{"path":"research/decomposition-axes.md","content":"# Decomposition Axes: How Many Ways Can You Slice a Claim, and When Should You?\n\n**Date**: 2026-08-14\n**Occasion**: The founder observed that scheme-derived critical questions are not a sufficient unbundling template, and asked what the research says — linguistics, category theory — about slicing sentences \"in any and all ways required\", without overdoing the structure.\n**Status**: Research synthesis with one architectural warning that needs answering before more decomposition is built.\n\n---\n\n## 1. Why the critical questions cannot be the whole answer\n\nThe ontology doc's observation is real: Walton's expert-opinion scheme asks about credibility, domain match, peer agreement and evidence basis, and those *are* the seams where \"Dr. Smith is a credible expert\" should split. But that template slices along exactly one axis, and four limits follow.\n\n**They decompose the inference, not the proposition.** A critical question asks where an *argument* can be attacked. It has nothing to say about the internal structure of a claim considered on its own — which participants it involves, which modifiers it carries, what it presupposes. \"Dr. Smith is credible as an expert in labor economics\" has propositional structure that no critical question touches.\n\n**They require a scheme first.** The pipeline must classify the argument into one of a closed enum before any template applies. The taxonomy work already established that a closed enum induced from one register breaks on the next, and that a schema with no \"does not fit\" value returns the nearest match and reports success.\n\n**They are fixed per scheme, so they cannot see this sentence.** Every expert-opinion argument gets the same four questions. What is specific to *this* claim — a smuggled evaluative adjective, a quantifier, a frame-laden noun — is invisible to a template by construction.\n\n**And a claim can carry no scheme at all** while still being thoroughly bundled. Most of the corpus is not an argument-from-expert-opinion.\n\n## 2. The uncomfortable finding, and it should be answered before building more\n\nThe applied literature on decompose-then-verify has moved since the pipeline was designed on DnDScore, and it has moved *against* the assumption that finer is better.\n\n**Decomposition is not a reliable improvement.** Hu, Long & Wang (NAACL 2025, *Decomposition Dilemmas*) found the effect inconsistent across systems, with a trade-off between accuracy gained and noise introduced.\n\n**And the condition that decides it is evidence alignment.** *The Alignment Bottleneck in Decomposition-Based Claim Verification* (arXiv 2602.10380) separates two setups: evidence aligned **to each sub-claim**, versus the same claim-level evidence repeated for every sub-claim. Decomposition helps significantly in the first and **fails to help or actively degrades** in the second, across three datasets. Their summary is that without sub-claim-aligned evidence, decomposition \"adds structure without resolving ambiguity\".\n\n**This is a warning aimed squarely at Deliberus.** The graph attaches evidence and strength at the level of whatever claim exists, and a decomposition that mints four children does not thereby mint four evidence sets. Splitting \"Dr. Smith is credible\" into publication record, appointment, domain match and what-credible-means without attaching *distinct evidence to each* is the degrading configuration, not the improving one. Before the next decomposition axis ships, the honest question is whether the architecture creates evidence alignment or merely creates nodes.\n\n**The related finding is a gift, because the project already does it.** The same paper found that conservative **abstention** on sub-claims sharply reduces error propagation compared with confident wrong answers. Deliberus's `undecided` residue verdict, `unknown` attribution role, and propose-only classifiers are exactly that discipline, arrived at independently.\n\n**Two more results reshape the goal itself.** Gunjal & Durrett (EMNLP Findings 2024, *Molecular Facts*) argue that **fully atomic facts are the wrong representation**, and propose two criteria in tension — *decontextuality* (does it stand alone) and *minimality* (how little was added to achieve that) — with the good target being molecular rather than atomic. And *Optimizing Decomposition for Optimal Claim Verification* (ACL 2025) makes atomicity a measurable quantity and finds that **each verifier has its own optimum**: there is no universally correct grain, and the correct grain depends on what the claim is being checked against.\n\nSo \"decompose as far as possible\" is refuted as a goal by the literature the pipeline is built on. What replaces it is in §4.\n\n### 2b. Routing evidence instead of duplicating it — the founder's answer, and what it requires\n\nThe founder's response to the warning: could claim-level evidence not be *intelligently reused* across related sub-claims, judging generalizability, rather than requiring new evidence per child? Yes, and it reframes the distinction correctly. **Aligned-versus-repeated is not about where evidence came from; it is about whether the link between a piece of evidence and a sub-claim is specific.