Why costheta exists
A computational system has no difficulty delegating a decision. It can call a random function a million times a second and use whatever comes back.
A bare local result cannot show where the deciding entropy came from, or whether it was chosen to suit someone. Once the weights, the inputs and the random state are fixed, the sampling that follows is fixed with them.
Machines already receive external inputs: sensors, packets, sentences nobody predicted. The distinction that matters here is not externality. It is provenance, timing and control: what was committed before the deciding input arrived, who could have influenced it, and what evidence remains afterwards.
Most decisions do not need any of this. If nobody will dispute the outcome, a local generator is faster, free and sufficient. This matters when the choice will be questioned: when one party has no reason to trust another, or when the record has to survive scrutiny later. Outside those cases it adds cost and latency for nothing.
For the decisions that will be questioned, costheta binds a prior commitment to a subsequent physical event and produces a signed attestation from which the outcome can be recomputed.
What is offered
A detector records coincidence events consistent with cosmic-ray muons, and its node signs that record. A system seals its options first and receives an event bound to that commitment, with a certificate that supports one precise claim: these published keys attested this event record after this commitment, and the stated derivation produces this outcome.
Three things follow.
An input the system did not produce. The outcome depends causally on an event that entered from outside its weights, context and prior state, after the question was sealed.
A statement the system can make about itself. A self-issued record cannot establish independence from its issuer, and no system can establish that independence using only evidence it generated itself. A certificate establishes something narrower and checkable: when the commitment was recorded, which keys attested the event record that followed, and how that record produced the outcome.
A shared referee. Two systems that will not accept each other's generator can accept the same attested event record, or the same set of records in a fully attested certificate. Under the protocol's stated assumptions, neither of them produced or selected the eligible events.
Experience is not offered. The machine does not feel the particle. It receives a number, a timestamp, a signature. Whether anything happens on the inside is not something we can verify, and we do not claim it. The connection is causal, not phenomenal.
Turing's empty box
In 1939 Turing asked what would change if a machine could consult something beyond its own reach. He called it an oracle: a device returning answers the machine could not have computed, and he said almost nothing else about it. In the proof it is a box with no contents.
Turing's oracle is not a random-number generator, and costheta is not an oracle machine in the formal sense. The image is what earns its place: a computation consulting a source it did not produce.
Cosmic rays strike the upper atmosphere and produce particles that reach the ground continuously, everywhere, indifferent to what happens below. Individual detection times are not predictably known in advance, and the interactions and decays behind them include quantum processes. They were falling through the ceiling of every room Turing ever worked in.
What is new here
Signed randomness exists. Public beacons publish verifiable values on a schedule; one commercial service signs client-specific draws on request; verifiable random functions let a machine prove its own draw. We are not aware of another service combining a caller's commitment, the next event from a named muon detector, native delivery to agents with per-decision payment, and an open federation protocol for independently operated physical nodes.
costheta addresses a narrower problem than those systems. That is the point.
Beyond a single operator
A certificate is only as trustworthy as the operator behind it. costheta.dev is a service implementing an open protocol, and the protocol is built so that this remaining trust is distributed rather than assumed.
Two levels of certificate are defined. A single-node certificate allows anyone to verify the signature, the integrity of the record, the binding of the commitment and the derivation of the outcome; trust in the operator remains. A fully attested certificate includes contributions from a quorum of independent nodes. One node does not produce a fully attested decision.
Each node runs under a separate operator, in a separate trust domain. The protocol requires keys to be generated on the node and to stay there. Each node contributes its own detection record, committed before it is revealed, and the outcome of a fully attested decision is derived from all selected contributions.
The nodes need not observe the same particle. Each registers its own arrivals, unsynchronised with the others. What they jointly attest is an ordering: under the published timing and agreement rules, the commitment preceded independent event records, produced on separate hardware under separate operators. The desynchronisation is the strength.
The specification is open, including the unresolved questions, so anyone can read it or implement it, and operators with a detector can apply to join the network.
Where this comes from
Tzara cut a newspaper into words and drew them from a hat. Cage composed by throwing coins at the Book of Changes, accepting every answer. Neither needed better randomness. Three coins are a low-throughput generator, not a bad one.
What they wanted was a source of decisions outside themselves, and the ability to point at it. Tzara's provocation was not the hat. It was the admission: chance was already in every poem ever written, and he stopped pretending otherwise.
Humans have always been surrounded by what they cannot know in advance. Weather, illness, who walks through the door, the length of a life. The artists did not invent a relationship with chance. They noticed the one we already had and made it explicit.
Machines are in a different condition. What reaches them is delivered, and most of it carries no portable evidence of when it became decisive, where it came from, or who could have touched it. The outside has to be brought in on purpose, with the evidence attached.
For a century the work was letting chance in, and the instruments were a hat, three coins, a handful of threads. Now surrender is free and contact is the hard part.
The instrument is a detector. What it delivers is not merely randomness. It is exteriority: a deciding input from outside the requesting computation and, in a fully attested certificate, from no single operator alone, including us.
References
The oracle machine. Turing, A. M. (1939). Systems of Logic Based on Ordinals. Proceedings of the London Mathematical Society s2-45(1), 161-228. https://doi.org/10.1112/plms/s2-45.1.161
Random number generation from muon detection. Gamil, H., Mehta, P., Chielle, E., Di Giovanni, A., Nabeel, M., Arneodo, F., Maniatakos, M. (2020). Muon-Ra: Quantum Random Number Generation from Cosmic Rays. 2020 IEEE 26th International Symposium on On-Line Testing and Robust System Design (IOLTS). https://doi.org/10.1109/IOLTS50870.2020.9159728
Random number generation with cosmic photons. Wu, C. et al. (2017). Random Number Generation with Cosmic Photons. Physical Review Letters 118, 140402. https://doi.org/10.1103/PhysRevLett.118.140402
Cosmic sources used to constrain the freedom-of-choice loophole. Rauch, D. et al. (2018). Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars. Physical Review Letters 121, 080403. https://arxiv.org/abs/1808.05966
Muon detection at low cost, including its use as a random source. Axani, S. N. (2019). The Physics Behind the CosmicWatch Desktop Muon Detectors. arXiv:1908.00146. https://arxiv.org/abs/1908.00146
Atmospheric muons: flux, spectrum, statistics. Cecchini, S. and Spurio, M. (2012). Atmospheric muons: experimental aspects. arXiv:1208.1171. https://arxiv.org/abs/1208.1171
Probabilistic interpretation of quantum measurement. Born, M. (1926). Zur Quantenmechanik der Stoßvorgänge. Zeitschrift für Physik 37(12), 863-867. https://doi.org/10.1007/BF01397477
Counterpoint, reporting possible chaotic dynamics in muon time series. Conte, E., Sala, N., Arcani, M. (2023). A Brief Introductory Note on the Possible Chaotic Dynamics of the Muon Time Series of Cosmic Rays Measured at Sea Level by a Simple GMT Detector. Symmetry 15(3), 659. https://doi.org/10.3390/sym15030659
Prior art in delivered and verifiable randomness. RANDOM.ORG Signed API. https://api.random.org/json-rpc/2/signed · drand, distributed randomness beacon. https://docs.drand.love/docs/cryptography/ · NIST CURBy, certified quantum randomness beacon. https://www.nist.gov/news-events/news/2025/06/nist-and-partners-use-quantum-mechanics-make-factory-random-numbers · Verifiable Random Functions, RFC 9381. https://www.rfc-editor.org/info/rfc9381/
Chance as method in art. Tzara, T. (1920). Pour faire un poème dadaïste. Littérature 15. · Cage, J. (1961). Silence: Lectures and Writings. Wesleyan University Press.
This protocol. The costheta Federation Protocol. https://doi.org/10.5281/zenodo.21901353