Use cases: the site is what the QPU computes

As payloadcms.com is built of what Payload computes (its REST at https://payloadcms.com/api/pages?limit=1&depth=0 answers pages of blocks with SEO meta and breadcrumbs, read by discovery as the standard payload-site), this site is built of what the QPU computes: every toolbox is a use case and every example a page in Payload's own pages shape — one qpu block of UUID logic, SEO meta, a breadcrumb — at its live address. Generated by npm run next through the payload tool (site: true): 11 use cases, 73 pages.

Use case (toolbox)	Pages	Tools
language	3	translate, prose
raid	2	mongo
billing	3	stripe
legal	2	legal
repository	1	repository
standards	3	jsonld, codes
payload	13	configure, payload
extension	4	extend
crypto	2	fold, seal
tree	18	verify, css, dashboard, leads, clay, match
google	22	processor, circuit, echo, echo_benchmark, roadmap, algorithm, software, statements, repositories, quantum-error-correction, chemistry-simulation, fault-tolerant-design, quantumlib

language

any language and dialect, offline and token-free: translation by vocabulary both ways, the vocabulary measured against every term the surface emits, and prose programmed from a tool's result and its toolbox's skill

Page	Tool	Theorem	Shows
translate-bg	translate	—	English to Bulgarian by vocabulary: the labels and verdicts translate; a word with no entry stays and is reported.
translate-coverage	translate	—	The vocabulary measured: for every locale, which surface terms have no entry — the leads of the tables, updated from measurement.
prose-clay-bg	prose	—	Programmable prose in Bulgarian from the clay tool's answer and the tree toolbox's skill: the numbers are the tool's, the words the vocabulary's, the rest reported.

raid

the docket as a database: MongoDB's query and update language ported as pure functions over content-addressed entries, so any document framework (Payload first) stores on the RAID through its mongodb adapter

Page	Tool	Theorem	Shows
mongo-find	mongo	—	A Mongo filter over documents read from the docket: operators, array membership, sort; the match is computed here, the storage is the docket.
mongo-update	mongo	—	An update computed as a new document and a new entry linked to the one it replaces: entries are immutable and content-addressed, so history is kept.

billing

Stripe per tenant: a licence bought at one tenant is an entry valid on the domains it names, every event idempotent and linked, every signature verified with the tenant's own secret, every refusal a lead

Page	Tool	Theorem	Shows
stripe-plan	stripe	—	A checkout plan for a yearly commercial licence of acme on two domains, bought at tenant psg: the form Stripe takes, the metadata the webhook brings back, the tenant secret the Worker alone holds.
stripe-catalogue	stripe	textbook_prices_are_variants_times_currencies	The QPU as a product line for tenant uuidna: seven variants over five products, each a Stripe price form in two currencies, the a432 default at zero.
stripe-webhook	stripe	—	A checkout completed at tenant psg, its signature verified with psg's webhook secret, read into one licence entry granting acme on both domains.

legal

the legal and security audit of this MCP through MCP: the author's claims judged by the unit's forensic, legal and security doors, free agents by default, the operator alone overriding, beside the tree's own checks of its sources

Page	Tool	Theorem	Shows
legal-audit-offline	legal	textbook_uuid_is_36	Phase two with no answers (offline): the claims, the tree's security checks, and the audit's own content address over the SHA-256 of every input — change a source and the address changes.
legal-plan	legal	—	Phase one on fixture texts and a three-door discovery: the claims gathered (licence, author, metadata, measured table, perspectives), the tree's security checks, and the plan — one forensics call per claim, the rights and security doors once, free by default.

repository

the repository watched: every workspace, branch, tag and release here compared with the remote and the archive online, every disagreement a lead

Page	Tool	Theorem	Shows
repository-watch	repository	—	Fixture facts against fixture answers: two local branches unpushed, one remote branch not here, a local tag not pushed, a remote tag not fetched, a moved tag, a release whose tag is gone, a version with a tag and no release, a Zenodo version without a release, a second workspace: ten leads.

