Paper statuses — A work’s standing in this record: whether it is worth reading. Not whether its findings are true — that is the THEORY scheme’s business, and the two can disagree in either direction.
Watching — promising and unproven; the note says what would settle it.
32 of 2004 LIT documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| LIT-005 v3 | Adding causality to the information-theoretic perspective on individuality | Bourrat (2024), DOI-10.1007/s13194-023-00566-1. Of Krakauer et al.’s (2020) three mutual-information “individuality” terms (A* = I(S_{t+1}; S_t), A = I(S_{t+1}; S_t | E_t), nC = I(S_{t+1}; E_t | S_t)), Bourrat argues that nC and A* are not individuality measures. He then proposes the interventional  = I(S_{t+1}; Ŝ_t) (Eq. 6) and two ETI criteria: C1, a normalised Â_{S2}/H(Ŝ2) ≥ Â_{S1}/H(Ŝ1)|θ₀, and C2, low Var(Â_{S2} | Ê2 = ê2k). None of these is computed on any system. The paper’s claim that  ≡ I(S_{t+1}; S_t | E_t) = A in Krakauer’s model is false in general. | Proposed — read in full 2026-09-25 (NOTE-027); a clear conceptual argument that information-theoretic individuality should be interventional. It is unproven as a measure. Three things would settle it: a worked computation of Â, C1 and C2 on an explicit model (for example Black et al.’s ecological-scaffolding model); a corrected account of how  relates to the observational A; and a correct adjustment set for its own Fig. 3 example. |
| LIT-009 v3 | An 800 Myr-old Impact Shower on the Terrestrial Planets from the Breakup of the Eulalia Parent Body | Bottke et al. (2026), ARXIV-2606.05036. The paper builds a collisional-plus-dynamical source model. In its preferred Solution 5, the Eulalia parent body breaks up T = 865 Myr ago at a_c = 2.48 au next to the Jupiter 3:1 resonance. The model sends 6,995 D ≥ 2 km and 833 D ≥ 5 km fragments into the J3:1 (Table 1, before a ≈1.5× collisional correction). With impact probabilities per resonance entrant of 5.4×10⁻³ (Venus), 4.2×10⁻³ (Earth) and 0.6×10⁻³ (Mars), and the Moon at 1/20 of Earth, the expected largest impactor is D ≈ 8 km on Earth and Venus, 4.5 km on Mars and “>3 km” on the Moon. A Monte Carlo of 7 lunar projectiles puts the seven lunar craters dated 760–820 Ma “generally … within the 1σ” envelope. The authors conclude the breakup “can plausibly account for” the ~800 Ma lunar crater cluster, although on average the model’s projectiles are too small to make Copernicus. | Proposed — read in full 2026-09-25 (NOTE-002); a careful, well-sourced plausibility model for a hypothesised 800 Ma impact shower, and worth reading as the source model for it. It is unproven: its lunar dates are scaled from a single sample-dated crater (Copernicus), and only Solution 5, the most favourable, is carried forward. Whether the shower happened, which radiometric dating of samples from the other six ~800 Ma craters or a CI-like projectile signature at more than one of them would settle, is THEORY-1195, Proposed; the reading of the model is THEORY-499, Active. The Earth, Mars and Venus material in §7 is self-declared speculation. |
| LIT-017 v2 | Spectral Networks and Betti Lagrangians | Casals & Nho (2025), ARXIV-2504.08144. For any rank n, and for Lagrangians with non-algebraic (positive-braid) asymptotics, spectral networks exist and are characterised by pseudo-holomorphic strips in the adiabatic limit (Theorems 1–2). For exact Betti Lagrangians, a Family Floer functor equals Gaiotto–Moore–Neitzke non-abelianization in the adiabatic limit (Theorem 3, i.e. 5.24) and is realised by A∞-operations in wrapped and partially wrapped Fukaya categories of T*S (Theorem 4). The analysis in §§4–5 leans on Ekholm 2007 and on the second author’s 2024 preprint, and Theorem 5 (spectral networks from Demazure weaves) is recorded without a written proof. | Proposed — read in full 2026-09-25 (NOTE-022); an unrefereed v1 preprint that is carefully motivated, but whose analytic core (§4 adiabatic convergence, §5 continuation strips) leans on Ekholm 2007 and on the second author’s 2024 preprint, and whose Theorem 5 has no written proof. What would settle it: a refereed version or independent expert check of §§4–5, a written proof of Proposition 7.5, and theorem statements narrowed to the hypotheses the proofs use (creative networks, exactness, trimmed limits). Only §1 is useful to a non-specialist here. |
| LIT-031 v2 | Moving away from lexicalism in psycho- and neuro-linguistics | Krauska & Lau (2023), DOI-10.3389/flang.2023.1125127. The authors argue that lemma-based production models encode two lexicalist assumptions: a morphology/syntax split, and a stored meaning–syntax–form “triad”. On that basis the models mishandle Inuktitut polysynthesis, separable Vietnamese idiomatic collocations, Hiaki number suppletion and English verb–object idioms. Updating the representations (treelets) is not enough, because the algorithms — separate lexical retrieval and structure building, word-sized increments — also have to change. They sketch an 8-stage non-lexicalist model and derive qualitative aphasia predictions from it. There are no new data and no implementation. | Proposed — read in full 2026-09-25 (NOTE-029); This is a clear diagnosis of where lemma models build in lexicalism, but its positive model is a verbal sketch (the full model is “in prep.”) and its aphasia predictions are untested; an implemented model, or lesion or aphasia data that separate its predictions from lemma-model ones, would settle it. |
