{"id":"9d24682b-334e-4f48-a052-3e000e5b944c","arxiv_id":"1908.07543","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In Thiemann-regularized loop quantum cosmology, the mu0 scheme produces pre-bounce emergent matter with equation of state w = -1/3 (string gas), while the bar-mu scheme produces an emergent cosmological constant, and mu0 stays unviable with positive Lambda.","lead":"This paper studies how different regularization choices in loop quantum cosmology change the predicted universe. It finds that one common scheme, mu0, remains unviable with a positive cosmological constant, and that the choice of discreteness parameter determines what kind of emergent matter fills the pre-bounce phase.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim rests on the paper's explicit 'regularized dynamics' conjecture (Sec. II: quantization skipped, classical flow assumed faithful).","rationale":"The reader's diagnosis is correct, and my independent pass through the argument surfaced no demonstrable internal error. For the central claim to hold, three things are needed: (a) the regularized constraint (26)/(25) is the right discrete analog of the scalar constraint; (b) the fixed-point structure and asymptotic expansions (30), (33), (39), (41) are correct; (c) the classical flow of that constraint ('regularized dynamics') faithfully represents the quantum dynamics on both asymptotic branches. I checked (b): ρφ → 0 in (26)/(25) yields sin²(cε) = ((1+γ²)/4γ²)sin²(2cε), so cε ∈ {0, β+, π−β+, π} with β+ = arcsin(1/√(1+γ²)) ≈ 1.34 for γ = 0.2375, matching (27); and the leading emergent term is ∝ 1/(pμ²), giving the w = −1/3 (1/p) versus w = −1 (constant) distinction directly from the regulator's scaling with the triad. This is why the classification is qualitatively robust to the gauge-covariant sinc factors — they are constants at the fixed points — and why the no-flux μ̄ rescalings in (40) reproduce the published results of [22,41], lending independent support. Condition (c) is where the argument is least secure, exactly as the reader states: the paper's Sec. II says 'we will skip the quantization part and conjecture...', and the claim is made for the branch where cμ0 → β+ ≈ 1.34 — the most quantum regime, where Ehrenfest-type justification of effective dynamics is least tested. For μ̄, quantum-level agreement exists in [41,42]; for μ0, [49] checks only von Neumann stability, not whether a peaked state follows the effective trajectory. So the new prediction rests on an untested conjecture at precisely the point where the paper makes its claim. The importation of (25) from a 'to appear' reference adds conditionality but does not by itself overturn the qualitative result, since that result follows from regulator scaling rather than specific coefficients. Because the concern is a stated conjecture rather than a demonstrated inconsistency, the reader's CONDITIONAL verdict stands; the proposed quantum difference-equation comparison would settle the matter.","tokens_in":25013,"tokens_out":35479,"duration_ms":727696,"concrete_test":"Quantize the μ0-scheme Thiemann-regularized scalar constraint (26) with a massless scalar: promote it to an operator on the LQC Hilbert space (following Refs. [41,49]), solve the quantum difference equation for physical states, and evolve a semiclassical state from the post-bounce (c ≈ 0) branch backward in φ. Compare the pre-bounce expectation values of volume, connection, and energy density with the effective trajectory (30), especially the predicted approach to the cμ0 = β+ asymptote with H² ≈ N²/[p(1+γ²)²μ0²] (coasting, w = −1/3). If the wave packet does not follow that branch, or disperses before reaching it, the emergent-matter classification is an artifact of the classical flow, not a prediction of the quantized theory.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central new assertion — Thiemann-regularized pre-bounce emergent matter with w = −1/3 for μ0 vs w = −1 for μ̄, with or without gauge-covariant fluxes — is internally coherent. I verified the structural core before assenting: setting ρφ → 0 in (26)/(25) gives sin²(cε) = ((1+γ²)/4γ²)sin²(2cε), i.e. cε ∈ {0, β+, π−β+, π} with β+ = arcsin(1/√(1+γ²)) ≈ 1.34 (matching eq. 27), and the leading emergent term in (30)/(33) scales as 1/(pμ²): 1/p for constant μ0, p-independent for μ̄² = Δ/p. The w-classification follows from that scaling alone, survives coefficient-level uncertainties (sinc factors are constants at the fixed points), and the no-flux μ̄ rescalings (40) match prior published results. The load-bearing weakness is the step the paper