frames in either direction, paid |change in dimension|; public MOVEs still ascend strictly. The strict predecessor rule rejects exactly those events and nothing else. This is assumption A6 as declared in #6883, with the P112 backward word as precedent (an owned centre accumulated, moved up by rank 3 and 5, read, cleared). Every number is conditional on it, as #6934 and #6936 are.

Checks

Two commands, about 100 s each. check.py: sha256 of the objects; exact Fractions replay of both natives with the odd certificate S = 1125 (and a wrong-alpha control); both Whitehead roots with controls; exact kappa and the invoice move; the target arithmetic; the 104-port native regenerated from its construction, replayed in exact Fractions and mod 2^61 - 1, its 208 x 208 transfer matrix, price, floor, budget lines and 100 mutants. checks/check_joint_w.py: the joint caller (one stream, 78 roles) replayed mod p at four characters with controls, and the invoice rebuilt from the roots. Validator: python3.12 -B scripts/research_package.py --package research/p104-whitehead-native-objects.

Disclosures and not claimed

• Model replay only; no human has reviewed the words or the package.
• The the hosted Whitehead word's second engine, physical streams, ordinary-call and outer checks come from its build record; they are listed in the package as recorded, not rerun.
• The kernel ledger (the 1702.405 and 111.573 baseline, the break-even table, free-native ceilings) is quoted, not recomputed; the arithmetic from it is replayed.
• The window native has no caller; its 2 x 2 caller block is checked, the joint replay is not. The rho = 1 root has no native.
• Not claimed: a candidate, any admission, or that any open route will pay.

Credit: Ali Romman (#5599, the split lemma and helper pricing the invoice rule rests on), CubeJerry (#6912 caller blocks, #6914 owned-rise argument, #6916 split application), unpaidmoon (#6930 width-2 phase test), icekylinx (#104 odd grid and the S = 1125 certificate), and the retained work of #6936 and its predecessors.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code