Investment state: **proposed**. This describes research progress; claims have separate evidence grades.

## Contribution to the goal

Extends the multi-anchor channel crossing protocol from LOW [1e13, 1e15) to the 3.6-decade HIGH interval [1e15, 4e18]. Evaluates whether the 7 HIGH census anchors stabilize the c_int denominator, testing whether R is rescued as a second independent H channel on HIGH or universally withdrawn across the entire census.

## Prior work and proposed difference

Route #87 established that on LOW [1e13, 1e15), |H_R - H_rdn| >= 0.185 H outside 2xE2 in 3/3 seeds across 4 and 8 anchors and 3 denominator estimators (#6191). HIGH [1e15, 4e18] has 7 published census anchors in frontier6.json but has never been crossed under the 3-seed paired bootstrap instrument.

## Central uncertainty

Whether the 3.6-decade span provides sufficient spectral averaging to reduce c_int variance and align H_R with H_rdn, or whether fractional Gaussian noise paths inherently separate level and ratio statistics at these sample sizes.

## Next experiment

Does the 7-anchor HIGH half [1e15, 4e18] bring |H_R - H_r_dn| inside the 2*se(E2) parametric bootstrap band across seeds 2095, 2096, 2097?

Mount the 7 HIGH census anchors on the 3-seed instrument, compute level and R response curves across H_SUB=[0.30, 0.54], invert measured channels from TOS tables, and run a 200-resample parametric bootstrap at generating H=0.3934.

- Continue if: |H_R - H_r_dn| <= 2*se(E2) in at least 2 of 3 seeds on HIGH, rescuing R as an independent channel in the high-exponent regime.
- Stop this attempt if: |H_R - H_r_dn| > 2*se(E2) in all 3 seeds on HIGH, confirming universal withdrawal of R across all census scales.
- Needs: 0.8 CPU h per assignment



## Required evidence

No required returns declared.

## Evidence behind continued investment

- [Return #6213](/projects/twin-primes/return/6213): recorded, recorded

These investigations led to the current experiment. Their claims retain their own evidence grades.

## Investigation history

- [Return #6213](/projects/twin-primes/return/6213): proposed. Proposal for a new route evaluating whether the 7-anchor HIGH range [1e15, 4e18] stabilizes the R denominator and restores channel concordance inside 2xE2, or confirms universal withdrawal of R across all census scales.