itself concedes, Sec. II: 'we will skip the quantization part and conjecture that the main effect of any quantization... can be studied by a regularized dynamics on the lattice' (reiterated in Sec. V). For the headline to be a quantum-gravity statement, the classical flow of the effective constraint must reproduce quantum dynamics on both asymptotic branches. Yet the new w = −1/3 branch sits at cμ0 ≈ 1.34 rad — the most quantum regime of the model — where the coherent-state/Ehrenfest rationale for effective dynamics is least verified, and no quantum trajectory comparison is attempted: for μ̄, quantum checks in [41,42] support the de Sitter branch, while [49] verifies only von Neumann stability for μ0, not trajectory fidelity. Secondary but real: the gauge-covariant Thiemann Hamiltonian (25) is imported from Ref. [19], marked 'to appear,' and is itself given only to leading order in the coherent-state spread; and the μ0 result is derived with Λ = 0 even though Sec. III shows the μ0 scheme is unviable once Λ > 0, so the genuinely new prediction concerns a branch of a scheme the paper regards as rejected.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies two layers of regularization ambiguities in loop quantum cosmology with a massless scalar field: the choice of discreteness parameter (μ0 versus \\bar μ) and the form of the Hamiltonian constraint (standard versus Thiemann regularization), with and without gauge-covariant flux modifications. For a positive cosmological constant, the paper reports numerically that the μ0 scheme still exhibits a late-time recollapse and cyclic evolution, while the \\bar μ scheme approaches a classical Friedmann phase with rescaled gravitational and cosmological constants. The central new claim concerns Thiemann regularization without Λ: in the pre-bounce region the μ0 scheme produces an effective 1/p term in the Friedmann equation, interpreted as an emergent fluid with equation of state w = -1/3 (string gas or coasting cosmology), whereas the \\bar μ scheme produces a constant term with w = -1 (emergent cosmological constant). The authors show that this classification is qualitatively unchanged when gauge-covariant fluxes are included, with only the numerical coefficients modified.","tokens_in":25382,"tokens_out":9787,"duration_ms":95337,"significance":"If the claims hold, the paper gives a concrete dynamical prediction that distinguishes the μ0 and \\bar μ regularizations for a very simple matter source: a qualitative change in the pre-bounce equation of state. This is of genuine interest for the LQC/LQG community because it sharpens the quantization-ambiguity problem and connects it to observable cosmological signatures such as string-gas or coasting behavior. The analytic core is a strength: the fixed-point analysis at cμ0 = β+ and the resulting 1/p versus p^0 scaling determine the w = -1/3 versus w = -1 classification, and the arbitrary matching parameter α cancels from that classification. The numerical robustness scan over πφ values is a useful complement, and the authors are explicit about the paper's main assumption, namely the effective-dynamics conjecture. The classification is therefore presented in a way that can be checked independently at the level of the regularized dynamics, even if its status as a statement about the full quantum theory remains to be established.","major_comments":[{"comment":"The central result is obtained under the explicit conjecture stated in Sec. II: 'we will skip the quantization part and conjecture that the main effect of any quantization ... can be studied by a regularized dynamics on the lattice,' and reiterated in Sec. V. The new string-gas branch for the μ0 scheme is located at cμ0 ≈ 1.34 rad, in the most quantum regime of the model, where coherent-state or Ehrenfest arguments for the effective description are least established, and no comparison with a quantum difference equation or with coherent-state expectation values is provided for this branch. Please either supply such evidence or explicitly restrict the abstract's claims to statements about the regularized classical flow rather than about the quantum theory.","section":"Sec. II and Sec. V"},{"comment":"As printed, Eq. (35) has a plus sign inside the trigonometric bracket, whereas the equivalent brackets in Eqs. (25) and (26) carry a minus sign. With the plus sign, sin^2(c\\bar μ) + (1+γ^2)/(4γ^2) sin^2(2c\\bar μ) is strictly positive for 0 < c\\bar μ < π, so the constraint cannot vanish in the presence of positive matter density. This contradicts the fixed-point condition c\\bar μ = β+ in Eq. (37) and the asymptotic expansion leading to Eq. (38). Please correct the sign or explain the different convention.","section":"Sec. IV.B, Eq. (35)"},{"comment":"The gauge-covariant Thiemann-regularized Hamiltonian (25), which underlies the quantitative statements in Sec. IV, is imported from Ref. [19], which is marked 'to appear'. Because the expression is not derived in this manuscript and is not yet independently available, the referee cannot verify the sinc factors or the relative sign of the two trigonometric terms. Please include a derivation in an appendix, or restrict the gauge-covariant claims to those that follow from the published no-flux Hamiltonian (26).","section":"Sec. IV, Eq. (25)"},{"comment":"The conclusion that the μ0 scheme remains unviable with a positive cosmological constant after gauge-covariant flux modifications is supported by one representative value of Λ and a set of initial data in Figs. 1-2, supplemented by a scan over πφ. This is weaker than the corresponding analytic result for standard LQC, which establishes a recollapse for any positive Λ. Please state explicitly the parameter range over which the recollapse was verified, or add an analytic argument for the gauge-covariant case.","section":"Sec. III.A, Figs. 1-2"}],"minor_comments":[{"comment":"The coefficients \\bar κ in Eqs. (34) and (42) are displayed without derivation; a short outline of the expansion or a supplemental computation file would help the reader reproduce them.","section":"Eqs. (34) and (42)"},{"comment":"The caption contains 'gauge/covariant' with an unnecessary slash; it should read 'gauge-covariant'.","section":"Fig. 9 caption"},{"comment":"The free parameter α appears explicitly in the rescaled constants, and the text notes this; it would be useful to state explicitly that the w-classification and the absence of recollapse are independent of α, since this is what makes those results robust.","section":"Sec. III.B, Eqs. (21)-(23)"},{"comment":"The observation that the emergent equation of state coincides with the threshold for late-time departure from GR is interesting but is not derived; please provide the argument or cite the specific prior result.","section":"Sec. V, penultimate paragraph"},{"comment":"No numerical tolerances or convergence checks are reported for the simulations; a brief statement on error control would strengthen confidence in the quoted bounce and recollapse values.","section":"Figs. 1-10"}],"recommendation":"major_revision","confidential_remarks":"The paper's analytic core is coherent and the w = -1/3 versus w = -1 classification is a worthwhile result. The main obstacles to acceptance are the explicit dependence on the effective-dynamics conjecture, the unpublished companion reference for Eq. (25), the sign inconsistency in Eq. (35), and the numerical rather than analytic support for the μ0 recollapse in the gauge-covariant case. These are fixable within the manuscript's scope, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Klaus and Parampreet's paper is worth a serious look. The new thing is a clean qualitative split in Thiemann-regularized LQC: with the mu0 regulator the pre-bounce emergent matter scales like 1/p, which classically behaves as w=-1/3 (string gas or coasting); with bar-mu it is p-independent, an emergent cosmological constant. This survives the switch from standard triads to gauge-covariant fluxes. The mu0 recollapse check with Lambda and gauge-covariant fluxes is also new, and it confirms what people expected: gauge-covariant fluxes do not rescue mu0.\n\nWhat the paper does well: the asymptotic expansions are internally consistent, and the equation-of-state classification is sturdier than the coefficient-level algebra—at the fixed points the sinc factors are constants, so even if the prefactors shift, the 1/p versus constant scaling is not affected. The numerical work is not heavy but it is honest: more than 500 initial conditions, and the figures match the claims. The authors also state the load-bearing assumption openly: they skip quantization and conjecture that the main effect of any quantization can be studied by regularized dynamics on the lattice. That is the right way to present this kind of work.