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DOE OSTI2022

Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations ($3$, $2$) 1/6 , ($\overline{3}$, $1$) -2/3 and ($1$, $1$) 1 . For the family B 3 (Δ$^{°}_{4}$) consisting of $\mathcal{O}$(10 11 ) F-theory QSM geometries, we argue that more than 99.995% of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario in the O(10 11 ) QSM geometries B 3 (Δ$^{°}_{4}$). The QSM geometries come in families of toric 3-folds B 3 (Δ°) obtained from triangulations of certain 3-dimensional polytopes Δ°. The matter curves in X Σ $\large{ϵ}$ B 3 (Δ°) can be deformed to nodal curves which are the same for all spaces in B 3 (Δ°). Therefore, one can probe the vector-like spectra on the entire family B 3 (Δ°) from studies of a few nodal curves. We compute the cohomologies of all limit roots on these nodal curves. In our applications, for the majority of limit roots the cohomologies are determined by line bundle cohomology on rational tree-like curves. For this, we present a computer algorithm. The remaining limit roots, corresponding to circuit-like graphs, are handled by hand. The cohomologies are independent of the relative position of the nodes, except for a few circuits. On these jumping circuits, line bundle cohomologies can jump if nodes are specially aligned. This mirrors classical Brill-Noether jumps. B 3 (Δ°) admits a jumping circuit, but the root bundle constraints pick the canonical bundle and no jump happens.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

HarDWR - Harmonized Water Rights Records

For a detailed description of the database of which this record is only one part, please see the HarDWR meta-record. Here we present a new dataset of western U.S. water rights records. This dataset provides consistent unique identifiers for each spatial unit of water management across the domain, unique identifiers for each water right record, and a consistent categorization scheme that puts each water right record into one of 7 broad use categories. These data were instrumental in conducting a study of the multi-sector dynamics of intersectoral water allocation changes through water markets (Grogan et al., in review). Specifically, the data were formatted for use as input to a process-based hydrologic model, WBM, with a water rights module (Grogan et al., in review). While this specific study motivated the development of the database presented here, U.S. west water management is a rich area of study (e.g., Anderson and Woosly, 2005; Tidwell, 2014; Null and Prudencio, 2016; Carney et al, 2021) so releasing this database publicly with documentation and usage notes will enable other researchers to do further work on water management in the U.S. west. The raw downloaded data for each state is described in Lisk et al. (in review), as well as here. The dataset is a series of various files organized by state sub-directories. The first two characters of each file name is the abbreviation for the state the in which the file contains data for. After the abbreviation is the text which describes the contents of the file. Here is each file type described in detail: XXFullHarmonizedRights.csv: A file of the combined groundwater and surface water records for each state. Essentially, this file is the merging of XXGroundwaterHarmonizedRights.csv and XXSurfaceWaterHarmonizedRights.csv by state. The column headers for each of this type of file are: state - The name of the state the data comes from. FIPS - The two-digit numeric state ID code. waterRightID - The unique identifying ID of the water right, the same identifier as its state uses. priorityDate - The priority date associated with the right. origWaterUse - The original stated water use(s) from the state. waterUse - The water use category under the unified use categories established here. source - Whether the right is for surface water or groundwater. basinNum - The alpha-numeric identifier of the WMA the record belongs to. CFS - The maximum flow of the allocation in cubic feet per second (ft3s-1). Arizona is unique among the states, as its surface and groundwater resources are managed with two different sets of boundaries. So, for Arizona, the basinNum column is missing and instead there are two columns: surBasinNum - The alpha-numeric identifier of the surface water WMA the record belongs to. grdBasinNum - The alpha-numeric identifier of the groundwater WMA the record belongs to. XXStatePOD.shp: A shapefile which identifies the location of the Points of Diversion for the state's water rights. It should be noted that not all water right records in XXFullHarmonizedRights.csv have coordinates, and therefore may be missing from this file. XXStatePOU.shp: A shapefile which contains the area(s) in which each water right is claimed to be used. Currently, only Idaho and Washington provided valid data to include within this file. XXGroundwaterHarmonizedRights.csv: A file which contains only harmonized groundwater rights collected from each state. See XXFullHarmonizedRights.csv for more details on how the data is formatted. XXSurfaceWaterHarmonizedRights.csv: A file which contains only harmonized surface water rights collected from each state. See XXFullHarmonizedRights.csv for more details on how the data is formatted. Additionally, one file, stateWMALabels.csv, is not stored within a sub-directory. While we have referred to the spatial boundaries that each state uses to manage its water resources as WMAs, this term is not shared across all states. This file lists the proper name for each boundary set, by state. For those whom may be interested in exploring our code more in depth, we are also making available an internal data file for convenience. The file is in .RData format and contains everything described above as well as some minor additional objects used within the code calculating the cumulative curves. For completeness, here is a detailed description of the various objects which can be found within the .RData file: states: A character vector containing the state names for those states in which data was collected for. More importantly, the index of the state name is also the index in which that state's data can be found in the various following list objects. For example, if California is the third index in this object, the data for California will also be in the third index for each accompanying list. rightsByState_ground: A list of data frames with the cleaned ground water rights collected from each state. This object holds the the data that is exported to created the xxGroundwaterHarmonizedRights.csv files. rightsByState_surface: A list of data frames with the cleaned surface water rights collected from each state. This object holds the the data that is exported to created the xxSurfaceWaterHarmonizedRights.csv files. fullRightsRecs: A list of the combined groundwater and surface water records for each state. This object holds the the data that is exported to created the xxFullHarmonizedRights.csv files. projProj: The spatial projection used for map creation in the beginning of the project. Specifically, the World Geodetic System (WGS84) as a coordinate reference system (CRS) string in PROJ.4 format. wmaStateLabel: The name and/or abbreviation for what each state legally calls their WMAs. h2oUseByState: A list of spatial polygon data frames which contain the area(s) in which each water right is claimed to be used. It should be noted that not all water right records have a listed area(s) of use in this object. Currently, only Idaho and Washington provided valid data to be included in this object. h2oDivByState: A list of spatial points data frames which identifies the location of the Point of Diversion for the state's water rights. It should be noted that not all water right records have a listed Point of Diversion in this object. spatialWMAByState: A list of spatial polygon data frames which contain the spatial WMA boundaries for each state. The only data contained within the table are identifiers for each polygon. It is worth reiterating that Arizona is the only state in which the surface and groundwater WMA boundaries are not the same. wmaIDByState: A list which contains the unique ID values of the WMAs for each state. plottingDim: A character vector used to inform mapping functions for internal map making. Each state is classified as either "tall" or "wide", to maximize space on a typical 8x11 page. The code related to the creation of this dataset can be viewed within HarDWR GitHub Repository/dataHarmonization.

Economics↗