arXiv subjects

Hiroyuki Chuma

Publications and source records attributed to Hiroyuki Chuma.

7 recordsLinked to original sources

arXiv2026

Computational Prosopography across a Millennium: Mathematically Oriented Lineages Traced from the Fields Medalists

We reconstruct the mentor--student network through which documented scholarly training passed across roughly nine centuries, and subject both the network and the means of reconstructing it to source criticism. From Wikidata, which aggregates the Mathematics Genealogy Project and the MacTutor Archive, we extract approximately 470,000 mentor--student assertions, yielding a directed acyclic graph of 372,853 persons. Using all 64 historical Fields Medalists as a fixed, ex ante tracer set, backward traversal enumerates some 25.5 million distinct paths reaching 57 generations. Three structural observations follow. Genealogical traffic through Leibniz forms an hourglass: thin upstream, 5.3 paths per node on average, and thick downstream, 53.4, a ratio near 10:1, with no counterpart at Newton, who lies on only four of the 64 lineages. Across a window centered on Leibniz, seven independently extracted predicate dimensions reorganize together, and recorded learned-society membership rises from 6.5 to 82.1 percent of the cohort. Upstream, 54 of the 64 lineages converge on the same five twelfth- and thirteenth-century Islamic and Byzantine scholars before terminating at an eleventh-century boundary we name the Monastery Wall. We argue that such observations cannot be assessed without tool criticism. The traversal engine is algebraically reversible, so every ranking decision it makes can be reconstructed afterward. We characterize its measurement bias in closed form, show that the macro-structures survive switching that bias off, and report the family of lineages the traversal returns at different resolutions rather than a single ranked list.

physics.soc-ph↗

arXiv2026

How to Build Marcus's Algebraic Mind: From Thagard's Brain--Mind Viewpoint

This paper reports a convergence neither program was looking for. Marcus's The Algebraic Mind named three things any architecture needs -- operations over variables, recursive structure, and individuals distinct from kinds -- showed multilayer perceptrons have none, and left a register-and-treelet implementation as conjecture. Thagard's Brain-Mind ran it from the other end, making binding the mechanism from which the whole of mind is assembled, and circular convolution load-bearing. Marcus leaves his register algebra open; Thagard's is lossy, degrading under the very recursion his own account demands. VaCoAl is a hyperdimensional computing architecture built end-to-end on XOR-and-shift over GF(2) via primitive-polynomial LFSRs; PyVaCoAl is its extended software realization (all results here); the silicon substrate exists as CASRAM. Bind(R,F) = R XOR Shift(F) is exactly reversible and non-commutative: it supplies all three pillars at fixed dimension and removes convolution's depth degradation. Capability: exact reversible binding at O(N) yields compositional generalization with post-hoc auditability, which no lossy or learned substrate offers. Necessity: two independent architecture programs and the dentate gyrus-CA3 circuit require the same algebra -- convergence, not biomimicry. New here: discrimination and failure-tolerance are one. Repair every collision (RR = 1) and the system is bit-identical to a hash dictionary: candidates become indistinguishable and the confidence path-integral collapses; a memory that never fails keeps no record of which routes were hard. Position: we do not surpass large language models but supply the auditable, multi-hop relational reasoning embeddings lack. No consciousness is implemented and no cognitive experiment reported; bit-exactness holds in silicon, approximately under biological noise; speed and power remain unbenchmarked.

cs.NE↗

arXiv2026

How to Build Marcus's Algebraic Mind: From Minsky's Emotion-Machine Viewpoint

This paper reports a step that had already been taken. Marcus's three components of an adequate cognitive architecture -- variables, recursive structure, individuals vs kinds -- left the neural substrate open; a companion paper answers it with VaCoAl, built on XOR-and-shift over GF(2). Those pillars are horizontal: how a mind represents the world. Minsky's Emotion Machine supplies the orthogonal, vertical dimension -- a mind reasoning about its own reasoning. The vertical step needed no new machinery. A representation exactly recoverable becomes introspection when what is recovered is the reasoner's own deliberative trace: Minsky's Reflective layer. Pillar 2 says nothing about whose structure is recovered; point the same unbind inward and Reflection follows. Only the argument changes. Capability: exact reversible binding at O(N), kept exact within a Frontier Size, yields a trace readable constituent by constituent: a self-report faithful by construction, not verbalization. Only exact-algebraic traces, not probabilistic ones, make the reflexive read faithful. Necessity: audit and valuation are one circuit at opposite settings of one parameter. Repair every collision and the trace is exactly auditable but no path outranks another; tolerate them and the CR2 decay that credits the direct route makes the read approximate. Position: we claim neither to have built the Reflective layer nor to surpass large language models; it supplies the auditable trace probabilistic deliberation cannot leave. The same substrate gives panalogy (content-addressable retrieval scored by CR) and credit assignment as counterfactual unbind-rebind, meeting Pearl's causal axis. Not claimed: Reflection's sufficient conditions (meta-control loop, context-tagging) are future work; Reflection is introspection, not evaluation; its reachability is argued, not shown; speed and power unbenchmarked.

cs.NE↗

arXiv2026

Institutions and the transmission of upper-tail human capital: scientific lineages across a millennium

