{ "schema": "essay-abstractions/v1", "date": "2026-10-08", "purpose": "Shared human and machine reading cards, not a Research Kernel import contract.", "format": [ "label", "symbol", "phrase", "meaning", "boundary", "links" ], "essays": [ { "path": "essays/the-maze-that-remembers.html", "cards": [ { "id": "idea-loop", "label": "Neurosymbolic loop", "symbol": "Propose → check → remember", "symbol_reading": "Propose → check → remember", "phrase": "Let the last check improve the next proposal.", "meaning": "The model produces a candidate; an external checker returns a scoped verdict and evidence; the record informs later proposals.", "boundary": "Acceptance establishes the checker’s exact obligation under its assumptions. Rejection or timeout does not prove the underlying conjecture false.", "links": [ { "label": "Open the loop", "href": "#neurosymbolic" }, { "label": "Lean checking assumptions", "href": "#source-lean" } ] }, { "id": "idea-distinct", "label": "Distinct work", "symbol": "Tₖ(N) = ⌈N/k⌉", "symbol_reading": "T sub k of N equals the ceiling of N divided by k", "phrase": "Share the work before multiplying the workers.", "meaning": "N distinct candidates take ceiling(N/k) rounds with k positive workers, one completed equal-cost check per worker per round, and no duplicate assignments.", "boundary": "More workers cannot increase this round count, but may leave it unchanged. Unequal jobs, coordination costs, and verification bottlenecks are outside the model.", "links": [ { "label": "Read the scaling argument", "href": "#scaling" }, { "label": "Checked scheduling proof", "href": "#proof" } ] }, { "id": "idea-rejection", "label": "Scoped rejection", "symbol": "Reject the branch; keep the fork.", "symbol_reading": "Reject the branch; keep the fork.", "phrase": "Carry forward the reason a route failed.", "meaning": "A certified-invalid candidate can be removed without discarding a solution. A whole branch needs evidence covering that whole branch for the same target and revision.", "boundary": "A rejected script, a refuted conjecture, and an interrupted attempt mean different things. A timeout remains unresolved.", "links": [ { "label": "Read the evidence distinctions", "href": "#memory" }, { "label": "Inspect the pruning proof", "href": "#proof" } ] }, { "id": "idea-stop", "label": "Bounded persistence", "symbol": "Launches ≤ B", "symbol_reading": "The number of launches is at most the initial budget B", "phrase": "Stop with evidence the next researcher can use.", "meaning": "An external controller atomically reserves one unit per attempt from a finite budget B, enforces permissions and deadlines, and returns success, scoped exhaustion, a pause, or a question.", "boundary": "A prompt alone does not enforce the bound. Budget exhaustion proves that the run stopped, not that a solution does not exist.", "links": [ { "label": "Open the stopping policy", "href": "#stopping" }, { "label": "Connect it to containment", "href": "abstraction-is-compression.html#autonomy" } ] } ] }, { "path": "essays/research-taste-and-scientific-memory.html", "cards": [ { "id": "idea-taste", "label": "Research taste", "symbol": "q: capacity per compute unit", "symbol_reading": "q: capacity per compute unit", "phrase": "Choose the next experiment well.", "meaning": "In the planning model, q converts usable experimental compute into reference-equivalent capacity for a fixed task regime. TasteVal separately estimates task-specific compute multipliers.", "boundary": "The benchmark does not establish general intelligence, live swarm scaling, safe stopping, or Research Kernel’s added effect.", "links": [ { "label": "Read what TasteVal measures", "href": "#tasteval" } ] }, { "id": "idea-dividend", "label": "Memory dividend", "symbol": "ΔA = qG", "symbol_reading": "Extra capacity equals efficiency q times net recovered compute G", "phrase": "A better researcher can do more with the same saved compute.", "meaning": "G is compute recovered after avoidable duplication and memory overhead. In the stated linear, separable model, multiplying G by efficiency q gives the extra capacity supplied by memory.", "boundary": "The monotonic result requires G ≥ 0 with the other assumptions held fixed. Capacity is not a direct measure of discoveries, revenue, or scientific value.", "links": [ { "label": "Open the capacity model", "href": "#value-model" } ] }, { "id": "idea-ceiling", "label": "Capacity ceiling", "symbol": "Useful output = min(K, A)", "symbol_reading": "Useful output is the lesser of the cap K and available capacity A", "phrase": "Saved effort helps only where useful work remains.", "meaning": "The essay’s saturation example caps useful output at K. Once both systems reach K, additional capacity can leave the output gain at zero.", "boundary": "K is an illustrative cap, not a measured scientific frontier. The example refutes an unconditional claim that stronger agents always produce a larger realized memory benefit.", "links": [ { "label": "Read the counterexample", "href": "#limits" } ] }, { "id": "idea-handoff", "label": "Resumable stop", "symbol": "Stop reason + frontier + retry condition", "symbol_reading": "Stop reason + frontier + retry condition", "phrase": "Leave the next attempt a place to start.", "meaning": "Preserve the exact scope, evidence, unfinished work, spent budget, and what changed evidence or resources would justify another attempt.", "boundary": "The record supports a decision to resume; it does not grant permission or make a prior timeout into a permanent prohibition.", "links": [ { "label": "Read the handoff example", "href": "#stopping" }, { "label": "Inspect bounded persistence", "href": "the-maze-that-remembers.html#stopping" } ] } ] }, { "path": "essays/abstraction-is-compression.html", "cards": [ { "id": "idea-compression", "label": "Sound abstraction", "symbol": "Keep every route to danger.", "symbol_reading": "Keep every route to danger.", "phrase": "Make