| LIT-046 v3 | The Computational Foundations of Collective Intelligence | Pilgrim et al. (2025), ARXIV-2509.07999. A conceptual framework, with no model, data or derivation. It sets out individual and collective computational resources in four dimensions: sensing ΣI_i, states S_c × ∏S_i, processes F_c + ΣF_i, and actions ∏A_i (Table 1). It then maps the collective’s surplus onto familiar mechanisms (aggregation with noise σ_i²/n, distributional beliefs P(H), memory persistence T_c, division of labour). Coordination and cooperation are given as the constraints that make the trade-off, and three animal case studies are retold in these terms. | Proposed — read in full 2026-09-25 (NOTE-055); a clear, well-referenced vocabulary for collective intelligence (Marr’s levels run bottom-up). Its central claim, that the known forms of collective intelligence are “aspects of a single unifying principle”, is asserted and illustrated, not derived. It would be settled by one case where the resource-and-constraint accounting yields a quantitative prediction that existing mechanism-specific models do not. |
| LIT-047 v3 | Is It Good to Cooperate? Testing the Theory of Morality-as-Cooperation in 60 Societies | Curry et al. (2019), DOI-10.1086/701478. Coding 3,460 eHRAF paragraphs on the 60 Probability Sample Files societies found 962 morally valenced mentions of seven cooperative behaviours, 961 of them positive. The one negative is Chuuk admiration of open theft as dominance. Presence varied widely by domain: property 54/60 (90%), kin 47 (78%), group 44 (73%), reciprocity 43 (72%), respect 35 (58%), bravery 32 (53%), fairness 9 (15%). Presence correlated with ethnographic coverage (r = 0.43). The design can detect a morally positive mention but has almost no way to register a negative one, so the 99.9% is weak evidence for universality. | Proposed — read in full 2026-09-25 (NOTE-034); the clearest statement of morality-as-cooperation, with an unusually good commentary set (Bloom; Smith & Kurzban; Wong) that states the objections exactly. Its empirical test is weakly diagnostic: the codebook defines the behaviours in virtue terms, the authors’ footnote 3 recodes conflicts as cooperation-vs-cooperation, and the first-pass selection was not blind. It would be settled by blind coding of all moralized content in the same sample, testing whether non-cooperative domains (purity, sex, harm) are moralized as often. |
| LIT-049 v2 | A coarse-graining account of individuality: how the emergence of individuals represents a summary of lower-level evolutionary processes | Bourrat (2023), DOI-10.1007/s10539-023-09917-x. Bourrat proposes that a partition of particles into collectives defines individuals when the “projected” prediction (coarse-grain at t1, then evolve the coarse-grained state) differs from the “truthful” one (evolve at the fine grain, then coarse-grain at t2) by δC = C_T − C_P < θ, across many traits (Eqs. 1–2). He argues that, because measurement and computation are finite, coarse-graining can be the only way to predict at all: in his example, 100 operations predict 10 entities for 10 timesteps or 2 collectives for 50. That indispensability is his whole case for the “quasi-ontological” status of collectives at Godfrey-Smith and Kerr’s fifth stage. Nothing is computed on any model. | Proposed — read in full 2026-09-25 (NOTE-064); a lucid philosophical statement of “individual = a coarse-graining worth its cost”. Its formal criterion is informal and, as written, degenerate: minimal δC picks the finest partition, and the cost term the argument depends on is never put into the criterion. It would be settled by a worked ETI model in which an explicit accuracy–cost objective is computed and picks out the collectives. |
| LIT-057 v2 | Effect of delay on the emergent stability patterns in generalized Lotka–Volterra ecological dynamics | Saeedian et al. (2021), ARXIV-2110.11914. The paper studies random delayed generalized Lotka–Volterra dynamics, ẋ_i = x_i(r_i + Σ_j b_ij x_j(t−τ)), with instantaneous interactions switched off (A = 0) in every delay result. A feasible, stable equilibrium loses stability by a Hopf bifurcation at τ_c = min over eig(J) of (1/|j|) arctan(Re j/Im j) (Eq. 14), where J = diag(−B⁻¹r)B, and this matches simulation (Fig. 5b; S = 100 is stable at τ = 12 and oscillates at τ = 18). In the oscillatory regime, at τ = 20 and 22 for S ≲ 70, community-level CV falls with S while mean species-level CV rises (Fig. 6). The paper reads this as a positive diversity–stability relation but tests it against no averaging null. | Proposed — read in full 2026-09-25 (NOTE-061); A modest, partly numerical preprint whose critical-delay formula is the standard linear delay result applied to a random community matrix. Its diversity–stability claim would be settled by comparing CV_c(S) against the √S averaging expected from weakly correlated oscillators (the “statistical inevitability” null of Tilman et al. 1998, which the paper cites as ref. 40), and by resolving whether the “divergent” phase is numerical or real. |
| LIT-059 v3 | The Strongest El Niño Ever | Hausfather (2026), https://www.theclimatebrink.com/p/the-strongest-el-nino-ever. Hausfather reports that the July 2026 runs of 14 seasonal models (667 members, model-weighted) put the median peak Niño 3.4 anomaly of the 2026-27 El Niño at 3.6 °C, against his computed record of 2.75 °C (2015-16). That gives about a 91% chance of a record, or about 77% on a relative index where 1982-83 holds the record at 2.69 °C. He cautions that no model has been verified at this intensity. - NOAA’s own series agree on the rankings but give lower record values: 2.67 monthly for 2015-16 and 2.6 in ONI. - Observations through mid-September 2026 are on a record-setting track: weekly Niño 3.4 +3.0 °C on 16 Sep, and monthly ERSSTv5 +2.17 in August. The event has not yet peaked, so the forecast cannot yet be verified. | Proposed — read in full 2026-09-25 (NOTE-031); This is a dated forecast. What settles it is the observed 2026-27 peak, i.e. monthly ERSSTv5 Niño 3.4 and RONI through about February 2027. The observations to mid-September are consistent with a record but do not yet reach 3.6 °C. |