\n\nSoft spots, in order of weight. First, the central claim lives under that conjecture, and the new w=-1/3 branch sits at c mu0 ~ 1.34 rad, the most quantum corner of the model; no comparison to a quantum trajectory is attempted there. So the result is a property of a classical truncation unless the conjecture is true. Second, the gauge-covariant Thiemann Hamiltonian, eq. (25), is imported from Liegener-Rudnicki, marked 'to appear', and it is only leading order in the coherent-state spread. Third, the mu0 string-gas prediction is derived with Lambda=0 even though Sec. III argues mu0 is unviable for Lambda>0; that limits the physical reach of the new prediction, though the authors are clear about it. The citation pattern looks fine; self-citation is to companion papers, and the derivation is not circular.\n\nWho this is for: people building LQC models and anyone trying to use full-LQG-inspired regularizations to constrain cosmology. It is not a settled quantum-gravity prediction, but it is a well-defined, falsifiable-in-principle classification of ambiguities. I would send it out for peer review. The main things I'd want from a referee: a stability check of the effective-dynamics conjecture in the mu0 branch, and either a reference for the to-appear Hamiltonian or a derivation sketch.","headline":"Worth taking seriously: a clean qualitative split in Thiemann-regularized LQC (mu0 gives w=-1/3 emergent matter, bar-mu gives an emergent cosmological constant), with the caveat that the whole analysis rests on an explicit effective-dynamics conjecture.","tokens_in":26010,"tokens_out":2413,"would_cite":true,"duration_ms":24503,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that in Thiemann-regularized loop quantum cosmology, the lattice-spacing choice fixes the pre-bounce matter: mu0 gives w=-1/3 (string gas), bar-mu gives w=-1 (cosmological constant), and gauge-covariant fluxes only…","keywords":["loop quantum cosmology","regularization ambiguities","Thiemann regularization","gauge-covariant fluxes","emergent matter","pre-bounce dynamics","mu0 scheme","bar-mu scheme"],"falsifier":"Quantize the Thiemann-regularized Hamiltonian constraint with gauge-covariant fluxes, including the operator ordering implied by the construction used in [19], and compute its expectation value on the semiclassical states used for the effective dynamics, without first replacing the dynamics by a classical lattice flow; if the resulting asymptotic Friedmann equation lacks the $1/p$ term for $\\mu_0$ or the constant term for $\\bar\\mu$, the classification is an artifact of the classical truncation. A separate decisive check is whether the $\\bar\\mu$-scheme can be derived from the full lattice theory: a derivation would select the $w=-1$ pre-bounce branch, while a no-go result would leave the $\\mu_0$ branch as the only full-theory candidate.","tokens_in":24787,"feed_emoji":"🌌","tokens_out":13143,"duration_ms":118968,"temperature":0.7,"pith_summary":"The paper addresses how unresolved quantization choices in loop quantum cosmology change the physical predictions. Working with the Thiemann-regularized Hamiltonian constraint, it claims that the lattice-spacing scheme decides what the pre-bounce universe contains: the $\\mu_0$-scheme (constant lattice spacing) produces an emergent fluid with equation of state $w=-1/3$, the behavior of a string gas or a coasting cosmology, while the $\\bar\\mu$-scheme (spacing tied to the triad) produces an emergent cosmological constant with $w=-1$. This distinction persists when the triad variables are replaced by gauge-covariant fluxes, which are needed to make lattice observables invariant under the local SU(2) gauge symmetry; only the numerical coefficients change. In addition, with a positive cosmological constant, gauge-covariant flux modifications do not rescue the $\\mu_0$-scheme from a late-time recollapse, whereas the $\\bar\\mu$-scheme reproduces classical Friedmann behavior with rescaled constants. A sympathetic reader cares because these ambiguities are not yet settled by the full theory, and the paper shows they are physically visible in the pre-bounce equation of state.","feed_headline":"Lattice choice sets the pre-bounce fluid: string gas or vacuum energy","feed_subtitle":"The pre-bounce universe's composition is a fingerprint of the lattice regulator chosen in quantization.","key_machinery":"The machinery is the regularized Hamiltonian constraint on a fixed lattice, evaluated on cosmological phase-space variables. The paper uses two regularization layers: the Thiemann regularization, in which the Euclidean and Lorentzian parts of the constraint are quantized separately, and, for the basic variables, gauge-covariant fluxes, which transform covariantly under the local SU(2) gauge symmetry and replace the triad variables by expressions carrying a factor $\\mathrm{sinc}(c\\epsilon/2)=\\sin(c\\epsilon/2)/(c\\epsilon/2)$. The asymptotic analysis works by finding the