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Jesus Salas

Publications and source records attributed to Jesus Salas.

17 recordsLinked to original sources
arXiv2026

Governance Records as Supervision: Verifier-Selected Self-Training for Structured Workflow Repair

Machine-verifiable workflows produce governance records linking a task contract, model attempt, verifier decision, accepted output, and target origin. We test whether these records can supervise bounded models, consolidating occasional or expensive capability into reliable one-shot execution. On fresh, structure-disjoint PlanBench replanning cases, Qwen3-14B thinking generated 24 plans admitted by the independently authored VAL verifier. Those plans trained the same checkpoint for non-thinking execution, without oracle targets or a stronger teacher. On 80 unopened cases, VAL-accepted plans increased from 1 to 57, with 56 paired gains and zero regressions; thinking reached 30. The adapter was schema-valid on all cases and used approximately 1/56 of thinking's mean latency. The separate paired interface-cure gate did not pass. A matched ablation fixed the source cases, 52-candidate pool, 24-target count, model, recipe, and seed while changing target selection. On 160 new cases, base, schema-selected, model-self-selected, and VAL-selected execution reached 1, 55, 69, and 102 accepted plans. VAL exceeded self-selection by paired net +33 (p=0.0000019647), with gains in both difficulty strata. Independent semantic selection is therefore load-bearing relative to matched alternatives within this band. A complementary Phi stronger-teacher arm raised base Phi-4 from 2 to 51 accepted plans and from 35 to 80 schema-valid outputs. Earlier synthetic experiments establish teachability, cumulative learning, construction robustness, and stopping boundaries. The results support verifier-selected supervision for bounded, machine-checkable capabilities, not arbitrary planning, enterprise validity, or unrestricted self-improvement.

cs.AI↗
arXiv2026

Correct Is Not Governed: Provenance Integrity in Agentic Workflows

Agentic workflows are commonly evaluated by whether they reach the correct outcome. That is insufficient in institutional settings, where a correct action may rely on the wrong authority, an unsupported completion claim, or work made stale by a later change. We define governed execution as work whose decisions, completion, and response to change are supported by inspectable provenance. We present Matrix, a deterministic causal-state layer that records authority and fact dependencies, verifies completion evidence, and selectively invalidates affected work. Across controlled comparisons, governed and direct workflows often reached the same outcomes, but only the governed path consistently preserved governing evidence, refused unsupported closure, and limited recovery to dependent tasks. A role-separated transfer challenge then failed: a deterministically enforced completeness contract severely over-blocked synthetic packets produced outside its authoring context. These results do not establish Matrix as a general accuracy enhancer; they support its primary role as an institutional integrity layer for making agentic work auditable and independently verifiable.

cs.AI↗
arXiv2025

Beyond Worst-Case Subset Sum: An Adaptive, Structure-Aware Solver with Sub-$2^{n/2}$ Enumeration

The Subset Sum problem, which asks whether a set of $n$ integers has a subset summing to a target $t$, is a fundamental NP-complete problem in cryptography and combinatorial optimization. The classical meet-in-the-middle (MIM) algorithm of Horowitz--Sahni runs in $\mathcal{O}^*(2^{n/2})$, which remains the best-known deterministic bound. Yet in practice, many instances exhibit abundant collisions in partial sums, so the true difficulty is often governed by $U = |Σ(S)|$, the number of unique subset sums. We present a structure-aware, adaptive solver that enumerates only the distinct subset sums, pruning duplicates on the fly and achieving deterministic runtime $\mathcal{O}(U \cdot n^2)$ and expected randomized runtime $\mathcal{O}(U \cdot n)$. Its core is a canonical unique-subset-sums enumerator combined with a double meet-in-the-middle strategy, supporting anytime and online modes. To ensure worst-case gains even on unstructured inputs, we introduce a Controlled Aliasing technique that provably reduces the enumeration space by a fixed constant factor. This yields a guaranteed global runtime of $\mathcal{O}^*(2^{n/2 - \varepsilon})$ for some $\varepsilon > 0$, strictly improving upon classical bounds. Empirical results show that the solver adapts efficiently to structured inputs with low entropy (e.g., instances with small doubling constants, duplicates, or additive progressions) often approaching near-dynamic programming performance. We conclude by outlining how this adaptive framework can be extended to other NP-complete problems.