| LIT-060 v2 | The Mothership Vortex: An Investigation Into the Firm at the Heart of the Democratic Spam Machine | Bonica (2025), https://data4democracy.substack.com/p/the-mothership-vortex-…. From FEC filings, Bonica reports that a core network of PACs linked to Mothership Strategies raised about 159M went to Mothership, out of 11M reached candidates, campaigns or national party committees, a “fundraising efficiency rate of just 1.6 percent”. The headline numbers cannot be reproduced from the published repo: its inputs are missing, it has a fatal undefined variable, and it computes several reported figures nowhere. As documented, its disbursement queries cover only the latest two-year period and at most 1,000 disbursements per committee, largest first, which would bias the $11M downward rather than cap it. The post’s own infographic contradicts several of its figures. | Proposed — read in full 2026-09-25 (NOTE-042); A plausible and important claim about political-fundraising efficiency, not established by what was published. It would be settled by a run that reproduces the figures, with the input files committed, all cycles queried and paginated fully, and independent expenditures and field spending counted explicitly in or out of “reaching campaigns”. |
| LIT-069 v2 | Surface optimization governs the local design of physical networks | Meng et al. (2026), DOI-10.1038/s41586-025-09784-4. The degree counts in Fig. 1d show k = 4 nodes making up 4.6–17.7% of branch points across the six datasets. The pooled 16.6% is 96% human-neuron nodes. Bifurcation angles also fail to peak at 2π/3. From this the authors infer that local branching minimises sleeve surface area under a minimum circumference w, not wire length. For a regular tetrahedron their numerical minimiser merges two bifurcations into a trifurcation at χ = w/r ≈ 0.83, and a thin branch sprouts orthogonally below ρ = w′/w ≈ 0.6. Per-dataset empirical thresholds are ρ_th = 0.52–0.92. The “exact mapping” to string-theory worldsheets covers only the unconstrained minimal-area problem. The SI says the implemented method yields surfaces that are only locally area-minimising (§5). | Proposed — read in full 2026-09-25 (NOTE-075); a promising and cleanly falsifiable hypothesis, but the evidence does not yet separate it from simpler accounts. Three things would settle it: recomputing the empirical P(λ) without the SI’s trifurcation-merging rule, running the actual surface minimiser (rather than a sigmoid fitted to one tetrahedron) on random terminal sets, and testing the branching-to-sprouting breakpoint against a no-breakpoint null. |
| LIT-079 v2 | Causal Claims in Economics | Garg & Fetzer (2024), ARXIV-2501.06873. GPT-4o-mini is run in nine passes per paper over the first 30 pages of 44,852 NBER/CEPR working papers. Edges kept in at least 4 of 9 passes, JEL-mapped, give “claim graphs” in which the share of edges backed by DiD/IV/RCT/RDD/synthetic control rises from 7.7% (1990) to 31.7% (2020). In year-fixed-effect-only regressions, doubling causal edges is associated with +1.36 pp top-five probability and +11.2% citations, while non-causal counterparts are flat or negative. The validation checks paper-level method labels, and only weakly: RCT and field labels have precision ≤ 0.10. It never checks the edges themselves against human labels. | Proposed — read in full 2026-09-25 (NOTE-083); a promising, openly released claim-extraction infrastructure whose headline associations rest on edges never validated against human labels and on regressions with year fixed effects only. An edge-level human-annotated audit, and outcome regressions with field and method controls on a common sample, would settle it. |
| LIT-083 v2 | Toward interoperable representation and sharing of disinformation incidents in cyber threat intelligence | Sánchez González et al. (2025), ARXIV-2502.20997. The paper shows that a DISARM-labelled disinformation incident can be encoded in plain STIX 2.1 with four object types (IntrusionSet for the incident, ThreatActor, AttackPattern, Location) and three relationships (uses, attributed-to, targets), then served by an open-source microservice platform (DISINFOX) to OpenCTI through a custom connector. Its validation is a demonstration that 118 hand-labelled incidents passed through the pipeline; it reports no measurement of fidelity, usefulness or scale. | Proposed — read in full 2026-09-25 (NOTE-028); a working, clearly described proof of concept for carrying disinformation incidents as CTI. It is an unreviewed preprint with a deliberately minimal mapping and no evaluation beyond “it ingests”; what would settle it is peer-reviewed publication plus evidence that analysts use the shared incidents, or a comparison with DAD-CDM, which the authors themselves name as the emerging standard. |
