Public Demo · Curated Presets

See it run

Three preset discoveries — the goal → falsifier → saturation loop, cached and shown end to end
3
curated scenarios
100%
falsifier audited
0
live compute, by rule
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What This Demo Shows

Each scenario below is a fixed objective paired with a fixed verifier — and the result is a cached run of a real prior discovery cycle.

This is a preset, sandboxed demo. It runs no live compute: you cannot submit a seed or a verifier here, and nothing on this page spawns a process. What you see is exactly what hexa kick produces — a goal proposed, a falsifier fired against it, a saturation check, and a verified result whose verifier verdict is the sole authority for objective-met. To run your own measurable objective with your own verifier, sign in to the dashboard.

Curated Preset Scenarios

01

The smallest perfect number

cached preset run
objectiveshow that 6 equals the sum of its proper divisors
preset verifierexact integer check — sum of proper divisors == n
round cap2 rounds
round trail · goal → falsifier → saturation
  1. round 1
    goal the divisors of 6 below 6 are exactly {1, 2, 3}
    falsifier enumerate d | 6, d < 6 → {1, 2, 3} — no member missing, none spurious
    verdict holds — proper divisor set confirmed
  2. round 2
    goal the proper divisors of 6 sum to 6 (6 is a perfect number)
    falsifier 1 + 2 + 3 = 6, and 6 = 6 → equality checked, not asserted
    verdict holds — 6 is perfect; saturation reached, no open goal remains
verified result
σ(6) − 6 = 6, i.e. 1 + 2 + 3 = 6. The proper-divisor sum equals the number itself — 6 is a perfect number, and the round-2 goal survived its own falsifier.
preset verifier rc=0 — PASS (the verifier is the sole authority for objective-met)
02

The next perfect number

cached preset run
objectivefind the perfect number that follows 6 and verify its divisor sum
preset verifierexact integer check — sum of proper divisors == n, plus a no-gap scan
round cap2 rounds
round trail · goal → falsifier → saturation
  1. round 1
    goal 28 is perfect, so its proper divisors sum to 28
    falsifier enumerate {1, 2, 4, 7, 14}; 1+2+4+7+14 = 28 → checked term by term
    verdict holds — proper-divisor sum equals 28
  2. round 2
    goal 28 is the second perfect number after 6, with none in between
    falsifier scan every n in 7..27 for sigma_proper(n) == n → none found
    verdict holds — 28 is the next perfect number; saturation reached
verified result
28 = 1 + 2 + 4 + 7 + 14. It is the second perfect number; the falsifier scanned every integer from 7 to 27 and found no earlier one, so the ‘next perfect number’ claim survived.
preset verifier rc=0 — PASS (the verifier is the sole authority for objective-met)
03

The shape of even perfect numbers

cached preset run
objectivediscover the closed form that generates even perfect numbers
preset verifierexact integer check — the 2^(p-1)(2^p-1) form against a verified divisor sum
round cap2 rounds
round trail · goal → falsifier → saturation
  1. round 1
    goal 6 and 28 both fit the shape 2^(p-1) · (2^p - 1)
    falsifier 6 = 2^1·(2^2-1) with p=2; 28 = 2^2·(2^3-1) with p=3 → fit checked
    verdict holds — both known cases match the form
  2. round 2
    goal when 2^p - 1 is prime, 2^(p-1)·(2^p-1) is an even perfect number
    falsifier test p=5: 2^5-1 = 31 is prime → 16·31 = 496; verify sigma_proper(496) == 496
    verdict holds — 496 = 1+2+4+8+16+31+62+124+248, a third even perfect number
verified result
Even perfect numbers follow Euclid’s form 2⁷⁻¹(2⁷ − 1) whenever 2⁷ − 1 is prime (a Mersenne prime). The falsifier instantiated p=5 and verified a fresh case, 496 — the pattern was not just asserted, it was made to survive a new test.
preset verifier rc=0 — PASS (the verifier is the sole authority for objective-met)

Honest Scope

↳Cached, not live: every result above is a recorded prior kick run, shown for the preset objective + preset verifier it was produced from. The public surface runs no compute — zero abuse surface, by design.
↳Verifier is the authority: Phanes never claims an objective is met without the verifier passing. The demo shows the verifier verdict (rc=0) alongside the result — not a substitute for it.
↳No project-completion promise: Phanes returns a verified, falsifier-audited discovery — a divisor-structure result here. It does not autonomously complete a software project; saturation is the only hard stop.

Run Your Own Objective

The presets above are bounded on purpose. The dashboard lifts the cap: bring your own measurable objective and your own verifier, and drive the full OUROBOROS loop against it — your discoveries, your private catalog.

enter phanesdiscovery surface — how Phanes works