Hogwash Removal
"Category theory is an extremely insightful subject but its generality, the plethora of structural heuristics it provides, as well as its apparent conceptual simplicity make it very prone to cargo-culting." -- Matteo Capucci, "No, the Yoneda Lemma Doesn't Solve the Problem of Qualia" (2023)
Trit: -1 (VALIDATOR) Color: #E84040 (Red) Status: Production Ready
What This Skill Does
Given a codebase or document, systematically audit every mathematical claim against these criteria:
- Is the terminology used correctly? (e.g., "topos" means a specific thing, not "any structure")
- Is the claim a theorem or an analogy? If analogy, is it labeled as such?
- Are citations relevant? Does the cited work actually support the claim?
- Is novelty overclaimed? Is this a straightforward instance of a known construction?
- Does the code match the math? Is the implementation what the docs say it is?
The Hogwash Scoring Rubric
Score each claim 0-10:
| Score | Meaning | Action | |-------|---------|--------| | 0 | Correct, precisely stated | Keep | | 1-2 | Minor imprecision, reasonable shorthand | Note but keep | | 3-4 | Slightly oversold but defensible | Add qualifier | | 5-6 | Analogy presented as theorem, or trivial result presented as novel | Rewrite | | 7-8 | Technical term misused, cargo-cult citation | Remove or replace | | 9-10 | Fabricated mathematical claim, actively misleading | Delete and explain why |
Common Hogwash Patterns
Pattern 1: Topos/Site Name-Dropping (severity: 7-8)
Symptom: "X IS the site", "Y IS the classifying topos" where X and Y are not sites/toposes.
Why it's hogwash: A site is a category with a Grothendieck topology. A topos is a category with finite limits, power objects, and a subobject classifier. Using these words for things that aren't them is like calling a bicycle a "jet engine" because both involve wheels.
Fix: Use honest language. "Different semirings give different views" not "the semiring IS the site."
Reference: Caramello (2017) defines sites precisely. Capucci warns about this in his qualia post.
Pattern 2: Trivial Instance Presented as Novel (severity: 5-6)
Symptom: "We fill a gap by combining X and Y" where X(Y) is a one-line instantiation.
Why it's hogwash: If your "novel combination" is just instantiating a known construction at a specific parameter, the gap is shallow. The engineering may be valuable but the math isn't new.
Example from graded-optic: GradedOptic g s t a b is literally Optic_{Kl(Writer g)}(s,t,a,b). The "gap" between graded monads and optics is bridged by a single observation: use the Kleisli category of Writer g as your base.
Fix: Say "concrete library combining..." not "novel construction filling a gap."
Pattern 3: Name Attribution Inflation (severity: 3-4)
Symptom: Attributing a standard construction to a specific researcher to sound more authoritative.
Example: "Hedges' teleological counit" for a standard existential quantification that every optics library uses. Hedges did important work on open games, but the existential residual in optics predates him (it's the coend variable in Riley's formulation).
Fix: Cite the mathematical object, not a researcher's name, unless they actually introduced it.
Pattern 4: Citation Mismatch (severity: 7)
Symptom: Citing a paper/book that doesn't support the claim.
Example: Citing Caramello's Theories, Sites, Toposes for a construction that involves no Grothendieck topologies, geometric theories, or actual toposes.
Fix: Only cite works whose actual content supports your claim. If you're inspired by an analogy, say "inspired by" not "following."
Pattern 5: Forward-Only → "Bayesian" Inflation (severity: 3-4)
Symptom: Calling any use of Log Double "Bayesian inference."
Why it's hogwash: Bayesian inference involves priors, likelihoods, conditioning, and posterior computation. Multiplying log-domain weights is likelihood accumulation, not inference. monad-bayes actually does Bayesian inference (with sampling, MH, SMC). Using its weight type doesn't inherit its capabilities.
Fix: Say "log-likelihood accumulation" or "log-domain scoring."