| LIT-188 v5 | Scaffolding individuality: coordination, cooperation, collaboration and community | Griesemer & Shavit (2023), DOI-10.1098/rstb.2021.0398. The paper sets out an idealized three-stage sequence of interaction types, which it calls a “first and rough sketch” (§1). Stage 1 is coordination in collections (pairwise, “aggregative” interactions of co-located individuals). Stage 2 is cooperation in conexuses (a connected web of binary interactions whose benefits can still be counted per member). Stage 3 is collaboration in communities: heterogeneous multi-way interactions around a shared goal, in which generatively entrenched “core” interactions give organizational closure. Table 1 puts the transition to a new level of individuality between stages 2 and 3 only. The paper asserts, rather than argues, that this describes evolutionary transitions non-circularly and that individuality is a special case of collectivity. Its one argued conclusion is hedged: community-level inheritance “seem[s] likely to evolve in tandem” with community-level individuality (§3). | Proposed — read in full 2026-09-26 (NOTE-173); a short programmatic sketch, and the authors call it one. It is worth knowing as the compact statement of Griesemer’s scaffolding, reproducer and generative-entrenchment view applied to human social transitions. Its headline claims (non-circularity; individuality as a special case of collectivity) appear only in the abstract. Two things would settle it: the model of community “reliability” and endogenization the authors promise in §2 (“We hope to explore such models in future work”), or an application of the 3Cs to a worked case, such as the companion Neolithic paper (LIT-1935, registered unread), that separates collection, conexus and community by measurable criteria. Re-read 2026-11-01 (NOTE-173, version 3). |
| LIT-190 v2 | The coherent and fluent mind: how unified consciousness is constructed from cross-modal inputs via integrated processing experiences | Winkielman et al. (2015), DOI-10.3389/fpsyg.2015.00083. An opinion piece proposing an extra route to the unity of consciousness across the senses. Different modalities feed one global, content-nonspecific experience of processing quality (fluency, familiarity, coherence), and this integrated feeling then enters decisions about its source and relevance. The main support is the authors’ own finding (Ziembowicz et al. 2013; three experiments) that coherent but unrelated background patterns in one modality made targets in another modality be judged more “regular”, “familiar” and “possible”. The authors state that direct evidence is still needed that such effects run through changed experience and that its integration is causal (p. 2). | Proposed — read in full 2026-09-26 (NOTE-146); a promising, explicitly unproven hypothesis. It would be settled by showing, inside the cross-modal coherence paradigm itself, that the effect depends on an experienced feeling: for example, that it disappears when participants are led to attribute their sense of coherence to the background (the discounting manipulation the authors cite from other paradigms), and that reports of felt coherence mediate the judgement shift. |
| LIT-193 v2 | Better to be a Pig Dissatisfied than a Plant Satisfied | Terrill & Veit (2024), DOI-10.1007/s10806-024-09922-4. The paper argues conditionally. Suppose (A1) sentience comes in degrees, (A2) plants may be “quasi-sentient”, and (A3) moral status comes in degrees and is fixed by degree of sentience. Then plants may have partial moral status, generating “some” obligations that are “outweighed by animal interests in most cases” (Table 1). Animals keep prima facie priority, so granting plants moral status “does not require” treating eating plants and eating pigs alike. The authors propose assigning plants “a very low value” of moral status until evidence accumulates (p. 13). A1–A3 are assumed, not argued, and A2 rests on a survey of contested plant-behaviour findings. | Proposed — read in full 2026-09-26 (NOTE-120); a coherent but unproven conciliatory position, useful as a clear template of the graded-sentience-to-graded-status inference. What would settle it is evidence for or against plant valenced states. Footnote 21 names the two gaps: the degree of plant-specific valenced states, and whether plants have high harm thresholds or harm-numbing mechanisms. The second author’s later work signals a move against plant consciousness (see LIT-105), so check his current view before citing it as his. |
| LIT-200 v2 | Wave-functionalism | Allori (2021), DOI-10.1007/s11229-021-03332-z. Allori proposes that the wave function be defined by three roles — empirical, nomological and explanatory. On this view it is an ingredient that “partially realizes” the law, not a law and not a material field. So its time-dependence and non-uniqueness (a phase shift, a density matrix) are harmless, it counts as non-epistemic and ontic, and it can take part in constructive explanation. Each of these is argued informally, and the escape from PBR is by relabelling the ontic/epistemic distinction, not by engaging the theorem. | Proposed — read in full 2026-09-26 (NOTE-154); a distinct and clearly placed option in the ψ-as-law family (LIT-204 §4.2). It is unproven until “part of the law” and “non-representational yet ontic” are given content that separates the view from Humean nomologism, and until it answers the “too cheap” objection it invites. |
