Measured by the lab
0.85
Is the ?world=phasemap screen's central claim — a 2-D diagram with two roughly independent axes (μ binds, α moves), four corner regimes, and a RIGOROUS static line along α = 0 at every μ — actually honoured by the substrate, and can any part of that map be validated against an exact law rather than read off a heat-grid on faith?
Units: per-sim-step (dt = 1/45 s) COM velocity decay factor everywhere on the α = 0 edge — the map's rigorous static line, exact at every μ because shift and clamp preserve the symmetry that makes every pair force cancel
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Particle Life 2-D phase map — the map's α = 0 edge is exactly solvable at EVERY μ: the uniform shift and the setAttract clamp both preserve bitwise Float32 symmetry, so Newton's third law holds along the entire 'static line' and the 1200-body COM decay factor comes back 0.8499999999 ± 6.0e-10 vs 0.85 (rel 9.9e-11) INVARIANTLY across all 6 grid-μ × 3 seeds — from the repulsion-clamped gas (6/25 entries clamped, still exactly symmetric) to the dense condensate — with the kicked trajectory point-by-point to 1.5e-7 over a 566× swing at both edge ends and every settled edge cell's drift ≤ 1.8e-9; on that calibrated edge the module's own verbatim snake grid shows the four-corner structure the screen claims: μ carves gas → condensate on BOTH horizontal edges (0.316 → 0.920 at α = 0, 0.197 → 0.891 at α = 1; gas BELOW the calibrated random floor 0.4645), α wakes activity 17×/339× at the two μ ends, the α = 0 row sits at drift ≤ 3.7e-10 while the α = 1 row sustains ≥ 7.7e-2 (2.1e8× separation), and the μ_c the module measures reconciles on BOTH clocks (−0.222 as the screen samples it at the engine's 4 Hz cadence, −0.245 in the sim-time mirror — a 0.023 clock systematic, gated ≤ half a grid spacing); rival A (α = 1 at the SAME condensed corner, SAME friction) misses the law by rel 235 (1.5e9× separation) with drift 0.58 at n = 200 where the law predicts 9.6e-15 — the droplet's stillness is reciprocity, not stuckness — and rival B (one-knob map: activity a monotone function of binding) is killed by the sign-reversed corners (active gas: 0.21× the static condensate's binding, 158× its activity); NOW CERTIFIED HONEST-MODULE: the shipped ParticleLifeModule + ClusterMetricsModule + ParticleLifePhaseMapModule (sha-pinned, type-stripped, executed headlessly) run bit-exactly against an independent replica for all 25,920 fl(1/120) engine calls of the seed-7 default boot — PL trajectory (9,719 steps), the live-mutated matrix through all 30 snake-cell setAttract windows (opens 1200…25589, commits 1501…25890), 864 cluster samples, all 30 cells {μ, α, bound, activity, drift}, 3,238 status + 3,238 SVG heat-grid writes byte-exact — with the replica's instrument being the oracle's OWN measureSample (the lockstep IS a live closure, 864 configs), the final screen 'done · α=0 edge drift≡0 (momentum conserved) · μ_c≈-0.22' pinned as executed output whose α=0 row sits at drift ≤ 2.4e-10 vs the α=1 row's ≥ 8.8e-2 (3.7e8×) — the status line's physics claim is executed, not prose — and a seed-8 twin moving every displayed digit (μ_c≈-0.16)
The generator is ParticleLifeModule + ParticleLifePhaseMapModule + ClusterMetricsModule transcribed verbatim headless (mulberry32 stream, Float32 state; _stepSim's cell list, triangular profile, FORCE = 50, FRICTION = 0.85, dt = 1/45; the phase-map module's S = (A+Aᵀ)/2, Q = (A−Aᵀ)/2 split, _apply = clamp(S + α·Q + μ) via setAttract, the 6 μ × 5 α grid, the snake traversal with carry-over and 10/4.5/2.5 s timings, _sampleVel's ⟨|v|⟩/|v_cm|; the ClusterMetrics union-find bound fraction, R = 2, MIN_SIZE = 4). It integrates forces and never forms v_cm nor any closed form. Exactness probe: settle 10 s at (μ, α = 0), add a uniform velocity kick, fit ln|v_cm| vs n over n = 1..40 — repeated at all 6 grid μ × 3 seeds; premise witness gates that clamp(S+μ) stays bitwise symmetric at every μ (Object.is entrywise). Phenomenon: the module's exact snake protocol at seed 7 → all 30 cells; corner/axis/μ_c gates as a-priori branch separations. Rival A = identical kicked protocol at (μ = +0.2, α = 1); rival B = the corner-ordering test. 20 gates in scripts/phasemap-derisk.mjs (~30 s; L–P are the module certificate); tamper ⇒ exit 1. ?world=phasemap.
6.0000e-10
18
6.3600e-9
per-μ mean factor deviations −5.8e-10 … +6.4e-9 across μ = −0.4 → +0.2 with 6/25 → 0/25 entries clamped — the law does not notice the binding state OR the clamp
Newton's third law / momentum conservation (Principia, Law III + Corollaries III–IV) extended from the active oracle's single symmetrized matrix to an ENTIRE EDGE of a phase diagram: the new exact content is that the phase-map's own transformation clamp(S + μ) preserves bitwise Float32 symmetry for every uniform shift μ — including where the clamp saturates 6/25 entries — so the COM law holds invariantly from gas to condensate, whatever union-find says about the binding underneath. Non-circular: the generator integrates ~4×10⁴ pair forces per step through the cell list and never forms v_cm or any power law; the known value 0.85 is the generator's own FRICTION constant (disclosed circularity exactly as in the active finding), defused because rival A runs the IDENTICAL generator with the IDENTICAL constant at the same condensed μ and misses by rel 235 — the gate reads reciprocity, not the numeral. The four-regime structure itself (Ivlev et al. PRX 2015 for the broken-reciprocity half; Gilbert 1961 for the random floor the gas digs under) is validated only as a-priori branch separations: the corner observables' functional forms, μ_c(α), and boundary sharpness have no citable closed form and stay OPEN. The honest-module certificate adds no physics claim: it proves the ?world=phasemap SCREEN is this validated computation (bit-for-bit, from boot to the final heat-grid), that the shipped instrument is the oracle's instrument on every configuration the sweep generates, and that the one number the screen quotes (μ_c) is clock-qualified.
npm run derisk -- phasemap (scripts/phasemap-derisk.mjs — 20 gates: the 15 rung-5 gates (clamp-symmetry premise witness, 18-cell edge factor + μ-invariance, both-ends trajectory + transverse purity, no-kick floor, μ-axis, α-axis, static-line separation, μ_c reconciliation, one-knob rival, reciprocity rival ×3, determinism pin) + the honest-module certificate L–P (sha-pin + strip + answer-free scan; executed seed-7 boot; 25920-call lockstep vs independent replica with the oracle's own measureSample as replica instrument; display reconciliation incl. the screen's own static line + seed-8 twin; shipped-μ_c closure + #156 clock-systematic gates + dt twins). Tamper self-test verified: known_value 0.85 → 0.86/0.84 exit 1 with the recovered value unchanged; sha/rulepl/rulecm/rulepm all exit 1 (see result.module_certificate.tampers).)scripts/oracles/phasemap.reference.jsonI. Newton, Principia (1687), Law III + Corollaries III–IV; A. V. Ivlev et al., 'Statistical Mechanics where Newton's Third Law is Broken', Phys. Rev. X 5, 011035 (2015); E. N. Gilbert, 'Random Plane Networks', J. SIAM 9, 533 (1961) — the calibrated random floor cross-referenced from the condense oracle.