Pattern 6: "Novel" Para (severity: 3)
Symptom: Calling a parametrised lens "the Para construction."
Why: Capucci/Gavranović's Para is a category with morphisms (P, f: P.X → Y) — forward only. Adding a backward channel makes it a parametrised optic or "learner" (Fong/Gavranović). These are different things.
Fix: Say "parametrised lens with backward channel" or "learner in the sense of Gavranović" if it has both directions.
Pattern 7: Compositionality Assumed (severity: 4-5)
Symptom: Claiming a construction "composes" without proving it satisfies category laws.
Reference: Capucci (2023) explicitly warns: "Behaviours are not compositional on the nose." Theories of behaviour are only lax functorial. Compositionality is a theorem, not a given.
Fix: If you claim composition, prove identity and associativity laws (or at least test them).
Audit Procedure
- Collect all mathematical claims from README, module docs, comments, and examples
- For each claim, identify: the mathematical object referenced, the technical terms used, the novelty assertion
- Check against primary sources: Does the cited paper define the term this way? Is the construction actually what's claimed?
- Score each claim using the rubric
- Produce a table: Claim | Score | Why | Fix
- Apply fixes: Replace hogwash with honest language. The code doesn't change — only the words around it.
Key References for Checking Claims
- Optics: Riley (2018) "Categories of Optics", Capucci (2022) "Optics in Three Acts"
- Para: Capucci (2021) "Open Cybernetic Systems II", Gavranović (2024) PhD thesis Ch. 3
- Cybernetics: Capucci, Gavranović, Hedges, Rischel (2021) "Towards Foundations of Categorical Cybernetics"
- Graded monads: Katsumata (2014), Orchard/Wadler/Eades "Unifying graded and parameterised monads"
- Actegories: Capucci & Gavranović (2022) "Actegories for the Working Amthematician"
- Contextads: Capucci & Myers (2024) "Contextads as Wreaths" — the actual state of the art for grading in optics
- Sites/Toposes: Caramello (2017) "Theories, Sites, Toposes" — what sites actually are
- Anti-cargo-cult: Capucci (2023) "No, the Yoneda Lemma Doesn't Solve the Problem of Qualia"
Bidirectional Neighbor Index
| Neighbor | Direction | Scope |
|----------|-----------|-------|
| aristotle-lean | outgoing | scope:verify — formal verification of claims |
| code-review | bidirectional | scope:compose — hogwash check as part of review |
| refuse-mediocrity | incoming | scope:change — mediocre framing triggers audit |
| accept-no-substitutes | bidirectional | scope:verify — honest terminology |
| acsets-algebraic-databases | outgoing | scope:verify — check ACSet claims |
| open-games | outgoing | scope:verify — check game theory claims |
| discopy-operads | outgoing | scope:verify — check categorical claims |
GF(3) Triad
hogwash-removal (-1) + refuse-mediocrity (+1) + code-review (0) = 0
The validator (-1) catches inflated claims, the generator (+1) pushes for better framing, the ergodic coordinator (0) integrates both into the review process.
Example: graded-optic Audit (2026-02-08)
Applied to plurigrid/graded-optic. Results:
| Claim | Before | After | Score | |-------|--------|-------|-------| | "semiring IS the site" | Cargo-cult Caramello | Removed entirely | 8→0 | | "optic IS the classifying topos" | False | Removed entirely | 8→0 | | Caramello citation | Irrelevant | Removed | 7→0 | | "Novel gap" | Oversold | "Concrete library combining..." | 5→1 | | "Hedges' teleological counit" | Name-drop | "coend variable in the optic formula" | 4→1 | | "Bayesian bidirectional inference" | Inflated | "log-likelihood accumulation" | 3→0 | | Para attribution | Slightly loose | "Extends Para with backward channel" | 3→1 | | Composition (|>>>|) | Correct | Unchanged | 0→0 | | Examples | Honest | Unchanged | 1→1 |
Net effect: Average hogwash score dropped from 4.3 to 0.4.