| LIT-208 v2 | Distributional Semantics, Holism, and the Instability of Meaning | Grindrod et al. (2024), ARXIV-2405.12084. The authors argue that distributional models answer the instability objection to meaning holism if meaning is read “differentially”, as a word’s relations to its nearest neighbours, and not as its position in the space. They illustrate this with two corpus-expansion demonstrations. In a ±10-word count model on Stein’s The Making of Americans (about 522k tokens), adding Hemingway’s “A Clean, Well-Lighted Place” (under 1,500 words) shifts every cosine value for “know” by at most about 0.0005 (e.g. 0.95231 → 0.95284 for “understand”) and leaves its top-10 neighbours in the same order, while “glass” gets a new neighbourhood. A Word2vec CBOW model on 143M words of Wikipedia shows the same pattern when about 21M words of the Stanford Encyclopedia of Philosophy (SEP) are added: “atomism” shifts, “can” barely moves. The residual instability, they argue, is a virtue. | Proposed — read in full 2026-09-26 (NOTE-158); promising as a philosophical reply, but its empirical half rests on top-10 neighbour tables for four hand-picked words, with no stability metric and no seed replication. It would be settled by a systematic measurement of neighbour-set stability against word frequency across corpus increments and random seeds, which Antoniak & Mimno (2018) partly supply and the paper cites but does not reproduce. |
| LIT-267 v3 | The Lattice Representation Hypothesis of Large Language Models | Xiong (2026), ARXIV-2603.01227. Thresholding linear attribute directions (Fisher-LDA probes) gives a crisp object–attribute incidence, and the paper’s Theorem 1 is the standard fact that any such incidence has a complete concept lattice. The geometric meet is half-space intersection; the join is defined as the set union of two cones and “approximated by the conic hull” of their directions, which as written is not a lattice join. On five WordNet domains with GPT-4o-annotated attributes, the probes recover the incidence at F1 69.7–83.2 on three 7–8B models, and profile-based subsumption reaches F1 57.1–77.1. No lattice law is ever tested. | Proposed — read in full 2026-09-27 (NOTE-240); promising as a bridge between probe geometry and formal concept analysis, and unproven as a hypothesis about LLMs. It would be settled by three things. The attributes would have to come from something other than another LLM’s annotations. The region-level join would have to be defined correctly, as the Galois closure of the shared intent. And lattice identities (closure, absorption, meet/join agreement with the recovered context) would have to be tested, not pairwise subsumption and candidate ranking alone. |
| LIT-310 v2 | A topos foundation for theories of physics: IV. Categories of systems | Döring & Isham (2008), DOI-10.1063/1.2883826. Proposes axioms for a category Sys of physical systems, symmetric-monoidal under composite ⋄ and under disjoint sum ⊔, whose arrows are translations of local languages. Each arrow j : S₁ → S is realised by a left-exact functor τ(j) between the systems’ topoi, together with arrows φ(j) : Σ_{S₁} → τ(j)Σ_S and β(j) : τ(j)R_S → R_{S₁}. Classical physics satisfies the scheme exactly. In quantum theory the disjoint sum H₁⊕H₂ satisfies it (the pulled-back arrow of Â₁⊕Â₂ is δ̆(A₁)), but the composite H₁⊗H₂ does not: the natural pull-back of δ̆(A₁) differs from δ̆(A₁⊗1̂) off the image of V(H₁), which the authors attribute to “operator entanglement”. | Proposed — read in full 2026-09-29 (NOTE-285); promising and unproven. The rules are explicitly “experimental”, the quantum composite fails the commutativity condition the rules state, and the key negative claims ((4.46), and that no operator B̂ gives the pulled-back arrow) are asserted, not shown. What would settle it is a proof of (4.46) and of the non-existence of B̂, plus a variant of the rules (or of the context category) under which tensor-product composites satisfy (3.18). |
| LIT-369 v2 | Grokking and Generalization Collapse: Insights from HTSR theory | Prakash & Martin (2025), arXiv:2506.04434. A depth-3, width-200 ReLU MLP trained on 1,000 MNIST images (the Omnigrok recipe, with weights and biases scaled ×8, MSE loss, AdamW, WD = 0) for 10⁷ steps goes through three phases read off the accuracy curves. In pre-grokking (to ~10⁵ steps) training accuracy saturates while test accuracy stays low. In grokking (~10⁵–10⁶) test accuracy rises to ~0.85. In “anti-grokking” (~10⁶–10⁷) it falls to ~0.45–0.5 while training accuracy stays near 1. The average HTSR power-law exponent α of the two hidden weight matrices goes 4.0 → 2.9 → 1.1 at the phase ends (Table 1). In the collapse phase, correlation traps (outlier eigenvalues of the elementwise-shuffled weight matrix) appear. The paper’s own weight-decay control shows FC2’s α below 2, and traps in both layers, without a collapse (Fig. 6, Table 2). That undercuts its headline claim that α < 2 “invariably” heralds collapse. | Proposed — read in full 2026-09-30 (NOTE-317); worth knowing as the report of a late generalisation collapse after grokking at WD = 0, but it is one architecture on one 1k-sample MNIST subset, with the seed count unstated, and its central diagnostic (α < 2 ⇒ collapse) is contradicted by its own WD = 0.01 control. What would settle it: several seeds and architectures, with α and traps reported for runs that reach α < 2 without collapsing, and a comparison against the ℓ² norm under the Omnigrok LU account, which the paper does not cite. |