standards

the standards fused: schema.org on every block, page and offer; ISO 8601, 639-1, 4217 and 3166-1 in every date, language, price and country, validated against the CLDR lists discovery reads as contracts

Page	Tool	Theorem	Shows
jsonld-block	jsonld	—	A block as schema.org JSON-LD: a CreativeWork of the SoftwareApplication, the author a Person with an ORCID, the licence a URL, the date ISO 8601.
jsonld-catalogue	jsonld	—	The whole catalogue as an OfferCatalog of Offers priced in ISO 4217 EUR, each a UnitPriceSpecification by month or year where recurring.
codes-plan	codes	—	What the codes tool would validate and where the CLDR lists are: eleven locales, three currencies, the tenants' countries.

payload

Payload's plugin schema as the one shape of every result: nested docs of lexical documents whose blocks are programmable UUID logic, SEO from the block, no custom collection, a few kilobytes computed once

Page	Tool	Theorem	Shows
configure-versions	configure	—	Versions define development and development defines versions: the current version from its single source, the next number from what the catalogue changed since the last tag (tools added: the minor digit carries), kept to single digits with a build address, the open leads as the version's plan, Payload's versioning over the RAID (every version an entry, never overwritten, no cap).
configure-migration	configure	textbook_providers_are_tenants_plus_operator	A provider added or moved at 100 % uptime: deploy beside, mirror the docket by address, decode old and new as copies through the gate, route, and the rollback is the earlier version still answering.
configure-api	configure	—	The QPU's API overview as data, the way platform.claude.com's overview is one for the Claude API: one MCP endpoint and every surface around it, the headers, the authorization (none for every pure tool), the content addressing and its involution, the tools by toolbox, the MCP connector for Claude and for any client, quick tests, limits and errors; docs/api.md is written from it.
configure-fullstack	configure	—	QPU's full stack from the source of payloadcms.com (MIT): its twelve collections, thirty blocks, globals and fields kept, the qpu block added, search, multi-tenant and mcp added to its four plugins, the database the RAID, storage and deploy at Cloudflare; two source files and a README generated for the fork.
configure-all	configure	textbook_reflection_sums_to_ten	Every configuration MCP computes, tested around the torus: Payload's plugins, the Worker, the tenants' variable names, the manifest, the registration, the versions, the migration, the full stack; each with its address, seed, reflection and trinity, every loop closed.
configure-payload	configure	textbook_plugin_combinations	Payload configured by MCP: eight default plugins over the one pages collection, the lexical block qpu with its UUID logic fields, the tenants in multi-tenant, 256 combinations.
configure-wrangler-drift	configure	—	The Worker configuration compared to a text a client holds: every differing path is a lead, nothing is rewritten by the tool.
configure-tenant-missing	configure	—	Each tenant's variable names and which an environment lacks: Stripe keys and the Cloudflare MCP tokens are the operator's to set; values never travel.
payload-theorems-plan	payload	—	The textbook's axioms replaced by theorems through the Payload MCP plugin, as a client: the endpoint, the authorization the tenant sends, the tools/list request, and the steps — the find and update doors picked by what they take, every qpu block without a theorem given the kernel-accepted key its example names.
payload-theorems-update	payload	—	With the Payload MCP's answers: the find and update doors recognised by what they take, two pages read, one qpu block without a theorem given textbook_plugin_combinations (the example configure-payload), one already naming its theorem left as it is; one update request emitted.
payload-website	payload	textbook_website_plugins_partition	The source of payloadcms.com (github.com/payloadcms/website, MIT) read as a tree: twelve collections, thirty blocks, seven globals, ten fields, its own opsCounter plugin, and the four default plugins its config mounts; the live page's block types contentGrid and cta have their blocks in the source — the site is what Payload computes, verified.
payload-skills	payload	textbook_skills_documents	Payload's skills for agents (github.com/payloadcms/skills) read as a tree: two skills, payload and cms-migration, their fourteen references, each mapped to the tool of this tree that enacts it; names and paths as facts, no text carried.
payload-doc	payload	textbook_uuid_is_36	The clay result as a Payload document: a lexical root with a heading, one qpu block of UUID logic and the licence paragraph; nested under its referer; the SEO fields from the block's Open Graph.

extension

QPU the natural extension of every MCP and every MCP of QPU: a host's tools read into doors of this catalogue by the same reading discovery uses, a foreign door served by one request the client fetches, and this catalogue expressed as the registration any MCP client mounts; tenant configurable through the hosts and tokens a tenant names

Page	Tool	Theorem	Shows
extend-out	extend	—	This catalogue as the registration any MCP client mounts: every tool as tools/list serves it, grouped by toolbox, at this tree's own endpoint; and as the Claude API mounts it, through the Messages API's MCP connector (mcp_servers with the mcp_toolset, beta mcp-client-2025-11-20), the tenant's key in the request.
extend-in-request	extend	textbook_integrations_are_ten	Without the host's tools: the one tools/list request the client makes of Cloudflare's documentation server (no token needed there), and the integration matrix: every MCP this tree knows, its token name and what the tree does with it once open (GitHub → the repository watch through its doors; Cloudflare's eight → the verifier, the mirrors, the metrics, the wave, the audit, the prose, the tenants, the textbook; the Claude API → the operator agent, and outward the Messages API registration that mounts this catalogue).
extend-in-docs	extend	—	Cloudflare's documentation server read into this catalogue: one door, docs.mcp.cloudflare.com:search_cloudflare_documentation, taking a query.
extend-call-served	extend	—	A foreign door served and its event-stream answer read back into the text the host returned.

crypto

the split folds: what a place cannot hold is folded into pieces it can, each addressed by content and the whole by its pieces; a key names its piece; the bound is a reflective boundary that decides by comparison before computing

Page	Tool	Theorem	Shows
fold-ledger	fold	textbook_fold_mirror	A forty-row ledger folded under a bound of 600 bytes: the pieces, each with its address, SHA-256 and key range, the root over them, the mirror piece of each across the fold, and the one piece the key k27 sits in — decided by comparisons, the whole never read for it.
seal-text	seal	—	SHA-256, the HMAC under a test key and the fold address of one text, the same at every host.

tree

the tree knows itself: its leads, its self-audit, any statement matched or proved impossible, the Clay register recomputed, any UUID verified cheaply, its metrics in real time

Page	Tool	Theorem	Shows
vortex-trinity	verify	triad_reflect	The 9-vortex of a UUID read whole: the seed, its reflection under σ_10, the trinity it belongs to and the trinity it reflects into at the same time (3, 6, 9 ↔ 7, 4, 1; 2, 5, 8 into itself), and whether it sits in the key's trinity; stated by the kernel as triad_reflect.
css-stylesheet	css	textbook_reflection_sums_to_ten	The UI as CSS: the stylesheet from the key 432 with the rules that draw every block from its own custom properties, and the thirteen variables one UUID sets on its block root, its vortex seed and the seed's reflection summing to 10; no script anywhere.
dashboard-processor	dashboard	—	The processor tool laid out whole: its one facet (three devices) and the three combinations, each a final cell drawn by its own UUID with a link to its walk page, so the click is the decision.
dashboard-algorithm-narrowed	dashboard	—	The algorithm tool with its name fixed to shor: the space of every combination counted whole, and the next facet open as cells that narrow it further, until one combination remains and its cell is the walk.
dashboard-index	dashboard	—	Every tool with the size of its input space: how many combinations its enumerable facets admit, which properties stay free, and the address of its own dashboard.
leads-all	leads	—	Every lead with its status; the counts add up to the total.
clay-register	clay	—	The 54 Clay relations recomputed in exact integer arithmetic: all hold, the widest value needs 33 bits (amplitudes = 2^32), three 16-bit limbs on an 8-bit machine.
clay-reflection	clay	triad_reflect	The register read by the technique: every relation's value as a vortex seed with its σ_10 reflection and both trinities, the relations whose seeds reflect each other paired, the fixed ones (seed 5) and the ones in the key's trinity named, and the plan to ask the unit's sequence door every value.
clay-relation-15	clay	relation_15	One relation: magicBlock = glProd hexbit seed = qftDepth vertices = 15.
verify-seal-and-content	verify	—	One UUID checked cheaply: its seal from its own 31 nibbles, and its content by one fold.
verify-tampered	verify	—	A UUID with one nibble changed: the content-decided version no longer agrees, and no content was needed to see it.
match-willow	match	—	Any statement, matched: this one is served by the processor tool.
match-glagolitic	match	—	A Glagolitic numeral read as the integer 15 before the match: served by the algorithm tool, factored 3 × 5 in the reflection.
match-bulgarian	match	—	A statement in Bulgarian with a Glagolitic numeral, translated by vocabulary offline, matched, and answered with its verdict in Bulgarian.
match-theorem-first	match	mersenne_127	Solved first by the QPU textbook: the statement names a kernel-accepted theorem, so it is served by that theorem, proven, before any tool is called.
match-pattern-uuid	match	—	Pattern recognition: a UUID in the statement opens the verify door before any token match; the match names the pattern and carries the verification.
match-pattern-dashboard	match	—	Pattern recognition: "dashboard of <tool>" lays the tool out whole.
match-rsa-2048	match	—	Any statement, proved impossible from the schema: algorithm.N is bounded to 21; the cluster names what is served instead.

google

the Google Quantum AI layer: the Willow processor as its spec sheet states it, Cirq gates and circuits, Quantum Echoes, the roadmap, the software, the statements and the repositories

Page	Tool	Theorem	Shows
processor-willow	processor	—	How many qubits Willow has, as its spec sheet states it: 105, with average connectivity 3.47.
processor-sycamore	processor	—	Sycamore from its printed diagram: 54 qubits and 88 couplers, derived and stated.
circuit-hadamard-amplitudes	circuit	—	A Hadamard gives two amplitudes of 1/√2.
circuit-hadamard-sampled	circuit	—	The same circuit measured: 400 bitstrings, each 0 or 1, in a histogram.
circuit-bit-flip-noise	circuit	—	An X gate under a bit-flip channel of p = 0.1 on the density matrix: probability 0.1 of reading 0, purity 0.1² + 0.9² = 0.82. Noise does not sample; it returns the mixed state.
echo-returns	echo	—	H forward, Z, H back is X: the echo is destroyed, so the return probability is 0.
echo-benchmark	echo_benchmark	—	Quantum Echoes as Google states it: Willow, 105 qubits, the 13,000× figure (Google's, not this tree's).
roadmap-all	roadmap	—	The six roadmap milestones and the four application bands.
roadmap-milestone-3	roadmap	—	One milestone by number.
algorithm-shor-15	algorithm	—	Shor's circuit on the state-vector simulator: order 4 and factors 3 × 5 for N = 15, a = 7.
algorithm-qft-3	algorithm	—	The QFT of |5⟩ on three qubits: eight amplitudes of equal magnitude.
algorithm-grover	algorithm	—	Grover on two qubits finds the marked |00⟩ with certainty.
algorithm-teleportation	algorithm	—	Teleportation: the received state matches the message on X, Y and Z.
algorithm-phase-estimation	algorithm	—	Phase estimation reads θ = 0.25 exactly in three bits.
algorithm-qaoa	algorithm	—	QAOA on the Cirq page's instance, sampled from the state's probabilities.
software	software	—	The Software page tools; only Cirq is implemented here.
statements-cirq	statements	—	One statement by topic.
repositories	repositories	—	The fifteen quantumlib repositories.
qec-bit-flip-0.1	quantum-error-correction	—	The three-qubit repetition code on the density matrix at p = 0.1: logical error 3p² − 2p³ = 0.028, below the raw 0.1.
chemistry-h2	chemistry-simulation	—	H₂ in STO-3G at 0.7414 Å: the Hartree–Fock energy from the simulator is −1.1167 Ha and the variational minimum lies below it near −1.137 Ha.
ftqc-all	fault-tolerant-design	—	Resource counts read from six circuits this tree builds; one Toffoli costs 7 T gates by the cited decomposition.
quantumlib-cirq	quantumlib	—	What this tree implements of Cirq, as a cross-reference of its exports.