Each of these can be verified directly in the published standards.
the core PDF specification
PDF was published by Adobe starting in 1993, and became an open ISO standard in 2008 as ISO 32000-1, corresponding to PDF 1.7. The specification defines the object model, page tree, content streams, filters, fonts, and security handlers.
Source: ISO 32000-1:2008 (PDF 1.7)
the current generation of the format
PDF 2.0 removes a number of deprecated features, tightens the specification, and adds capabilities including improved support for tagged content and accessibility. Files in the wild are still overwhelmingly PDF 1.x.
Source: ISO 32000-2 (PDF 2.0)
introduced object streams and cross-reference streams
Compressed object streams and cross-reference streams are what make lossless optimisation possible: they let a producer store the document's structure in compressed form rather than as plain-text tables. Rewriting a file with object streams is the main lossless size reduction available.
Source: ISO 32000-1, cross-reference table and stream definitions
the standard compression filter
PDF's standard lossless filter is Flate, which is the same Deflate algorithm used in ZIP archives. Content streams and embedded images may use it. Recompressing streams with Flate changes nothing about how the document renders.
Source: RFC 1951 (DEFLATE)
security handlers defined by the format
Standard PDF encryption is defined by security handler revision. Revisions 2 and 3 use RC4 with 40-bit or 128-bit keys and should be considered broken. Revision 6, using AES-256, is the current strong option. A file protected with revision 6 opens in any conforming reader.
Source: ISO 32000-1, standard security handler
PDF/A for long-term preservation
PDF/A is a constrained subset of PDF intended for archival storage. It requires all fonts to be embedded and prohibits features that may not render in the future, such as encryption, JavaScript, and external content references. Conformance is verified by a validator, not by a re-save.
Source: ISO 19005 (parts 1 to 3)
PDF/UA for accessibility
PDF/UA defines requirements for universally accessible PDF, including tagged content, a logical reading order, and alternative text for images. It is a separate conformance regime from PDF/A, and a document can be one, both, or neither.
Source: ISO 14289 (PDF/UA)
PDF/X for print exchange
PDF/X is a print-oriented subset designed to make files reliably reproducible in commercial printing. It is unrelated to the PdfPix brand name despite the similar spelling, and it is a common source of confusion in search results.
Source: ISO 15930 (PDF/X)
readers and libraries that are freely available
The format is specified openly and implemented openly. Mozilla's PDF.js renders pages in the browser, pdf-lib reads and writes documents in JavaScript, and Poppler and MuPDF are mature native implementations. This is why a browser can manipulate a PDF locally without a server.
Source: PDF.js, pdf-lib, Poppler, MuPDF