MC-Biquandles and MC-Biquandle Coloring Quivers

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Choi, Seonmi, Nelson, Sam
Format:	Preprint
Published:	2023
Subjects:	Geometric Topology Quantum Algebra
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Virtual Biquandle Cocycle Quiver Representations
by: Bishop, Alexander, et al.
Published: (2025)

Categorification of Biquandle Arrow Weight Invariants via Quivers
by: Nelson, Sam, et al.
Published: (2025)

Biquandle Power Brackets
by: Gügümcü, Neslihan, et al.
Published: (2024)

Biquandle Fares and Link Invariants
by: Nelson, Sam, et al.
Published: (2026)

New Polynomial Decategorifications of the Quandle Coloring Quiver
by: Kabra, Anusha, et al.
Published: (2025)

Quandle Cohomology Quiver Representations
by: Nelson, Sam
Published: (2024)

Quandle Action Quivers
by: Cai, Mason, et al.
Published: (2024)

The Forbidden Quiver of a Link
by: Nelson, Sam, et al.
Published: (2025)

Biracks and Switch Braid Quivers
by: Chao-Haft, Max, et al.
Published: (2021)

Birack Bracket Quivers and Framed Links
by: Nelson, Sam, et al.
Published: (2025)

Biquandles, quivers and virtual bridge indices
by: Khandhawit, Tirasan, et al.
Published: (2025)

A Geometric Approach to the Links-Quivers Correspondence I: Rational Tangles
by: Higgins, Jonathan A.
Published: (2026)

A Geometric Approach to the Links-Quivers Correspondence II: Rational Links
by: Higgins, Jonathan A.
Published: (2026)

Biquandle cocycle condition for invariants of immersed surface-links in the four-space
by: Jablonowski, Michal
Published: (2025)

Closed Formulas for $η$-Corrections in the Once Punctured Torus
by: Vargas, Nelson A. Colon
Published: (2025)

Colored sl(N) homology and SU(N) representations
by: Wang, Joshua
Published: (2022)

Psyquandle Brackets
by: Nelson, Sam, et al.
Published: (2025)

Persistent Homology of Biquandle Coloring Quivers
by: Kayaslan, Hamdi
Published: (2026)

Classical and Quantum Algorithms for Topological Invariants of Torus Bundles
by: Vargas, Nelson Abdiel Colón, et al.
Published: (2025)

Quandle Coloring Quivers of general Torus links by dihedral quandles
by: Elhamdadi, Mohamed, et al.
Published: (2024)

A Survey of Quantum Enhancements
by: Nelson, Sam
Published: (2018)

Yang-Baxter Hochschild Cohomology
by: Saito, Masahico, et al.
Published: (2023)

A lower bound for the genus of a knot using the Links-Gould invariant
by: Kohli, Ben-Michael, et al.
Published: (2023)

A minimality property for knots without Khovanov 2-torsion
by: Gujral, Onkar Singh, et al.
Published: (2023)

An $\mathfrak{sl}_2$ action on link homology of T(2,k) torus links
by: Roz, Felix
Published: (2023)

Quandles with one non-trivial column
by: Cazet, Nicholas
Published: (2023)

A boundary characterization of Turaev-Viro TQFTs
by: Steffen, Max-Niklas, et al.
Published: (2025)

Khovanov homology of strongly invertible knots and their quotients
by: Lipshitz, Robert, et al.
Published: (2022)

Fray functors and equivalence of colored HOMFLYPT homologies
by: Conners, Luke
Published: (2024)

Quantum Invariants of Ribbon Surfaces in $4$-Dimensional $2$-Handlebodies
by: Beliakova, Anna, et al.
Published: (2025)

The minimal Rickard complexes of braids on two strands
by: Wang, Joshua
Published: (2025)

Quantum Cocycle Invariants of Knots from Yang-Baxter Cohomology
by: Saito, Masahico, et al.
Published: (2025)

Floer homology and non-fibered knot detection
by: Baldwin, John A., et al.
Published: (2022)

3d Quantum Trace Map
by: Panitch, Samuel, et al.
Published: (2024)

Hennings TQFTs for Cobordisms Decorated With Cohomology Classes
by: De Renzi, Marco, et al.
Published: (2024)

Stated Skein Theory and Double Affine Hecke Algebra Representations
by: Matson, Raymond
Published: (2025)

Brunnian braids and the inclusion from double shuffle Lie algebra to Kashiwara-Vergne Lie algebra
by: Ren, Muze
Published: (2026)

Formal Contact Categories
by: Cooper, Benjamin
Published: (2015)

Skein modules of closed 3 manifolds define line bundles over character varieties
by: Korinman, Julien
Published: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"9272b72d78d7f92f1dab682b40d267dd"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790716050.9743 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "9272b72d78d7f92f1dab682b40d267dd" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=9272b72d78d7f92f1dab682b40d267dd; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"41168"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2311_00510/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2311_00510/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790716050.97
REQUEST_TIME	1790716050

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"9272b72d78d7f92f1dab682b40d267dd"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790716050.9743 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "9272b72d78d7f92f1dab682b40d267dd" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=9272b72d78d7f92f1dab682b40d267dd; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"41168"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2311_00510/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2311_00510/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790716050.97
REQUEST_TIME	1790716050

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: