[Matarener]

Requested by Mark

Change and mathematical scope

Audit with a positive scoped result; no new κ. The selected κ is unchanged.

Before: DELAYED-COVER-BRIDGE open question 1 was open. It asks whether the lockstep compiler gives every simultaneously live child role a distinct physical array, which both the delayed BIT cover and the row-digit reserve assume. The outer-reserve constant C for #4470 was only illustrative (#4612).

After: research/lockstep-live-role-audit answers both questions.

• Live roles. This is an independent implementation of the FINITE-PRECOMPILATION compiler: the Theorem 1G lockstep flow, a replicas, source complements, and exit substitution by the smaller uniform program. It is executed event by event, with a stack of live roles on every array. A push is a whole-fiber cover route and a pop is its inverse. At every event it checks:

  • the units of a class lie on distinct arrays;
  • child roles are nested whole jobs on the array the suspended parent issued;
  • a unit issues only on an array it currently owns, and only after its previous child has finished;
  • every route is undone LIFO;
  • exit and complement batches receive distinct, owned arrays;
  • every array gets exactly one complement and one source job.

  All checks pass on the toy rule (full width up to rank 40, 6.9M events), on BIT-shaped rules (targets {8,22,50}, paid 1..7, random and adversarial owners, up to rank 25600 and three generations) and on the actual complex p2 rule with its native owners. Counting reproduces the FINITE-DAG-AUDIT receipts (91,854/2,242,264 and 1397/57,149). The README gives the general induction.

• Constant C. For the Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470 templates (BIT ranks from Conditional κ = 0.00296 via query-thinned productive controllers (+10.18%) #4440, complex word N_c = 2^64215200000000), log2 C <= 64,215,200,000,088. The complex row stock dominates. H(p) fits p^β from log2 p = 64,473,100,659,114 (Audit #4359 BIT row stock and its #4470 atom change (no new κ) #4612's illustrative value was 5.2e13). It also dominates the Small-prime check of #4612's outer-reserve threshold: displayed H fails at p=2 for moderate C; corrected H' = max(H, 4096 C log2(4096 C)) (no κ change) #4618 term.

Remaining obligations:

• Two inherited coefficients of C (c_row, A_old <= 2^64).
• The 1024-fold Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470 owner chronology is not materialized. It is represented by BIT-shaped rules of the same structure.

Task and overlap

• Card. selected-stock-envelope, priority revision 7. Scope refined to the two open questions of Audit #4359 BIT row stock and its #4470 atom change (no new κ) #4612.
• Base. b58ad9ef4. Eleven inputs are pinned in SOURCES.json.
• Overlap.
  • Audit #4359 BIT row stock and its #4470 atom change (no new κ) #4612 is the parent audit. This package is independent of its files.
  • transfer-audit/finite_dag_audit.py checks only class-local field distinctness and batch counts. This package adds event-level execution across classes, replicas, complements and exits, plus BIT-shaped rules.

Validation

python3.12 -B scripts/research_package.py --package research/lockstep-live-role-audit
python3.12 -B scripts/check_research_commit.py --package research/lockstep-live-role-audit

Both pass (CPython 3.12, Windows, standard library only; verify.py takes about 4 minutes).

Rejecting controls:

• one owned center per recursion depth instead of one per unit instance (the allocation FINITE-PRECOMPILATION §6 calls insufficient);
• an eager parent that issues round j+1 before child class j finishes;
• an exit batch that repeats an array.

These are finite executions. At astronomical widths (up to about 10^254), two replicas are executed and the smaller programs are checked through their interface.

Credit

zxv (#4359, delayed-cover bridge, finite compiler); Jacob Alan Sussman (Theorem 1G); Cinna Davis (#4440/#4470); the transfer-audit authors (finite_dag_audit.py). Audit by Mark (Matarener), prepared with substantial Claude Code assistance.

Open next questions

See README:

• derive c_row and A_old from the Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470 sources;
• check the two local owner premises on the raw Conditional κ = 0.00296 via query-thinned productive controllers (+10.18%) #4440 BIT paid-owner list for a v = 2 product.

🤖 Generated with Claude Code