cs.DS↗
arXiv2025

Certificate-Sensitive Subset Sum: Realizing Instance Complexity

The Subset Sum problem is a classical NP-complete problem with a long-standing $O^*(2^{n/2})$ deterministic bound due to Horowitz and Sahni. We present results at two distinct levels of generality. First (instance-sensitive bound), we introduce, to our knowledge, the first deterministic algorithm whose runtime provably scales with the certificate size $U = |Σ(S)|$, the number of distinct subset sums. Our enumerator constructs all such sums in time $O(U \cdot n^2)$, with a randomized variant achieving expected time $O(U \cdot n)$. This provides a constructive link to Instance Complexity by tying runtime to the size of an information-theoretically minimal certificate. Second (unconditional worst-case bound), by combining this enumerator with a double meet-in-the-middle strategy and a Controlled Aliasing technique that enforces a simple canonical-normal-form (CNF) expansion policy on aliased states, we obtain a deterministic solver running in $O^*(2^{n/2-\varepsilon})$ time with $\varepsilon=\log_2(\frac{4}{3})$ - the first unconditional deterministic improvement over the classical $O^*(2^{n/2})$ bound for all sufficiently large $n$. Finally, we refine fine-grained hardness for Subset Sum by making explicit the structural regime (high collision entropy / near collision-free) implicitly assumed by SETH-based reductions, i.e., instances with near-maximal $U$.

cs.CC↗
arXiv2013

A generalized Beraha conjecture for non-planar graphs

We study the partition function Z_{G(nk,k)}(Q,v) of the Q-state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1<= k <= 7. We also consider two specializations of Z_{G(nk,k)}, namely the chromatic polynomial P_{G(nk,k)}(Q) (corresponding to v=-1), and the flow polynomial Phi_{G(nk,k)}(Q) (corresponding to v=-Q). In these two cases, we study their zeros in the complex Q-plane for 1 <= k <= 7. We pay special attention to the accumulation loci of the corresponding zeros when n -> infinity. We observe that the Berker-Kadanoff phase that is present in two-dimensional Potts models, also exists for non-planar recursive graphs. Their qualitative features are the same; but the main difference is that the role played by the Beraha numbers for planar graphs is now played by the non-negative integers for non-planar graphs. At these integer values of Q, there are massive eigenvalue cancellations, in the same way as the eigenvalue cancellations that happen at the Beraha numbers for planar graphs.

math-ph↗
arXiv2013

Is the five-flow conjecture almost false?

The number of nowhere zero Z_Q flows on a graph G can be shown to be a polynomial in Q, defining the flow polynomial Φ_G(Q). According to Tutte's five-flow conjecture, Φ_G(5) > 0 for any bridgeless G.A conjecture by Welsh that Φ_G(Q) has no real roots for Q \in (4,\infty) was recently disproved by Haggard, Pearce and Royle. These authors conjectured the absence of roots for Q \in [5,\infty). We study the real roots of Φ_G(Q) for a family of non-planar cubic graphs known as generalised Petersen graphs G(m,k). We show that the modified conjecture on real flow roots is also false, by exhibiting infinitely many real flow roots Q>5 within the class G(nk,k). In particular, we compute explicitly the flow polynomial of G(119,7), showing that it has real roots at Q\approx 5.0000197675 and Q\approx 5.1653424423. We moreover prove that the graph families G(6n,6) and G(7n,7) possess real flow roots that accumulate at Q=5 as n\to\infty (in the latter case from above and below); and that Q_c(7)\approx 5.2352605291 is an accumulation point of real zeros of the flow polynomials for G(7n,7) as n\to\infty.

math.CO↗
arXiv2012

The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models

We show how the Hintermann-Merlini-Baxter-Wu model (which is a generalization of the well-known Baxter-Wu model to a general Eulerian triangulation) can be mapped onto a particular infinite-coupling-limit of the Ashkin-Teller model. We work out some mappings among these models, also including the standard and mixed Ashkin-Teller models. Finally, we compute the phase diagram of the infinite-coupling-limit Ashkin-Teller model on the square, triangular, hexagonal, and kagome lattices.

cond-mat.stat-mech↗
arXiv2009

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.