What made useful knowledge cumulative was not discovery alone but the institutions that transmitted it. We provide the first exhaustive structural measurement of the network through which upper-tail human capital passed from master to student across a millennium. Using 470,000 mentor-student records from Wikidata (which integrates the Mathematics Genealogy Project and MacTutor Archive), and all 64 historical Fields Medalists as a fixed, ex ante tracer set, backward traversal yields a directed acyclic graph of 25.5 million paths reaching 57 generations. We document two institutional transitions. First, a 17th-century watershed concentrates lineage traffic on Leibniz: 47 of 64 lineages pass through him with a 10:1 downstream-to-upstream ratio, and seven independent attributes -- learned-society membership (a 46-fold rise per scholar), field, language, employer, institutional diversification, student production, and diffusion entropy -- re-organize coherently across the same window. This is the network signature of Mokyr's Republic of Letters, and it reframes the Newton-Leibniz priority dispute as a distinction between the possession and the transmission of upper-tail human capital: it is transmission that generates the spillovers on which growth depends. Second, 84% of lineages converge upstream on five 12th-13th-century Islamic and Byzantine scholars before terminating at an 11th-century boundary -- the ``Monastery Wall'' -- at which personal academic mentorship first becomes record-generating in Europe. Our claims are descriptive-structural, not causal. Because exhaustive traversal at this scale defeats standard tools, we also contribute a deterministic, algebraic graph-traversal instrument whose measurement bias we characterize in closed form, and report one emergent property of independent methodological interest.

cs.NE↗

arXiv2026

How to Build Marcus's Algebraic Mind: Algebro-Deterministic Substrate over Galois Fields

In The Algebraic Mind (2001), Marcus held that any adequate cognitive architecture needs operations over variables, recursively structured representations, and an individual/kind distinction, and that multilayer perceptrons support none of them; he left a register-and-treelet implementation as a conjecture. Twenty-five years later a memory architecture built for unrelated reasons (speed, power and cost on commodity silicon) meets that specification operation for operation, through one mechanism rather than three. PyVaCoAl/VaCoAl is a hyperdimensional computing architecture built end-to-end on one primitive: XOR-and-shift over GF(2), realised by primitive-polynomial linear-feedback shift registers (LFSRs). It gives reversible binding Bind(R,F) = R xor shift(F), non-commutative bundling that distinguishes "dog bites man" from "man bites dog", and address-space individual/kind separation, at fixed dimension. Capability: exact reversible binding at O(L) cost supplies each pillar as an architectural primitive, not a product of training, with inspectability no lossy substrate offers. Necessity: weaken the primitive to an approximate inverse, as circular convolution does, and all three pillars degrade together -- what cannot be exactly decomposed was never composed, only mixed. Position: this is not the mind, the brain is not an LFSR, and we do not beat large language models; the substrate supplies the auditable symbolic layer they structurally lack. We develop the correspondence pillar by pillar, recast the treelet as a register set identified by a primitive generator polynomial, cite a companion Perspective on the dentate gyrus-CA3 circuit as a biological instance, and show that inflecting an unseen pseudoverb is a rung-3 query in Pearl's sense. Bit-exact reversibility holds in silicon and only approximately under biological noise; biological claims are structural only.

cs.NE↗

arXiv2026

Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM

Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose the hippocampal-entorhinal circuit factorizes memory via a grid-cell scaffold for compositional replay. Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections, matching quasi-orthogonality while ensuring bit-exact reproducibility. Furthermore, the path-integral Confidence Ratio CR2 provides an algebraically tractable model for the empirically observed multiplicative replay decay. Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520-Myr conservation. Independent cellular evidence supports that the DG-CA3 pathway implements a biophysical homologue of Galois-field arithmetic. We also link this framework to Judea Pearl's Ladder of Causation. Reversible GF(2) binding provides the surgical algebra for the do-operator (Rung 2), and VaCoAl's dual-orthogonalizer architecture supplies the parallel substrate required for counterfactual reasoning (Rung 3). Ultimately, we prove these formal correspondences and derive testable iEEG predictions, uniting computational neuroscience, electrophysiology, and hyperdimensional computing.

cs.NE↗

arXiv2026

Beyond LLMs, Sparse Distributed Memory, and Neuromorphics

VaCoAl (Python: PyVaCoAl) attacks the Binding Problem algebraically rather than statistically: an SRAM/DRAM-CAM organised end-to-end around one primitive, XOR-and-shift over GF(2) via primitive-polynomial LFSRs. Rooted in Kanerva's Sparse Distributed Memory, it retrieves in a million-dimensional binary space by Galois-field diffusion; Binding and Unbinding are exactly reversible at O(L), giving compositional generalisation with post-hoc auditability. Unexpectedly, a path-dependent semantic selection mechanism emerges undesigned, functionally equivalent to Spike-Timing-Dependent Plasticity (STDP) and predictable a priori from a closed form matching measurement on tens of millions of records. It is the Don't Care (collision-tolerance) rule: not a defect to engineer away, but the source of its ability to rank paths by quality. Capability: reversible binding plus tolerated collisions yields a path-integral confidence measure (CR2) ranking candidates by accumulated reliability, absent from hash-based search. Necessity: repair the collisions fully and the ranking vanishes; a memory that never fails has no record of which paths were difficult. Position: we do not surpass large language models; the substrate is orthogonal, supplying the auditable path-ranking layer they lack. A mentor-student ontology of ~470,000 WIKIDATA scholars, traversed backwards from all 64 Fields Medalists to depth 57 and >25.5M paths, stress-tests multi-hop reasoning over a large DAG. Ablation shows Don't Care imposing a depth-dependent exponential penalty that prunes circuitous routes and preserves direct ones: an Occam's razor. Per-generation CR1 stays within 0.995-0.999, yet cumulative CR2 decays monotonically to ~0.905 by generation 56, matching the closed form 0.997^56 = 0.846 within observed variation. All measurements are from PyVaCoAl, a software DRAM-CAM; speed and power figures are projections.

cs.NE↗