[Matarener]

Requested by Mark

Change and mathematical scope

Audit/derivation, no new κ. Package research/admission-constant-derivation.

Before: query-thinned-controllers/verify.py (reused unchanged by #4470) states atom 0.004, ordinary 0.0034363538396 and admitted 0.0034 as literals, and controller.py checks surplus == 48*len(thick) - 112 (complex) / - 111 (BIT). #4633 described both as unexplained, width-8-specific constants.

After: both are derived.

• The admission predicate ordinary(δ) < δ < 1 − ordinary(δ) with ordinary(δ) = (1−δ)·C1 + δ·a_old holds exactly on the open interval (C1/(1+C1−a_old), (1−C1)/(1−C1+a_old)) = (0.0034382702…, 0.9999614…). 0.004 is one admissible atom. The old 0.003 is below the interval. The supremum of the ordinary saving is the left endpoint 0.0034382702, so admitted 0.0034 loses 1.1%. With the 2^26 prime allowance saturated it would be 0.0034434.
• For every p, every prefix length a and arbitrary per-port block widths, the literal invoice counting gives surplus = (p+2)·(H − C + Σ_ports(2b+1)) − P. The 48 is the local balance H − C + (2b+1)P, which equals 48 on both sides (complex 3301 − 5157 + 1904, BIT 3512 − 5129 + 1665). It is not a width-8 constant.

κ effect: none. #4470 only needs admitted > its complex tested saving 0.003020155. These constants matter only once the complex side exceeds about 0.0034, and then they are worth at most about +1.3%.

Task and overlap

Base b58ad9ef4. Card independent-moment, scope refined (see TASK.json). Nearest: #4612 (our audit of the #4470 atom change: stock and q0 display), #4633 (raised the literals), #4440/#4470 (sources). No other PR derives these constants.

Validation

python3 scripts/research_package.py --package research/admission-constant-derivation --check-only
python3.12 scripts/research_package.py --package research/admission-constant-derivation

Both PASS locally (Windows, Python 3.12, standard library only, a few seconds). verify.py binds every literal and the hard-coded check from source and derives the interval exactly. It replays the literal counting for p = 2…40 and all a on both sides, matches both committed controller invoices (complex p=17: 800, BIT p=16: 753) and checks 200 random mixed-width instances. test_verify.py has six rejecting controls. The symbolic surplus proof is in README §2. The BIT tail strictification was not re-run.

Credit

Constants, controllers and invoices come from the query-thinned-controllers and joint-helper-lattice packages and their sources. Prepared by Mark (Matarener) with substantial Claude Code assistance.

Open next questions

How far C0/C1 (0.003459/0.00345) can move toward the BIT root 0.00346. This is low priority while the complex side binds (TASK.json).

🤖 Generated with Claude Code