| LIT-370 v2 | New Evidence of the Two-Phase Learning Dynamics of Neural Networks | Zhou et al. (2025), arXiv:2505.13900. VGG-16 and ResNet-20 on CIFAR-10 (SGD with momentum, lr 0.1, 160 epochs) are compared across pairs of training times. Before an early “inflection point” (~2,500 iterations for VGG-16, ~100–500 for ResNet-20), a tiny parameter perturbation under identical SGD noise sends the run to a different basin by the end: loss barrier up to ~2, test disagreement ~0.15–0.5. After it, the same perturbation leaves the runs linearly connected. Also after it, the empirical NTK keeps changing step to step but stays within a bounded cosine distance of any later reference kernel (the “cone effect”, e.g. S ≈ 0.05–0.1 for VGG-16 vs ≈ 0.15–0.2 from initialisation). Switching to linearised training later gives better test accuracy (VGG-16 0.13 → 0.82 as the switch moves from ≤200 to 5,000 iterations). | Proposed — read in full 2026-09-30 (NOTE-318); a compact, readable demonstration that an early, short chaotic phase gives way to a confined, stable one in both basin and kernel terms, but it rests on two architectures on one dataset, one run each with no error bars. The chaos half largely re-measures Frankle et al.’s (2020) spawning / linear-mode-connectivity result with a parameter perturbation in place of fresh SGD noise, and the claimed role of the cone in generalisation is asserted. What would settle it: seeds and error bars, the batch size, a stated perturbation norm, other domains, and a quantitative test of confinement (e.g. an angular radius that stops growing) rather than a 3-D picture. |
| LIT-374 v3 | Structural Decoupling: A Scaffold-Flow Theory of Generalization and Alignment | Li (2026), arXiv:2506.20699. ‘Proposes “width”, the least number of cells in an open cover on each of which some predictor is γ-contractive with conditional risk ≤ δ, as a structural complexity separate from VC dimension. From an additive Rademacher bound, √(2d_str log(e(K−1)n/d_str)/n) + LK·R_n(G) (Thm 4.5), it argues that context routing (the “scaffold”) should be trained by different signals from within-context prediction (the “flow”), and that alignment failures are scaffold failures. The routine results are proved: coupon-collector Ω(w log w), Lipschitz composition, penalised model selection, multiclass Sauer–Shelah. The new ones are not. The phase transition at width is assumed in its proof. The bouquet witness of width/VC separation contradicts its own construction. The “fundamental theorem” is false as stated, because infinite pseudo-dimension does not prevent learnability. No theorem links the CS-Laplacian estimator to width. There are no experiments.‘ | Proposed — re-read jointly with LIT-373 and arXiv 2602.07974 on 2026-10-01 (NOTE-322); promising and unproven. Read jointly with the companion arXiv 2602.07974, which carries the fuller statements and several definitions this paper leaves implicit. The formal core holds in repaired form: width as a structural complexity incomparable with the per-cell VC dimension; an error floor below width; the Ω(w log w) discovery cost; an additive Rademacher bound for routed predictors. The flagged slips are repairable and not load-bearing: the bouquet cover, the non-degeneracy assumption in the appendix, Massart, and pseudo-dimension against fat-shattering in Thm 4.6. What remains unproven are the claims that would make it matter: that the CS estimator converges to width itself and not to a predictor-relative count; that a monolithic model cannot match K ≥ w routing; above all, that router/scaffold training should be decoupled from task loss. This is presented as derived from the additive bound, but the bound holds for joint training too. The alignment section is asserted. What would settle it: on synthetic benchmarks of known width, (i) a K-sweep showing the floor at K < w for routed learners and its absence or presence for capacity-matched monolithic models; (ii) CS width recovery from a cold start; (iii) decoupled against joint router training, compared on forgetting and boundary error. |
| LIT-375 v2 | Structural Learning Theory: A Metric-Topology Factorization Approach | Li (2026), arXiv:2602.07974. >- The formal core of Xin Li’s structural-learning programme. Width w(P; γ, δ) is the least number of open cells on each of which some predictor is γ-contractive with conditional risk ≤ δ. The paper proves that width is incomparable with the per-cell VC dimension (Thm 2.2). It shows that with K < w cells there is an n-independent error floor η(w, K), under a non-degeneracy assumption stated in the body (Thm 2.4, Assumption 2.3). Width is at least c·β₁·L/D₀ under a bounded-overlap assumption (Thm 2.5), and discovering all basins costs Ω(w log w) samples (Thm 2.6). The CS-Laplacian eigenvalue count converges uniformly to the predictor-relative count w_G(P) when n ≳ (H_G + d_X log(1/r_x) + log(1/δ′))/(r_x^{d_X} g_eff²) (Thm 3.5); no result shows that w_G equals width. There are no experiments. | Proposed — read in full 2026-10-01 (NOTE-324); >- Promising and unproven. It is the programme’s fullest and most careful formal statement, and it carries the learning theory of LIT-374 §3 with the assumptions in the body. Its routine results hold, and its bouquet slip is repairable. What would settle it: - a theorem that the CS count for a learned predictor equals w(P; γ, δ), not w_G(P); - a K-sweep on benchmarks of known width, showing the floor at K < w for routed learners, and testing whether a capacity-matched monolithic model shows it; - the decoupled-versus-joint training comparison it motivates but does not run. |
