The Deep Join Experiment

oxexp-deep-join · the join experiment

The discipline. This experiment closes the triangle the ladder has been walking — the line, π, and the primes under ONE registered instrument, with POSITION on the line and DIRECTION of the line as the registered variables — and it opens with two theorems, stated before any number froze: THE REVERSAL THEOREM (the fold commutes with reversal, so every post-fold observable is exactly blind to the line’s direction — the directional decision cannot be measured on the fold side, anywhere; it can enter only through a grown register, and the reduced walk is exactly such a register) and THE GAP ALGEBRA (a 0/1 window’s ambient-bias gap is log₂ tr(A₁₀^2B) − 1 exactly, B its block count — the archived Deep Fold minimum gaps are k = 32..16 to the last digit, so “the bias thins with the primes” is precisely “the block count falls with depth”). Both are kept as HJ1’s confirmation protocol; the live questions run where the algebra leaves them open: HJ2 the register’s direction (the register grown FORWARD vs BACKWARD over the same segment — landed either way); HJ3 the constellation discount (real block counts vs occupancy-matched uniform placement); HJ4 the line’s arrangement signature (the Cooling Spectrum protocol on the line’s own register — a directional signature where π showed none is the headline); HJ5 the span-surcharge association, registered at last (exact McNemar, P and L separately, fresh walks). The labels: HJ1–HJ5 are experiment-local hypothesis tags of a computational experiment, ordinal labels only, nothing chemical. No real backward register, block count, or station spectrum exists before its registration; the calibration is synthetic states, one synthetic stream, and pure algebra. THE FIREWALL binds every panel: no claim on any Millennium Prize problem, ever; no claim about π’s normality; no claim over the prime numbers’ own laws; no claim over machine learning’s own results, quantum computing, physical cosmology, quantum mechanics, consciousness, or phenomenal experience, ever. Acts, never eyes. The kin pages: /dlx · /dpx · /dfx · /ovx · /csx.

The gate — honest acceptance

The observable, the two theorems, the protocol, the synthetic-and-algebra calibration witness, and the ladder’s standing — derived from the engine’s own acceptance, never asserted here.

The ladder — registrations, runs, and verdicts

One rung per seeds-per-family count (64 · 128 · 256 · 512 · 1024; families P, G, and L-fwd/L-bwd). The acts are the operator’s; the engine refuses out-of-order acts; the deep rungs take minutes.

the ladder loads on page open; the button re-reads

The external anchor

A rung’s records to the immutable EXTERNAL record (mldata CKAN when configured; the dummy-node fallback otherwise) — the archive record is the citable object, never this host.

oxexp-deep-join · engine daemon/djx.py (the join by the Deep Fold counter, the Cooling Spectrum stations, and the reduced walk grown both ways; the order enforced fail-closed) · the design of record: ooi_network/docs/oxexp-djx-design.md (draft 0.1) · hypothesis before run, always; refutations displayed, never hidden.