** Repeated evidence fails because an undifferentiated blob is handed to every child, so nothing indicates which part bears on which. Routing *manufactures* the aligned condition from claim-level evidence, and is a genuine third option rather than a smarter version of the failing one.\n\nThree requirements follow, and the third was verified in code rather than assumed.\n\n**Routing must be able to abstain.** A mis-routed piece of evidence is worse than no evidence, because it manufactures apparent support — the same asymmetry as stance flattening, where a wrong link damages more than a missing one. The alignment paper independently supports this: the *type* of sub-claim error matters more than overall accuracy, and conservative abstention sharply reduces error propagation. So the un-routed fraction is reported, not hidden.\n\n**Generalizability is a scope judgment, not a relevance score.** Evidence that Smith published forty-seven papers is highly *relevant* to \"labor economics is the relevant domain for this claim\" and transfers to it **not at all**. Sibling sub-claims under one mother routinely have disjoint evidential scope, and a similarity-shaped router would get this exactly wrong. This is the hard part.\n\n**Generous routing inflates confidence under the current semantics.** `subclaim_energy` sums `(σ − 0.5) × 0.3` across siblings with no correlation term (verified by reading `deliberus/graph/qbaf.py`). One piece of evidence routed to three children raises all three, and the mother receives that lift three times. **Routing therefore has a built-in bias toward the flattering direction**, which is precisely the class of failure this project instruments against.\n\n**The fix for the third is already the corpus's own design.** `scheme-bounded-decomposition-and-evidence-as-subgraph.md` treats evidence as a subgraph rather than a property. Make evidence a **node** and routing it to three children makes it a shared child with three parents — a directed acyclic graph, where the shared provenance is visible and can be discounted. Copy it onto three children as a property and the correlation is invisible by construction. So the architectural instruction is: **route by linking, never by duplicating.**\n\nThe pipeline shape that follows is one new stage between decomposition and strength computation: for each evidence-and-sub-claim pair, judge scope transfer, link or abstain, and record what went unrouted.\n\n**Founder correction, 2026-08-15, and it resizes the discount rather than removing it.** The worked example above treats *\"she published 47 papers\"* as one unit of evidence, and it is not — those papers have contents, quality and relevance of their own, and everything else relevant in the graph bears on them. Follow that through and **most *apparent* sharing dissolves**: a publication-record child draws on all 47, a domain-activity child on the labor-economics subset, a standing child on citation data rather than counts. What looked like one fact behind three children was one *bundle* cited three times, so fair-share discounting was partly correcting an artifact of coarse evidence. It stays correct for **genuine** sharing, where a single atomic finding really does back several siblings, and the implementation is already granularity-indifferent — feed it leaves and it is right, feed it bundles and it is crude. What is missing is therefore an **evidence-decomposition pass**, distinct from routing and sequenced alongside it. Full note: [self-similar-decomposition-and-claim-ontology.md](self-similar-decomposition-and-claim-ontology.md) § The founder's correction.\n\n## 3. The axes, with the test that finds each seam\n\nThe founder's phrase was *in any and all ways required*, and that is the right shape: there is no single decomposition, there are orthogonal axes, and the pipeline currently runs one and a half of them. Each axis below has an established source and a mechanical test.\n\n| Axis | What it separates | The test | State |\n|---|---|---|---|\n| **Dialectical** (Walton) | where an inference can be attacked | the scheme's critical questions | **shipped** |\n| **Predicate–argument** (Davidson 1967, neo-Davidsonian) | event, participants, and each modifier | can you deny one modifier and keep the rest? | not built |\n| **Presuppositional** (Stalnaker, Karttunen, Beaver) | what you are committed to even under denial | negate the sentence; what survives is presupposed | not built |\n| **At-issue vs backgrounded** (Potts 2005) | asserted content that is not up for discussion | can a hearer reply \"that's false\" and target it? | not built |\n| **Degree / threshold** (Kennedy) | the fact from the standard it is measured against | does the term take *very* or a comparative? | not built |\n| **Frame** (Fillmore, FrameNet) | commitments a word carries by evoking a frame | does the other side use this word at all? | not built |\n| **Attributive** | who asserts versus who is reported | is the attributed party the source's author? | in progress |\n| **Scope / quantificational** | quantity, attitude, and content | vary the quantifier; does the rest survive? | not built |\n\n**The predicate-argument axis is the largest gap and the clearest win.