| LIT-376 v2 | Local Urysohn Width: A Topological Complexity Measure for Classification | Li (2026), arXiv:2603.15412. >- It defines local Urysohn width uw_{D₀}(P, γ): the least number of connected sets of diameter ≤ D₀, each carrying a continuous classifier correct on the margin-γ safe region it meets, needed to cover that safe region. It proves: - uw = w on a bouquet of w circles with safe balls at the antipodes, when 3γ/2 ≤ D₀ < L/2 − 3γ/4 (Thm 4.1); - uw ≥ w·m, with m = Θ(L/D₀) safe balls per loop, so uw = Ω(w·L/D₀) (Cor 5.1); - two-way non-determination with VC dimension (Thm 6.1); - an Ω(w log w) sample lower bound via label-permuted coupon collection (Thm 7.1); - uw ≥ 2β₁/Δ₀ for good, convex, bounded-adjacency covers (Thm 8.5). The proofs are correct. The obstruction is metric, as the paper concedes in Remark 8.11: patches cannot reach across the wedge point. Because Urysohn’s lemma makes local correctness automatic on any patch, the measure is a connected covering number of the safe region that does not depend on the labels. | Proposed — read in full 2026-10-01 (NOTE-323); >- Promising and unproven. It is the cleanest and most honest paper in Li’s programme: definitions are precise, the main theorems are correctly proved, a dependency table separates proved from conjectural results, and earlier errors are corrected openly. It is also the consistent construction that LIT-374’s and arXiv 2602.07974’s bouquet lacked. What would settle it: a result showing that this width governs error or sample cost for learners not built from local experts (for example local-learning or nearest-neighbour rates), or a proof of Conj 8.9 under conditions its motivating examples actually satisfy. Without one of these, it is a covering number with a topological headline. |
| LIT-496 | Mapping morality with a compass: Testing the theory of ‘morality-as-cooperation’ with a new questionnaire | Curry, Jones Chesters & Van Lissa (2019), DOI-10.1016/j.jrp.2018.10.008. The Morality-as-Cooperation Questionnaire, 21 Relevance and 21 Judgement items for seven domains, tested in UK (n = 1,392) and US (n = 469) online samples against the MFQ (UK n = 1,042). Seven factors fit the Relevance items (CFI .98) but not the Judgement items (CFI .87), and the combined seven-domain model is rejected (CFI .73). The MFQ’s five factors fit worse. MFQ purity items are rated about as morally relevant as its loyalty and authority items, which the authors concede contradicts the theory. | Proposed — read in full 2026-10-02 (NOTE-412), from the PsyArXiv manuscript; worth reading as the programme’s psychometric test and as the place its authors concede that purity items are rated morally relevant, which “appear[s] to contradict” the theory. Its seven-factor result is weaker than the abstract says. The items were written by the authors, three per domain, from the theory itself, and selected by fit within each domain. Seven factors then fit the Relevance items but not the Judgement items, and the combined seven-domain model is rejected (CFI .73), so the best model has fourteen correlated factors. No non-cooperative item is in the MAC-Q, so it cannot test whether morality is only about cooperation. It would be settled by an item pool written independently of the theory, with harm, purity and other non-cooperative content in it, factored blind, on data that can be shared. |
| LIT-503 | Morality as Cooperation: A Problem-Centred Approach | Curry (2016), DOI-10.1007/978-3-319-19671-8_2. Morality is “a collection of biological and cultural solutions to the problems of cooperation and conflict recurrent in human social life”. Nonzero-sum game theory yields seven problems (kin, coordination, exchange, hawkish and dovish contest displays, division, possession) and hence seven moral domains, illustrated but not tested. The chapter predicts that non-cooperative behaviour is morally neutral everywhere, and that MFT’s purity domain has no connection to cooperation. | Proposed — read in full 2026-10-02 (NOTE-408); the founding statement of morality-as-cooperation and the place its predictions are stated most sharply, including the one its own tests have not run: that behaviour unrelated to cooperation will be morally neutral, and that no culture’s morality will be about “aesthetics or nutrition” (p. 40). It reports no data. The seven domains are derived from game theory and then illustrated with quotations from philosophers and ethnographers, so the chapter shows the taxonomy is coherent, not that it is the right one. It would be settled by the test LIT-047 lacks: blind coding of all moralized content in one sample, asking whether non-cooperative domains are moralized. |
| LIT-509 | Moral Molecules: Morality as a Combinatorial System | Curry, Alfano, Brandt & Pelican (2021), DOI-10.1007/s13164-021-00540-x. The seven morality-as-cooperation domains are treated as elements that combine into “molecules”. For each of the 21 pairs a moral concept is proposed and an example found in the literature: fraternity, blood revenge, filial piety, honour, queuing and so on. Counting combinations gives 127 positive molecules and 2,186 of mixed valence. The test is confirmatory: no search protocol, blind judges or failed searches are reported. | Proposed — read in full 2026-10-02 (NOTE-399); a clear statement of the programme’s ambition, that seven cooperative elements generate “all moral ideas, possible and actual”, but its test is the weakest in the programme. For each of the 21 pairs the authors proposed a concept and then searched the literature until they found it (“We succeeded in every case”). No search protocol, judges or failed attempts are reported, and the theory “doesn’t predict which of these many possibilities will be actualities”. Two molecules (mendicance, common ownership) combine an element with the negation of another, which the paper’s own notation counts as mixed valence. It would be settled by blind judges classifying an independent list of moral concepts into the scheme, with a count of those that fit nothing. |