cond-mat.stat-mech↗
arXiv2009

A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm

We prove that for the class of three-colorable triangulations of a closed oriented surface, the degree of a four-coloring modulo 12 is an invariant under Kempe changes. We use this general result to prove that for all triangulations T(3L,3M) of the torus with 3<= L <= M, there are at least two Kempe equivalence classes. This result implies in particular that the Wang-Swendsen-Kotecky algorithm for the zero-temperature 4-state Potts antiferromagnet on these triangulations T(3L,3M) of the torus is not ergodic.

math.CO↗
arXiv2009

Phase transition in the 3-state Potts antiferromagnet on the diced lattice

We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically-driven long-range order at low temperatures (including zero). We then present Monte Carlo simulations, using a cluster algorithm, of the 3-state and 4-state models. The 3-state model has a phase transition to the high-temperature disordered phase at v = e^J - 1 = -0.860599 +- 0.000004 that appears to be in the universality class of the 3-state Potts ferromagnet. The 4-state model is disordered throughout the physical region, including at zero temperature.

cond-mat.stat-mech↗
arXiv2007

Phase diagram of the chromatic polynomial on a torus

We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L=5,6,7 for the square and triangular lattices. On the physical side, we obtain the exact ``phase diagrams'' for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases.

cond-mat.stat-mech↗
arXiv2006

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions

We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.

cond-mat.stat-mech↗
arXiv2006

Complex-temperature phase diagram of Potts and RSOS models

We study the phase diagram of Q-state Potts models, for Q=4 cos^2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on the Potts spins that are periodic in the longitudinal (N) direction and free or fixed in the transverse (L) direction. The relevant partition functions can then be computed as sums over partition functions of an A\_{p-1} type RSOS model, thus making contact with the theory of quantum groups. We compute the accumulation sets, as N -> infinity, of partition function zeros for p=4,5,6,infinity and L=2,3,4 and study selected features for p>6 and/or L>4. This information enables us to formulate several conjectures about the thermodynamic limit, L -> infinity, of these accumulation sets. The resulting phase diagrams are quite different from those of the generic case (irrational p). For free transverse boundary conditions, the partition function zeros are found to be dense in large parts of the complex plane, even for the Ising model (p=4). We show how this feature is modified by taking fixed transverse boundary conditions.

cond-mat.stat-mech↗
arXiv2005

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{βJ}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are ν= 1/d = 1/2 and α= 1.

cond-mat.stat-mech↗
arXiv2002

Exact Potts Model Partition Function for Strips of the Square Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex square-lattice strip graphs $G$ for a variety of transverse widths $L_t$ and for arbitrarily great length $L_\ell$, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,λ}} c_{Z,G,j}(λ_{Z,G,j})^{L_\ell}$. We give general formulas for $N_{Z,G,j}$ and its specialization to $v=-1$ for arbitrary $L_t$ for both types of boundary conditions, as well as other general structural results on $Z$. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite square lattice. Considering the full generalization to arbitrary complex $q$ and $v$, we determine the singular locus ${\cal B}$, arising as the accumulation set of partition function zeros as $L_\ell \to \infty$, in the $q$ plane for fixed $v$ and in the $v$ plane for fixed $q$.

cond-mat.stat-mech↗
arXiv2001

Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice

We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times L_y$ and arbitrarily great length $L_z$, for sizes $L_x \times L_y = 2 \times 3$ and $2 \times 4$ and boundary conditions (a) $(FBC_x,FBC_y,FBC_z)$ and (b) $(PBC_x,FBC_y,FBC_z)$, where $FBC$ ($PBC$) denote free (periodic) boundary conditions. In the limit of infinite-length, $L_z \to \infty$, we calculate the resultant ground state degeneracy per site $W$ (= exponent of the ground-state entropy). Generalizing $q$ from ${\mathbb Z}_+$ to ${\mathbb C}$, we determine the analytic structure of $W$ and the related singular locus ${\cal B}$ which is the continuous accumulation set of zeros of the chromatic polynomial. For the $L_z \to \infty$ limit of a given family of lattice sections, $W$ is analytic for real $q$ down to a value $q_c$. We determine the values of $q_c$ for the lattice sections considered and address the question of the value of $q_c$ for a $d$-dimensional Cartesian lattice. Analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph $K_{m,m}$.

cond-mat.stat-mech↗