Race Winner & Codec Racing

Tools

`race_winner`

Given N candidates with scores and costs, verify the race winner is valid (highest score), minimal (no unnecessary computation), and isolated (clear margin). Returns winner, validity checks, margin of...

`codec_racing`

Fork codecs, race per chunk, fold to overall winner. Simulates chunk-level codec competition with roundtrip correctness checking. beta_1 = codecs - 1 (degrees of freedom in the race). Returns per-chun...

`election_analysis`

Analyze a multi-round election or tournament as fork/race/fold topology. Checks bracket structure, fairness (monotone elimination -- no revived candidates), and whether the elimination order respects ...

`convergence_race`

Race multiple optimization strategies to convergence at varying budget levels. Returns the winner at each budget, crossover points where leadership changes, and the Pareto frontier of cost vs converge...

`server_optimality`

Given N servers with latency, throughput, and cost, compute optimal routing as a race. Returns optimal assignment, load balancing strategy, and race topology showing how requests should be distributed...

`codec_racing_sandwich`

Compute the codec racing sandwich: H(source) ≤ wire ≤ raw. Returns floor (entropy), ceiling (raw), gain bounds, and diversity convergence gap.

`thm_race_winner_validity`

The selected race winner has a valid result: complete status and result passes the validity predicate. Invalid branches cannot win. [LEDGER: THM-RACE-WINNER-VALIDITY]

`thm_race_winner_minimality`

The winner completes no later than any other valid branch. This is the "fastest correct answer" property of race operations. [LEDGER: THM-RACE-WINNER-MINIMALITY]

`thm_race_winner_determinism`

Ties are broken deterministically by branch index (C3). Among all valid candidates with the same completion time, the lowest-indexed branch wins. Satisfies deterministic fold. [LEDGER: THM-RACE-WINNER...

`thm_race_winner_isolation`

Venting a non-winner branch preserves the winner's validity. Formal content of C2 (branch isolation) applied to race operations. [LEDGER: THM-RACE-WINNER-ISOLATION]

`thm_race_winner_composable`

Race results compose through fold: given two valid race winners, their fold is valid when the fold function preserves validity. Connects race correctness to the monoidal category structure. [LEDGER: T...

`thm_topo_race_subsumption`

Per-resource codec racing subsumes any fixed codec: racing total is always less than or equal to any fixed-codec total. Adding a codec to the race never increases wire size. Racing achieves zero compr...

`thm_dual_protocol_pareto`

HTTP+Flow dual protocol dominates either protocol alone. Internal deficit of zero transfers advantage. Throughput conserved across the protocol boundary. Adding Flow never worsens HTTP clients [LEDGER...

`thm_server_race_elimination`

x-gnosis server lifecycle as fork/race/fold transition system: race terminates with exactly one winner. Fold preserves content-length invariant. Wallington Rotation achieves T=ceil(P/B)+N-1. Cache war...

`thm_server_optimality`

End-to-end composition theorem: a server with fork/race/fold at every layer, zero deficit at every layer boundary, and Wallington Rotation scheduling simultaneously achieves critical-path makespan (nu...

`thm_always_hypothetical_better`

For cost > 1, a cheaper compiler exists in principle [LEDGER: THM-ALWAYS-HYPOTHETICAL-BETTER]

`thm_universe_extensible`

Any finite competitor set can be extended [LEDGER: THM-UNIVERSE-EXTENSIBLE]

`thm_pareto_frontier`

Betty and aeon-logic neither dominates the other [LEDGER: THM-PARETO-FRONTIER]

`thm_local_optimality_provable`

Non-increasing cost sequence stabilizes [LEDGER: THM-LOCAL-OPTIMALITY-PROVABLE]

`thm_optimality_gap`

Hypothetical better always exists AND local optimality always achievable [LEDGER: THM-OPTIMALITY-GAP]

`thm_god_gap_nonneg`

God Gap >= 0 [LEDGER: THM-GOD-GAP-NONNEG]

`thm_god_gap_bounded`

God Gap <= initial cost [LEDGER: THM-GOD-GAP-BOUNDED]

`thm_god_gap_nonincreasing`

Each iteration narrows the God Gap [LEDGER: THM-GOD-GAP-NONINCREASING]

`thm_god_gap_converges`

God Gap converges to a final value [LEDGER: THM-GOD-GAP-CONVERGES]

`thm_god_gap_betty`

Betty God Gap = 661us (0.726ms - 0.065ms) [LEDGER: THM-GOD-GAP-BETTY]

`thm_god_gap_betti`

Betti God Gap = 9us (0.074ms - 0.065ms) [LEDGER: THM-GOD-GAP-BETTI]

`thm_self_hosted_closer`

Betti closer to god than Betty [LEDGER: THM-SELF-HOSTED-CLOSER]