| LIT-512 | Moral universals: A machine-reading analysis of 256 societies | Alfano, Cheong & Curry (2024), DOI-10.1016/j.heliyon.2024.e25940. A word-count dictionary for the seven morality-as-cooperation domains (MAC-D, built by expert brainstorming and WordNet expansion) is run over 9,653 eHRAF Ethics paragraphs from 256 societies. Most morals are detected in most societies, with small but significant differences by region and subsistence. Against the earlier hand codes the dictionary agrees only slightly to fairly (κ .08–.25) and overstates prevalence. It cannot tell praise from condemnation, so it says nothing about valence. | Proposed — read in full 2026-10-02 (NOTE-406); worth reading for the Morality-as-Cooperation Dictionary and for what it shows about the sixty-society result, not as a replication of it. The dictionary counts words and, by the authors’ own statement, “cannot be used to estimate the moral valence of cooperation”, so it does not test the 961-of-962 finding at all. Its agreement with the earlier hand codes is slight to fair (κ .08–.25), and it inflates fairness from 15% to 58% of societies. It detects significant, though small, regional differences, against the earlier claim of equal frequency. A spot-check of its paragraphs found admired theft in four more societies. It would be settled by valence-aware coding validated against blind hand codes, run with dictionaries for non-cooperative domains on the same corpus. |
| LIT-660 | Mode Connectivity Beyond Classifiers: Evidence from Generative and Contrastive Models | Yao, Zhang & Tian (2026), preprint. Extends layer-wise path construction (LLPF, Tian et al. 2026) to a DDPM on Flowers102 and a NanoCLIP model on Flickr30k. Layers move towards the target mode in a dataflow order (symmetric encoder–decoder pairs for the U-Net, alternating vision and text blocks for CLIP); each layer is rescaled to a fixed variance; the point is retrained with AdamW until its loss is below a threshold. The resulting chains keep training loss below 0.04 (DDPM) and 0.09 (NanoCLIP), where AutoNEB’s maximum NanoCLIP loss is 6.69. Intermediate DDPMs have worse FID than the endpoints at equal training loss. | Proposed — read in full 2026-10-03 (NOTE-534); watching, as the first claim of mode connectivity between independently trained generative and contrastive models: one pair of DDPMs on Flowers102 and one pair of NanoCLIP models on Flickr30k, joined by a chain of checkpoints along which the training loss stays below a threshold, where AutoNEB’s paths rise steeply on NanoCLIP. The path is built by moving layer groups towards the far end, rescaling each layer’s variance, and retraining with AdamW until the loss is under threshold, so every anchor is a retrained model. What would settle it: more than one pair per model, a barrier measure along the whole path rather than at the anchors, and a reason to think a path made of retrained anchors says more about the landscape than that retraining works. It is a preprint of 31 August 2026. |
| LIT-676 | Unveiling Mode Connectivity in Graph Neural Networks | Li, Chen, Han, Zeng, Liu & Tang (2025), preprint. GCN solutions for node classification from different seeds are connected by quadratic Bezier curves but often separated on the straight line, more so on co-authorship and heterophilous graphs than on citation graphs. GNN variants (GCN, GraphSAGE, GAT) give similar barriers, MLPs different ones. On CSBM graphs, barriers fall with density and feature separability and are highest at middling homophily. The authors bound the barrier through the spectral gap, bound the generalisation gap by the barrier, and propose a Wasserstein distance between graphs’ interpolation-loss curves that correlates with transfer gaps. | Proposed — read in full 2026-10-03 (NOTE-529); watching, as the first study of mode connectivity in graph neural networks. Two GCNs trained on the same graph with different seeds are usually joined by a low-loss quadratic Bezier curve but often not by a straight line, and the barrier depends on the graph more than on the GNN variant: it falls with density, with feature separability, and with homophily far from one half, in synthetic CSBM graphs and, by the authors’ reading, in 12 real ones. A loss-barrier bound, a generalisation bound in terms of the barrier, and a barrier-based distance between graphs are stated, but the appendix that should hold the proofs does not; the v1 text still carries an editor’s placeholder. What would settle it: the proofs, and numbers for the barriers the figures show. |
| LIT-677 | Unveiling mode-connectivity of the ELBO landscape | Zhang & Blei (2021), NeurIPS 2021 Bayesian Deep Learning workshop. Two SVI runs of LDA on the New York Times corpus give distinct local maxima of the ELBO; the simplified string method, with natural-gradient bead updates, is said to find an essentially flat maximum-energy path between them. Paths are said to flatten as data and the number of topics grow. The authors explain connectivity by over-parameterisation (more topics than the corpus holds) and by continuous statistical degeneracy, offering a landscape account of topic modelling’s “no best answer”. No results are reported in the paper. | Proposed — read in full 2026-10-03 (NOTE-522); watching, as the only work in the record to carry mode connectivity from neural networks to variational inference. It claims that local maxima of the LDA ELBO, from two SVI runs on the New York Times corpus, are joined by essentially flat maximum-energy paths found with the simplified string method, that paths flatten as the number of topics grows, and that statistical degeneracy explains this. The three-page workshop paper reports none of the results it describes: no path, no ELBO values, no synthetic-data experiment; its one figure is a schematic. What would settle it: the experiments themselves, which are not in this version. |