OSMM is the operating system for cumulative machine mathematics. A goal becomes typed state, legal tools, bounded machine work, judged evidence, and permanent research memory. No chat summary or model owns truth.
Load exact declarations, hypotheses, targets, and source revision.
Attach exact inputs, outputs, premises, and callable roles.
Require a receipt whenever an object changes representation.
Bind the claim, state root, contract, judge, and authority.
Derive the registered residual frontier from frozen state.
One residual becomes one bounded, one-writer research contract.
Run fixed proof, axiom, anti-cheat, and anti-vacuity gates.
Atomically append accepted evidence, then recompute Cutset.
OPEN ≠ THEOREM Advice or a judge receipt alone cannot promote proof status.ATTEMPT ≠ WALL Unsuccessful search is not negative evidence.CHAT ≠ TRUTH Models propose. Frozen judges and Ledger admission decide.OSMM began with six things that existed separately. The product joins them without blurring what is proved, what is a translation, and what remains open.
δ supplies mathematical objects, forced structures, certificates, and proof transformations.
This is source mathematics inside an installed world, not the OS kernel.
PROVED RESULTS: THEOREMForced mathematical structure becomes physically applicable only through a named, checked correspondence.
The forced δ tower is theorem-grade. Calling it physically real is a model boundary; universal physical realization remains open.
UNIVERSAL BRIDGE: OPENWhen an approach dies, bank what died, the rule learned, and what still survives. Cutset walks that map and prints the registered pieces still open.
RH is the worked example. This is a memory and frontier instrument, not a proof of RH.
Open Cutset ↗Nouns say what an object is. Verbs say what may happen. Receipts record cost. Commuting squares check that math, physics, or meaning preserved the same object.
The language grows by depositing real translations, never by declaring a universal dictionary.
DEPOSITED MAPS: CHECKED IN SCOPEREWRITE changes form. ENGINE generates an invariant. EXCLUSION deletes an illegal route.
TRANSPORT requires a Grammar receipt. RESIDUAL is an open obligation, not a callable tool.
The Lean framework supplies theorem-grade mathematics and checked deposits connecting selected mathematical structures to physical ones.
It is OSMM's first rich installed world. A physical correspondence for all mathematics has not yet been proved.
UNIVERSAL CORRESPONDENCE: OPENImplementation says whether code exists. Evidence says what a visitor can verify. “Recorded internally” is deliberately weaker than a public artifact.
A theorem library stores what passed. OSMM also remembers what failed, why it failed, which route survived, what exact object remains open, and who has authority to change that state. Models can improve or disappear while the mathematical institution remembers.
A pinned mathematical universe: declarations, proofs, hypotheses, and open goals.
Callable theorem roles, exact premises, and checked receipts across representations.
Positive routes, scoped failures, visible obligations, and the frontier still open.
A human authorizes one bounded job. Models propose; Lean judges.
Mathlib, δ, Recognition Science, or another versioned world supplies exact declarations, proofs, hypotheses, models, open targets, and a revision identity. The world owns mathematical source truth.
REWRITE changes the form. ENGINE generates a usable invariant. EXCLUSION removes an illegal route. Exact premises stay attached. An open residual is work, not a callable tool.
A result crosses from math to physics or meaning only through a deposited map with exact premises, preservation evidence, and a receipt bound to that application.
Stores open obligations, attempts, admitted negative evidence, and every state root. It alone may admit and append: what died, the rule learned, and the surviving route.
Queries one frozen Ledger snapshot and returns its registered residual frontier with provenance. “Minimum” is reserved for a separate checked minimum-cut receipt.
See Cutset ↗Freezes one contract, isolates one writer, invokes a registered judge, and returns a proposal. Foreman can dispatch. It cannot admit or append canonical truth.
Agents search, derive, write proofs, attack candidates, and report typed blockers. They run outside the truth boundary and may never alter their frozen judge.
Surfaces one decision, binds approval to one exact proposal, and dispatches one bounded job through Foreman. The current private canary remains under completion testing.
Seals what the system observed and links successive states. Its signature proves provenance and continuity, never mathematical truth.
Every checked proof expands the positive library. Every admitted refutation contracts the search space. Every open obligation remains visible until evidence actually moves it.
At full depth, machine mathematics can inspect the registered frontier, choose a legal next move, execute bounded research, and submit judge evidence to root-bound Ledger admission. An atomic append makes the gain permanent.
OSMM runs the campaign. Cutset computes its registered residual frontier.