The Participatory Modular Hamiltonian: Architecture for the Participatory Horizon Programme - Part I
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2026
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| _version_ | 1866901635830120448 |
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| author | O'Grady, Gregory |
| author_facet | O'Grady, Gregory |
| contents | <p>Persistent large-angle anomalies in observational cosmology including suppressed CMB correlations beyond $60^\circ$, excess source-count dipoles, and quadrupole--octopole alignment with the kinematic dipole, share an observer-dependent character that primordial mechanisms should not naturally produce. The participatory-horizon programme proposes that these anomalies arise because the observer's causal diamond acts as an information aperture whose geometry constrains which correlations are realised as classical records. This paper, the first of a companion triplet, proposes the <em>Participatory Modular Hamiltonian </em>(PMH): the pair $(\mathcal{K}_{\eta_0}, \mathcal{M})$ of the Casini--Huerta--Myers modular Hamiltonian and a local recording map evaluating the pointwise signal-to-noise ratio of coherent cosmological signals against quantum modular-energy noise.</p> <p>The PMH produces two observable channels: an angular filter $h^2(\ell) = 1 - \exp[-\ell(\ell+1)/\ell_c^2]$ with geometric transition scale $\ell_c^2 = 12.56$ from conformal horizon geometry, and a radial recording kernel $k_L(x) = x^L(1 - x^2)^4$, where $x = \chi/\eta_0$ is fractional comoving depth. The boundary order $m = 4$ equals the spacetime dimension $d$, derived from the volume Jacobian relating flat and hyperbolic coordinates. Given the recording prescription and the $g_1 = 1$ closure, both channels are fully determined with zero free parameters when the geometric prediction for $\ell_c^2$ is adopted.</p> <p>We prove that the modular Hamiltonian is irreducible within the concentric Bisognano--Wichmann weight basis, demoting the earlier nested-diamond construction to an effective approximation. A stress test confirms that the pointwise prescription recovers the boundary exponent ($3.93$, target $4.0$) and peak location ($0.333$, target $1/3$), while the operator alternative yields incorrect values. The derived `boundary-squeeze' mechanism suppresses monopole leakage at the last-scattering surface by a factor of $2{,}300$, ensuring the anomaly predictions remain physically consistent.</p> <p>The derived angular filter resolves the low-power anomaly, shifting the $S_{1/2}$ statistic from the 8.3rd to the 49.7th percentile of $\Lambda$CDM realisations, and the derived radial kernel predicts a universal source-count dipole excess $\mathcal{A} \approx 5$--$7$ consistent with CatWISE and RACS measurements across two wavebands. Falsifiable predictions include a depth-dependent dipole profile distinguishable by forthcoming spectroscopic tomography, and up to $62\%$ EE reduction at $\ell = 2$.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19713514 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Participatory Modular Hamiltonian: Architecture for the Participatory Horizon Programme - Part I O'Grady, Gregory cosmic microwave background CMB CMB anomalies low-power anomaly cosmic dipole anomaly source-count dipole quadrupole-octopole alignment axis of evil modular Hamiltonian Casini-Huerta-Myers causal diamond participatory horizon angular filter radial kernel boundary squeeze Bisognano-Wichmann Wheeler participatory universe algebraic quantum field theory CatWISE Planck <p>Persistent large-angle anomalies in observational cosmology including suppressed CMB correlations beyond $60^\circ$, excess source-count dipoles, and quadrupole--octopole alignment with the kinematic dipole, share an observer-dependent character that primordial mechanisms should not naturally produce. The participatory-horizon programme proposes that these anomalies arise because the observer's causal diamond acts as an information aperture whose geometry constrains which correlations are realised as classical records. This paper, the first of a companion triplet, proposes the <em>Participatory Modular Hamiltonian </em>(PMH): the pair $(\mathcal{K}_{\eta_0}, \mathcal{M})$ of the Casini--Huerta--Myers modular Hamiltonian and a local recording map evaluating the pointwise signal-to-noise ratio of coherent cosmological signals against quantum modular-energy noise.</p> <p>The PMH produces two observable channels: an angular filter $h^2(\ell) = 1 - \exp[-\ell(\ell+1)/\ell_c^2]$ with geometric transition scale $\ell_c^2 = 12.56$ from conformal horizon geometry, and a radial recording kernel $k_L(x) = x^L(1 - x^2)^4$, where $x = \chi/\eta_0$ is fractional comoving depth. The boundary order $m = 4$ equals the spacetime dimension $d$, derived from the volume Jacobian relating flat and hyperbolic coordinates. Given the recording prescription and the $g_1 = 1$ closure, both channels are fully determined with zero free parameters when the geometric prediction for $\ell_c^2$ is adopted.</p> <p>We prove that the modular Hamiltonian is irreducible within the concentric Bisognano--Wichmann weight basis, demoting the earlier nested-diamond construction to an effective approximation. A stress test confirms that the pointwise prescription recovers the boundary exponent ($3.93$, target $4.0$) and peak location ($0.333$, target $1/3$), while the operator alternative yields incorrect values. The derived `boundary-squeeze' mechanism suppresses monopole leakage at the last-scattering surface by a factor of $2{,}300$, ensuring the anomaly predictions remain physically consistent.</p> <p>The derived angular filter resolves the low-power anomaly, shifting the $S_{1/2}$ statistic from the 8.3rd to the 49.7th percentile of $\Lambda$CDM realisations, and the derived radial kernel predicts a universal source-count dipole excess $\mathcal{A} \approx 5$--$7$ consistent with CatWISE and RACS measurements across two wavebands. Falsifiable predictions include a depth-dependent dipole profile distinguishable by forthcoming spectroscopic tomography, and up to $62\%$ EE reduction at $\ell = 2$.</p> |
| title | The Participatory Modular Hamiltonian: Architecture for the Participatory Horizon Programme - Part I |
| topic | cosmic microwave background CMB CMB anomalies low-power anomaly cosmic dipole anomaly source-count dipole quadrupole-octopole alignment axis of evil modular Hamiltonian Casini-Huerta-Myers causal diamond participatory horizon angular filter radial kernel boundary squeeze Bisognano-Wichmann Wheeler participatory universe algebraic quantum field theory CatWISE Planck |
| url | https://doi.org/10.5281/zenodo.19713514 |