the map smaller without hiding the escape.", "meaning": "Exact decision summaries preserve the chosen answer. Conservative safety abstractions cover every concrete transition and map every concrete bad state into an abstract bad state.", "boundary": "A proof on the smaller graph transfers only when those coverage obligations hold. Fewer visible details alone do not establish soundness.", "links": [ { "label": "Open the abstraction definition", "href": "#compression" }, { "label": "Lean transfer theorem", "href": "../proofs/abstraction/Abstraction.lean" } ] }, { "id": "idea-witness", "label": "Containment witness", "symbol": "∃ means at least one", "symbol_reading": "The existential quantifier means at least one", "phrase": "A useful design that withstands every strategy in scope.", "meaning": "For a fixed environment contract, at least one admissible useful configuration withstands every physically modeled strategy. The same configuration must handle them all.", "boundary": "Existence does not imply uniqueness. The utility requirement, observer, time horizon, and resources are part of the claim. A model witness is not a validated physical deployment.", "links": [ { "label": "Read the quantified hypothesis", "href": "#hypothesis" }, { "label": "Inspect the worked witness", "href": "#lab" } ] }, { "id": "idea-observation", "label": "Noninterference", "symbol": "Same allowed information ⇒ same observations", "symbol_reading": "Same allowed information ⇒ same observations", "phrase": "Close the extra signal, including its timing.", "meaning": "At fixed authorized information and public schedule, protected internal differences and adversarial choices do not change the specified observable transcript.", "boundary": "Every relevant channel and receiver capability must be covered. This confidentiality property does not by itself rule out harm through authorized outputs.", "links": [ { "label": "Open the observation model", "href": "#channels" }, { "label": "Read the lab contracts", "href": "https://github.com/TheDarkLightX/CovertChannelLab/blob/ae90bb88273e82620f2e643c19f23aeea0d9b31c/CONTRACTS.md" } ] }, { "id": "idea-cegis", "label": "Counterexample-guided synthesis", "symbol": "Propose → refute or certify → refine", "symbol_reading": "Propose → refute or certify → refine", "phrase": "Make each checked failure constrain the next design.", "meaning": "Search for a candidate; check the required property; when a valid counterexample appears, retain it as an obligation for later candidates. A certificate can discharge a universal modeled obligation.", "boundary": "A finite attack sample or a timeout cannot certify an unrestricted universal claim. Counterexamples from an overapproximation may need concretization before rejecting a real design.", "links": [ { "label": "Read the research loop", "href": "#search-loop" }, { "label": "Open the preprint", "href": "#source-witness" } ] } ] }, { "path": "essays/meaning-before-mechanism.html", "cards": [ { "id": "idea-meaning", "label": "Meaning before mechanism", "symbol": "Purpose → model → implementation", "symbol_reading": "Purpose, then model, then implementation", "phrase": "Decide what should happen before choosing how to build it.", "meaning": "The human supplies goals and judges whether the explicit specification captures them. Agents propose realizations; checkers test stated obligations.", "boundary": "Formal conformance cannot establish an unstated intention. This case’s examples are AI-generated; no independent human approval is inferred.", "links": [ { "label": "Human steering", "href": "#meaning" }, { "label": "Case provenance", "href": "../examples/two-key-release/evidence/provenance.json" } ] }, { "id": "idea-effect-boundary", "label": "Effect boundary", "symbol": "D = Fₚ(S, C, X)", "symbol_reading": "Under policy P, decision D is a function of state, command and context", "phrase": "The core decides. The shell acts.", "meaning": "A pure core evaluates immutable explicit inputs under a fixed policy. Only a law-admitted committing decision yields the private publication consumed by the shell.", "boundary": "Purity alone does not prove the policy. Authentication, durable storage, external delivery, and toolchain trust remain separate obligations.", "links": [ { "label": "Open the boundary", "href": "#boundary" }, { "label": "Generated code", "href": "#code" } ] }, { "id": "idea-two-keys", "label": "Two keys, one release", "symbol": "A ≠ B; release intents ≤ 1", "symbol_reading": "Distinct approver IDs and at most one release intent per history from genesis", "phrase": "A second identity completes the approval; a repeat does not.", "meaning": "The illustrated policy requires two recognized distinct IDs to approve, and each finite history from genesis emits at most one release intent. A key here is an ID’s approval, not a cryptographic signature.", "boundary": "The caller IDs are simulated. The bound concerns a request’s logical history, not delivery retries, database rollback, multiple fresh requests, or proof of two distinct people.", "links": [ { "label": "Try the app", "href": "../examples/two-key-release/" }, { "label": "Lean policy model", "href": "../proofs/two-key-release/ReleaseDesk.lean" } ] }, { "id": "idea-two-views", "label": "One meaning, two views", "symbol": "parse(render(M)) = M", "symbol_reading": "Parsing a rendering of M returns M", "phrase": "Change the notation. Preserve the behavior.", "meaning": "ZAL’s symbolic and controlled-English projections target the same admitted typed model. A human can inspect the readable view while tools operate on its precise structure.", "boundary": "This is the prototype’s specified, tested round-trip target, not a proved frontend. Ordinary prose is not automatically formal; the local review record cannot authenticate a human.", "links": [ { "label": "ZAL and its limits", "href": "#zal" }, { "label": "Pinned specification", "href": "#source-zal" } ] } ] } ] }