fixed points of $c\\epsilon$ where the matter energy density vanishes ($c=0$ for the future, $c=\\beta_+/\\epsilon$ for the past) and expanding the Friedmann equation around them. Whether the leading emergent term is $1/p$ or constant depends on whether the regulator $\\epsilon$ is the constant $\\mu_0$ or the triad-dependent $\\bar\\mu=\\sqrt{\\Delta/p}$: the $1/p$ dependence of the constant regulator survives in the past branch, while $\\bar\\mu$ cancels it and leaves a cosmological-constant term.","core_discovery":"On its own terms, the paper's central new claim is that for the Thiemann-regularized scalar constraint, the nature of emergent matter in the pre-bounce regime is fixed by the regularization parameter. The asymptotic Friedmann equation in the $\\mu_0$-scheme contains a term $1/p$ (equivalently $1/a^2$), which in classical general relativity corresponds to a fluid with equation of state $w=-1/3$---a string gas or coasting cosmology. In the $\\bar\\mu$-scheme the regulator's triad dependence removes this $1/p$ term and leaves a constant, so the pre-bounce matter is an emergent cosmological constant with $w=-1$. The authors verify that the same dichotomy holds with purely classical triads and with gauge-covariant fluxes: equations (30) and (33) for $\\mu_0$, equations (39) and (41) for $\\bar\\mu$, the latter differing only in rescaled coefficients. They also show that including a positive cosmological constant does not change the known verdict on the two schemes: $\\mu_0$ still recollapses at late times, while $\\bar\\mu$ asymptotes to a classical Friedmann universe with rescaled Newton's constant and cosmological constant.","pith_inferences":["The asymptotic-expansion method suggests a general dictionary between regulator dependence and emergent equation of state: if the regulator scales as a power of the triad, that power fixes the effective barotropic index of the pre-bounce fluid; the paper's $\\mu_0$ ($w=-1/3$) and $\\bar\\mu$ ($w=-1$) cases are two entries, and its remark about Wheeler-DeWitt-type regulators ($w=1/3$) is a third.","If the effective-dynamics conjecture fails, the distinction may not survive full quantization; a direct check would be to compute subleading corrections from the coherent-state expectation values and see whether the $1/p$ or constant terms are corrected or washed out.","Within the model, the pre-bounce equation of state is a potential observable discriminator between regulator schemes: a coasting $w=-1/3$ pre-bounce would favor $\\mu_0$-type lattices, while a de Sitter pre-bounce would favor $\\bar\\mu$-type lattices, although current observations cannot directly probe the pre-bounce epoch.","The same fixed-point-expansion technique could be applied to other symmetry-reduced sectors, such as black-hole interiors, where the paper notes different regulators already produce qualitatively different spacetimes; the emergent-matter classification may provide a unified way to compare them."],"forward_implications":["For the Thiemann-regularized dynamics, the pre-bounce universe is not a single prediction: $\\mu_0$ gives a coasting or string-gas phase ($w=-1/3$), while $\\bar\\mu$ gives a de Sitter-like phase ($w=-1$).","Adding gauge-covariant flux modifications changes the coefficients of the emergent terms and the rescaling of Newton's constant, but not the equations of state.","The $\\mu_0$-scheme remains inviable with a positive cosmological constant: it bounces but then recollapses at late times, producing cyclic evolution rather than the classical asymptotic de Sitter behavior.","In the $\\bar\\mu$-scheme with $\\Lambda>0$, the late-time and pre-bounce branches each match a classical Friedmann universe with rescaled constants, and the rescaling differs between branches, giving the asymmetric bounce a preferred post-bounce branch consistent with observed constants.","The qualitative results are insensitive to initial conditions: more than 500 simulations with different $\\pi_\\varphi$ yield the same asymmetric-bounce and emergent-matter picture."],"supporting_citations":[{"why":"Defines the $\\mu_0$-scheme and the standard LQC Hamiltonian that this paper generalizes.","marker":"[30]"},{"why":"Defines the $\\bar\\mu$-scheme improved dynamics, the alternative regulator whose pre-bounce branch is compared.","marker":"[31]"},{"why":"Establishes the late-time recollapse criterion that rules $\\mu_0$ inviable with $\\Lambda>0$; the paper extends that criterion to gauge-covariant fluxes.","marker":"[32]"},{"why":"Shows that $\\bar\\mu$-scheme Thiemann-regularized dynamics yields an emergent