diff --git a/docs/ROUND-HISTORY.md b/docs/ROUND-HISTORY.md index 23ded7612b..e2feeed203 100644 --- a/docs/ROUND-HISTORY.md +++ b/docs/ROUND-HISTORY.md @@ -12,6 +12,7 @@ New rounds are appended at the top. Newest first. Anchor links work in markdown renderers that slugify `## Round N — ` to `#round-n-<title-slug>`. +- [Round 45 — QG isomorphism proof strategy foundation + Universal Infinite Poker Game cosmology formalization](#round-45--qg-isomorphism-proof-strategy-foundation--universal-infinite-poker-game-cosmology-formalization) - [Round 44 — in-flight](#round-44--in-flight) - [Round 43 — invariant-substrates program + empirical BP-03 harness evidence + agent-cadence telemetry](#round-43--invariant-substrates-program--empirical-bp-03-harness-evidence--agent-cadence-telemetry) - [Round 42 — First repeated iteration of Round-41 cadences + vibe-coding external legibility](#round-42--first-repeated-iteration-of-round-41-cadences--vibe-coding-external-legibility) @@ -41,8 +42,10 @@ slugify `## Round N — <title>` to `#round-n-<title-slug>`. - [Round 17 — storage specialist, BloomFilter, durability skeleton](#round-17--storage-specialist-bloomfilter-durability-skeleton) - [Round 16 — SDL / threat model / she-her storage specialist](#round-16--sdl--threat-model--she-her-storage-specialist) -Round 44 (current) is in-flight; the synthesis row lands at -round-close. When this file hits 5000 lines, split the pre- +Round 45 is the most recent landed round; Round 44 remains +in-flight per its own label (synthesis row lands at round-close +per the file convention; no partial synthesis). When this file +hits 5000 lines, split the pre- round-N portion into `docs/_archive/ROUND-HISTORY-pre-N.md` and leave this file as a rolling window of the most recent ~20 rounds; no ADR is needed for a mechanical archive move. @@ -84,13 +87,26 @@ Formalize Remember-When + Pay-Attention as categorical primitives: - **Internal modal operator `A`**: models Pay-Attention (QBism's observer-relative probability assignment, generalizes quantum measurement projection) -The combined structure `Zeta_{RA}` satisfies coherence conditions between `M` and `A`. +The combined structure `Zeta_{RA}` is intended to satisfy coherence conditions +between `M` and `A`. Post-round, [PR #3636](https://github.com/Lucent-Financial-Group/Zeta/pull/3636) + [PR #3639](https://github.com/Lucent-Financial-Group/Zeta/pull/3639) established that the +originally-proposed laws (`M(A(p)) = A(M(p))`, `A(μ_X) = μ_{A(X)} ∘ A(M(A(X)))`, +`A(η_X) = η_{A(X)}`) are not well-typed under the stated signatures +`M : Zeta → Zeta`, `A : Ω → Ω`. Only a **provisional propositional Law 1'** +(`A_*(M_*(p)) = M_*(A_*(p))` over `p : X → Ω`, contingent on a strength +`θ : M(Ω) → Ω`) is type-correct; Laws 2 (μ-coherence) and 3 (η-coherence) +are deferred to a new Step 1.5 pending an `A`-lifting `Ã : Zeta → Zeta` +(blocked by `A` not being a closure operator). See the Step 1 research doc +for the resolution-paths table. **Operational connections**: -- `M` connects to DBSP incrementalization (`D ∘ Q ∘ I` monad) +- `M` connects to DBSP via the **incrementalization identity** `Q^Δ = D ∘ Q ∘ I` + (a wrapping/conjugation identity over streams, not a monad — corrected by + [PR #3626](https://github.com/Lucent-Financial-Group/Zeta/pull/3626)) - `A` connects to QBism (observer-relative truth values) -- The monad laws correspond to integrate-differentiate coherence +- Whether the monad `M` on `Zeta` and the DBSP `I`/`D` pair share a deeper + categorical relationship (e.g., comonad-monad adjunction, distributive + law) is an open question, not a settled identity **Why this matters**: This formalization grounds the Manifesto V2.1 axioms in category theory, provides a mathematical foundation for the "Remember-When + Pay-Attention" @@ -128,8 +144,11 @@ The work earns its keep even at partial completion: ### Arc 5 — Open questions -- What is the precise relationship between the memory monad `M` and the DBSP - incrementalization monad? Are they the same structure, or is one a specialization? +- What is the precise relationship between the memory monad `M` (a monad on + the topos `Zeta`) and the DBSP `I`/`D` pair (the integrate/differentiate + operators participating in the incrementalization *identity* `Q^Δ = D ∘ Q ∘ I`, + not a monad — per [PR #3626](https://github.com/Lucent-Financial-Group/Zeta/pull/3626))? Possible structural relations: comonad-monad + adjunction, distributive law, or no direct categorical correspondence. - How does the attention modal operator `A` interact with the subobject classifier's Heyting algebra structure? QBism suggests it should be non-Boolean. - Can we derive the Clifford algebra structure from this categorical foundation?