** Davidson's move — treat a sentence as an event with participants, so that modifiers become separate conjuncts — is precisely the lossless unbundling being asked for, and it is the reason adverbs are detachable at all. Applied to a live corpus claim: *\"minimum wage laws cause unintended and unnecessary hardship for the low-skilled workers the laws are intended to assist\"* separates into the causal claim, the *unintended* modifier, the **`unnecessary`** modifier, the population restriction, and the intention ascription. **`Unnecessary` is a value premise smuggled inside an empirical claim**, and a reader can accept every fact while rejecting it. Nothing in the current pipeline surfaces that.\n\n### The classificatory premise, and it is detectable with no model at all (measured 2026-08-14)\n\nThe founder's observation on the run-6 pair: the denying side's whole argument requires the territory to be *occupied*, a word she uses fifty-four times and he never uses once. Neither text argues for the classification. She assumes it; he declines to engage it. His conclusion was that a premise of this kind must **always** be made explicit by the pipeline.\n\nMeasured across the two sources' extracted claims — not even the raw text — the asymmetry is stark, and it is the argument itself:\n\n| Used only by the affirming side | Used only by the denying side |\n|---|---|\n| non-state, actors | military, West, Bank, Strip, police, Israeli, power, population, conflict, since |\n\nOne author writes in the vocabulary of **inter-state armed-conflict law**, where the operative question is whether a non-state actor can trigger the right at all. The other writes in the vocabulary of **occupation administration** — occupying power, civilian population, policing, named territories. Each vocabulary carries a classification of the situation, that classification decides the case, and **neither author argues for theirs**. The dispute is settled before either of them starts reasoning.\n\nTwo things make this the most tractable unstated-premise signal in the corpus. It needs **no embedding, no similarity, and no model** — a term used many times by one side and never by the other is a counting operation, which is exactly why it catches what claim-level cosine could not. And its precision comes from the pairing: a word absent from one text means nothing on its own, and means a great deal when the opposing text leans on it.\n\n**It also names a real gap in the pipeline.** Implicit-premise extraction currently runs **within** a single source, which is how run 6 recovered the unwritten counter-premise on the affirming side. But a classificatory premise is invisible from inside one text, because inside that text it is not missing — it is simply what the author takes for granted. **One side's silence is only legible against the other side's insistence**, so this class of premise can only be found by comparing an opposed pair. That is a different pass from the one that exists.\n\n**The frame axis explains dogfood run 6 retroactively.** One text uses \"occupation\" fifty-four times and the other never once. That is not a vocabulary difference to be bridged by better embeddings; it is a difference in which frame is evoked, and the frame carries commitments about occupier, occupied and legality that the other author would refuse. Frame divergence is a *measurable* signal of deep disagreement and it needs no semantic similarity at all.\n\n## 4. The rule that stops this becoming over-structure\n\nThe founder's worry is exactly right and now has two evidence-backed answers rather than an aesthetic one.\n\n**Molecular, not atomic.** The target is the smallest form that still stands alone, not the smallest form. Minimality and decontextuality trade against each other and the balance point is the artifact.\n\n**Decompose along an axis only when someone contests along it.** A claim is never \"atomic\" and never \"decomposed\" — it is *undecomposed along axes A, B and C*, and the axes are enumerable. This replaces a boolean with a vector, it makes the completeness oracle able to say which *kind* of exposure is missing, and it is already the founder's own position from Session 9: *\"recursively decomposed (eventually, not instantly tho)\"*. The atomicity-optimum result gives it teeth — since the right grain depends on what the claim is checked against, decomposing before a challenge exists is decomposing against an unknown optimum.\n\nThis also preserves the sorry-marker philosophy exactly. An undecomposed axis is a marked gap, not a defect, and the invitation to descend is the product.\n\n## 5. Category theory, and it is not decoration\n\nThe founder asked whether category theory has anything to offer. It offers two things precisely, and both name questions this project already has.\n\n**Losslessness is a colimit condition.** A decomposition is lossless when the parts recompose to the whole. That is directly buildable as an instrument and it is the exact analogue of disagreement preservation: **after decomposing, can a model reconstruct the parent from the children alone?