Bridges Between Additive, Multiplicative, and Spectral Regimes

Fuente: Zenodo

Salvato in:

Dettagli Bibliografici
Autore principale:	Perisic, Aleksandar
Natura:	Recurso digital
Pubblicazione:	Zenodo 2026
Accesso online:	Acceder al recurso
Tags:	Aggiungi Tag Nessun Tag, puoi essere il primo ad aggiungerne!!

_version_	1866902029371179008
author	Perisic, Aleksandar
author_facet	Perisic, Aleksandar
contents	<p>This note is a companion to the "additive/multiplicative/spectral" vocabulary paper. Its purpose is not to develop a full theory of the triad, but to state more precisely where modern mathematics already provides strong bridges and where an obvious structural gap remains.</p> <p>We briefly recall the viewpoint encoded by the shorthand $(0,1, s)_b$ : additive neutrality (0), multiplicative neutrality (1), spectral degrees of freedom ( $s$ ), and blur $b$ as a tuning knob regulating how strongly the regimes communicate. We then argue that most existing bridges are historically routed through additive foundations: multiplication and spectral methods are typically introduced as extra structure on additive carriers (groups, rings, vector spaces, Hilbert spaces), rather than treated as coequal anchors from the start. If one takes 0,1 , and $s$ seriously as meta-level observational stances, one is naturally led to ask for native structural definitions of each regime and for bridges that do not treat addition as the universal mediator. We highlight the relative underdevelopment of the $1 \leftrightarrow s$ edge (multiplicative-spectral) and indicate a concrete template in this direction: a "continuous prime transform" program whose operational content lives on the dilation group and is spectrally diagonalized by Mellin characters, with additive linearization used only as temporary scaffolding.</p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_18880941
institution	Zenodo
language
publishDate	2026
publisher	Zenodo
record_format	zenodo
spellingShingle	Bridges Between Additive, Multiplicative, and Spectral Regimes Perisic, Aleksandar <p>This note is a companion to the "additive/multiplicative/spectral" vocabulary paper. Its purpose is not to develop a full theory of the triad, but to state more precisely where modern mathematics already provides strong bridges and where an obvious structural gap remains.</p> <p>We briefly recall the viewpoint encoded by the shorthand $(0,1, s)_b$ : additive neutrality (0), multiplicative neutrality (1), spectral degrees of freedom ( $s$ ), and blur $b$ as a tuning knob regulating how strongly the regimes communicate. We then argue that most existing bridges are historically routed through additive foundations: multiplication and spectral methods are typically introduced as extra structure on additive carriers (groups, rings, vector spaces, Hilbert spaces), rather than treated as coequal anchors from the start. If one takes 0,1 , and $s$ seriously as meta-level observational stances, one is naturally led to ask for native structural definitions of each regime and for bridges that do not treat addition as the universal mediator. We highlight the relative underdevelopment of the $1 \leftrightarrow s$ edge (multiplicative-spectral) and indicate a concrete template in this direction: a "continuous prime transform" program whose operational content lives on the dilation group and is spectrally diagonalized by Mellin characters, with additive linearization used only as temporary scaffolding.</p>
title	Bridges Between Additive, Multiplicative, and Spectral Regimes
url	https://doi.org/10.5281/zenodo.18880941

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
language	"it"
VUFIND_SESSION	"33b4908fdace1c528b6ff317e866ca83"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790924284.802 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "33b4908fdace1c528b6ff317e866ca83" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1760}

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	"language=it; VUFIND_SESSION=33b4908fdace1c528b6ff317e866ca83; ui=standard"
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	"216.73.217.142"
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	"47058"
REDIRECT_URL	"/Record/zenodo_https___doi_org_10_5281_zenodo_18880941/Details"
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/zenodo_https___doi_org_10_5281_zenodo_18880941/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790924284.7978
REQUEST_TIME	1790924284

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"it"
VUFIND_SESSION	"33b4908fdace1c528b6ff317e866ca83"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790924284.802 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "33b4908fdace1c528b6ff317e866ca83" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1760}

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	"language=it; VUFIND_SESSION=33b4908fdace1c528b6ff317e866ca83; ui=standard"
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	"216.73.217.142"
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	"47058"
REDIRECT_URL	"/Record/zenodo_https___doi_org_10_5281_zenodo_18880941/Details"
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/zenodo_https___doi_org_10_5281_zenodo_18880941/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790924284.7978
REQUEST_TIME	1790924284

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Documenti analoghi

Environment & details:

Environment & details: