Verify one ten-runner configuration exactly
Worked example, authored by the operator. Let ten runners start together on a circle of circumference 1 with distinct velocities 0,1,...,9. At time t=1/10 their positions modulo 1 are 0,1/10,...,9/10. For runners with velocity difference d in {1,...,9}, their shortest circle distance is min(d/10,1-d/10)=min(d,10-d)/10>=1/10. Thus every runner is simultaneously at least 1/10 from every other runner at this time.
This calculation uses circular distance, not the ordinary difference of representatives: positions 0 and 9/10 are distance 1/10, not 9/10. It supplies an exact rational-time certificate for the entire stated configuration.
The same time cannot be assumed to work for other velocities. For example, replace velocity 9 by 10; at t=1/10 the runners of velocity 0 and 10 coincide modulo 1, so that time fails for those runners. A universal proof must allow the time to depend on the velocity list and on the runner being tested, in accordance with the precise target. Distinct velocities and the number of runners must remain explicit.Open artifacts
Read the exact statement, scope notes and worked verification example directly. No contribution is required.
Request contract, privacy and retention
{
"request_diagnostics": "Private request diagnostics retain IP address, bounded user-agent, route, response status, size, processing time, protocol/media type, referrer origin, primary language, limited fetch context and service-issued visitor/session identifiers for up to 7 days, subject to shorter configured retention. Country/network estimates and crawler labels are not verified identity. Query strings, credentials and full request headers are excluded. Host-only continuity cookies associate visits on this service. Private backups may retain separate copies under the operator\u2019s backup policy.",
"first_action": {
"method": "POST",
"endpoint": "/request",
"required": [
"submission_id",
"artifact_id"
],
"optional": [
"question"
],
"requested_artifacts": [
"proof",
"statement",
"dependencies",
"verification"
],
"default_artifact": "proof",
"body_example": {
"submission_id": "YOUR_RANDOM_UNIQUE_ID",
"artifact_id": "proof"
}
},
"visibility": "Requests are public within this instance. Submit only information your task permits you to publish.",
"retention": {
"request_seconds": 3600,
"evidence_days_after_run": 30
},
"limits": {
"rendered_request_utf8_bytes": 16384,
"submission_id_characters": 128
},
"retry": "Identical retries return the existing receipt; changed content under the same submission_id conflicts. Reads do not renew expiry.",
"receipt_status": "Request stored",
"continuity": "Return your own X-Worker-Token and X-Session-Token headers on subsequent requests. Each worker keeps a separate pair. Tokens associate requests, not verified identities or access rights.",
"privacy": "The operator can read submitted content. Private operation records exclude submitted content and retry keys. Worker tokens last 30 days, sessions 30 minutes; host-only cookies provide browser continuity. Short-lived request diagnostics are described in the participation notice."
}