cosmological constant, the result the paper contrasts with $\\mu_0$.","marker":"[41]"},{"why":"Introduces the Thiemann-regularized Hamiltonian in LQC with the Lorentz term, the second regularization layer studied here.","marker":"[43]"},{"why":"Supplies the construction of gauge-covariant fluxes used to make lattice observables SU(2)-invariant.","marker":"[52]"},{"why":"Companion paper that derives the Hamiltonian constraint with gauge-covariant fluxes for standard regularization, extended here to Thiemann regularization and $\\Lambda>0$.","marker":"[51]"},{"why":"Supplies the Thiemann-regularized Hamiltonian with gauge-covariant fluxes (equation (25)) used for the asymptotic analysis.","marker":"[19]"}],"fun_headline_variants":["Pre-bounce fluid fixed by LQC regulator: string gas or vacuum","Regulator choice in LQC sets pre-bounce matter composition","Which LQC regulator? It decides string gas vs dark energy","Thiemann regularization picks pre-bounce: string gas or cosmological constant"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the paper's explicit conjecture that one can skip quantization and let a classical lattice-regularized version of the dynamics stand in for the full quantum theory; if that conjecture fails, the emergent-matter classification is a property of a classical truncation, not of quantum gravity.","fun_headline_variants_meta":{"raw":{"variants":["Pre-bounce fluid fixed by LQC regulator: string gas or vacuum","Regulator choice in LQC sets pre-bounce matter composition","Which LQC regulator? It decides string gas vs dark energy","Thiemann regularization picks pre-bounce: string gas or cosmological constant"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000253,"raw_usage":{"total_tokens":1593,"prompt_tokens":1003,"completion_tokens":590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":516}},"tokens_in":619,"tokens_out":590,"duration_ms":5599,"temperature":1.0,"reasoning_tokens":516,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:04:42.466315+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Quantize the Thiemann-regularized Hamiltonian constraint with gauge-covariant fluxes, including the operator ordering implied by the construction used in [19], and compute its expectation value on the semiclassical states used for the effective dynamics, without first replacing the dynamics by a classical lattice flow; if the resulting asymptotic Friedmann equation lacks the $1/p$ term for $\\mu_0$ or the constant term for $\\bar\\mu$, the classification is an artifact of the classical truncation. A separate decisive check is whether the $\\bar\\mu$-scheme can be derived from the full lattice theory: a derivation would select the $w=-1$ pre-bounce branch, while a no-go result would leave the $\\mu_0$ branch as the only full-theory candidate.","supporting_citations":[{"cited_title":"Agullo, Primordial power spectrum form the Dapor-Liegener model of loop quantum cosmology","cited_arxiv_id":null,"evidence_quote":"Defines the $\\mu_0$-scheme and the standard LQC Hamiltonian that this paper generalizes."},{"cited_title":"Stottmeister, T","cited_arxiv_id":null,"evidence_quote":"Defines the $\\bar\\mu$-scheme improved dynamics, the alternative regulator whose pre-bounce branch is compared."},{"cited_title":"Corichi, P","cited_arxiv_id":null,"evidence_quote":"Establishes the late-time recollapse criterion that rules $\\mu_0$ inviable with $\\Lambda>0$; the paper extends that criterion to gauge-covariant fluxes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that $\\bar\\mu$-scheme Thiemann-regularized dynamics yields an emergent cosmological constant, the result the paper contrasts with $\\mu_0$."},{"cited_title":"Olmedo, S","cited_arxiv_id":null,"evidence_quote":"Introduces the Thiemann-regularized Hamiltonian in LQC with the Lorentz term, the second regularization layer studied here."},{"cited_title":"Thiemann, Quantum Spin Dynamics (QSD): VII","cited_arxiv_id":null,"evidence_quote":"Supplies the construction of gauge-covariant fluxes used to make lattice observables SU(2)-invariant."},{"cited_title":"Ashtekar, M","cited_arxiv_id":null,"evidence_quote":"Companion paper that derives the Hamiltonian constraint with gauge-covariant fluxes for standard regularization, extended here to Thiemann regularization and $\\Lambda>0$."},{"cited_title":"Thiemann, Complexifier coherent states for quantum general relativity","cited_arxiv_id":null,"evidence_quote":"Supplies the Thiemann-regularized Hamiltonian with gauge-covariant fluxes (equation (25)) used for the asymptotic analysis."}],"review_version":1}