** If it cannot, something was dropped, and the gap is measurable rather than felt. Nothing in the pipeline currently checks that decomposition conserves content, which sits oddly beside the standing rule that every transform must account for where the removed value went.\n\n**Overlap coherence is a sheaf gluing condition, and this is the answer to the Dawkins question.** A sheaf is the mathematics of passing from local data to global data: local sections that agree on their overlaps glue into a global section. Abramsky & Brandenburger (2011) showed that contextuality *is* the obstruction to a global section existing, and Abramsky, Barbosa, Kishida, Lal & Mansfield (*Contextuality, Cohomology and Paradox*, CSL 2015) generalized it well beyond physics — to relational databases, constraint satisfaction, and logical paradoxes, all sharing one signature: **locally consistent, globally inconsistent.**\n\nTwo consequences worth holding.\n\n*Shared children are the normal case, not an anomaly.* \"Dawkins published in biology journals\" can support both \"expert in biology\" and \"expert in evolutionary theory\". The strength walk already memoizes, so a claim with two parents is computed once and used correctly by each — the structure is a directed acyclic graph, and overlapping subtrees are already legal.\n\n*And the failure to glue is itself a finding.* When local subtrees are each coherent but no consistent global assignment exists, that is not a bug to repair but a discovered incoherence, and it has a name and a literature. Deliberus **already ships one instance**: the discursive-dilemma flag, which detects premise-votes and conclusion-votes diverging, is the judgment-aggregation case of exactly this phenomenon (List & Pettit; Dietrich; Mongin). The generalization is that any decomposition graph can be asked whether its local sections glue, and the places they do not are the most informative in the corpus.\n\n## 6. What follows\n\nOrdered by evidence, not appetite.\n\n1. **Answer the alignment question before building more axes.** Does decomposition here attach distinct evidence per child, or repeat the parent's? The literature says the second configuration degrades rather than improves, and it is the cheaper thing to check.\n2. **Build the recomposition check.** Cheap, mechanical, and it makes \"as lossless as possible\" a number instead of an aspiration.\n3. **Replace the atomic boolean with per-axis exposure.** A claim carries which axes it has been decomposed along; the completeness oracle then reports the *kind* of gap rather than a fraction.\n4. **Predicate–argument decomposition next among the axes**, because smuggled evaluative modifiers are the highest-value thing the corpus currently cannot see.\n5. **Frame divergence as an instrument**, since run 6 supplied the motivating case and it needs no embedding at all.\n\n---\n\n## Sources\n\n- Hu, Long & Wang (2025). *Decomposition Dilemmas: Does Claim Decomposition Boost or Burden Fact-Checking Performance?* NAACL.\n- *The Alignment Bottleneck in Decomposition-Based Claim Verification*, arXiv:2602.10380.\n- Gunjal & Durrett (2024). *Molecular Facts: Desiderata for Decontextualization in LLM Fact Verification.* EMNLP Findings.\n- *Optimizing Decomposition for Optimal Claim Verification*, ACL 2025 (atomicity as a measurable quantity; per-verifier optima).\n- Wanner, Van Durme & Dredze (2025). *DnDScore.* EMNLP — the pipeline's own basis.\n- Metropolitansky & Larson (2025). *Towards Effective Extraction and Evaluation of Factual Claims* (Claimify). ACL.\n- Davidson (1967), *The Logical Form of Action Sentences*; neo-Davidsonian event semantics.\n- Potts (2005), *The Logic of Conventional Implicature*; Stalnaker and Karttunen on presupposition; Kennedy on gradable predicates; Fillmore, frame semantics.\n- Abramsky & Brandenburger (2011), *The Sheaf-Theoretic Structure of Non-Locality and Contextuality*, arXiv:1102.0264.\n- Abramsky, Barbosa, Kishida, Lal & Mansfield (2015), *Contextuality, Cohomology and Paradox*, CSL.\n- List & Pettit; Dietrich; Mongin — judgment aggregation and the discursive dilemma.\n\n**Read depth**: the six decomposition papers were read at abstract and results depth, with the Alignment Bottleneck and Optimizing Decomposition papers read into their findings sections. The category-theory sources were read at abstract plus the sections stating the global-section characterization. The linguistics is cited from standard results rather than re-read.\n\n## See also\n\n- [self-similar-decomposition-and-claim-ontology.md](self-similar-decomposition-and-claim-ontology.md) — the mother-claim pattern, and the reported-speech blind spot this extends\n- [taxonomy-gaps-and-the-closed-enum.md](taxonomy-gaps-and-the-closed-enum.md) — why a closed enum breaks on the next register\n- [the-load-bearing-unsaid.md](the-load-bearing-unsaid.md) — presupposition and hinge commitments, already in the corpus\n- [dogfood-run-6-israel-palestine-cross-domain.md](dogfood-run-6-israel-palestine-cross-domain.md) — the frame-divergence case\n- [../depth.md](../depth.md) — no copout axioms, the principle all of this serves\n"}