The lightgap model

Lightgap scorecard — how usable is fak, on an UNBOUNDED scale, per use case?

The sibling scorecards all answer bounded questions. industry_scorecard asks whether the competitive map is complete and honest (coverage + parity-debt). product_scorecard asks whether each concept is real and useful today. persona_* asks whether each persona is served. Every one of them tops out: you can score 100 on all of them and still not know whether anyone should switch.

This one answers the question a buyer actually holds:

Relative to the next best thing I could do instead, and relative to the best that is physically possible, how far does fak actually get me — and is that worth what it costs me to adopt it?

That question has no ceiling of 100, so this scorecard has no ceiling either.

Two anchors

symbol	meaning
`N`	the next-best option — what a competent team does today without fak. This is the origin; you are already here and it costs nothing.
`c`	the ceiling — the best possible for anyone, ever, on this axis. Derived, and labeled `physical` / `definitional` / `lower-bound`.
`F`	where fak actually measures, with committed provenance.

beta  = (F - N) / (c - N)                    0 = the alternative, 1 = physics
w     = artanh(beta)                         the lightgap score, in nats
load  = (fak_hours - alt_hours) / tolerance  signed share of patience spent
tau   = artanh(load)                         the tax, on the same scale
w_net = w - tau                              the verdict

beta needs no direction flag: for a lower-is-better metric the ceiling sits below the alternative, both differences flip sign, and the ratio comes out right with no special case.

Why rapidity and not a percentage

Unbounded and signed. w ∈ (−∞, +∞). Being worse than the alternative is a negative score, not a low one.
Additive. Relativistic velocities compose by a messy formula; rapidities just add. So layered gains add — and the adoption cost subtracts — on one scale.
It diverges at the ceiling. Closing the last 1% of the gap to physics is unboundedly harder than the first 50%. A system that is the only thing that does X scores arbitrarily high. That is what a moat is.
Zero at the alternative. “No better than what you already have” is 0, not 50.

The tax is differential

load subtracts the alternative’s adoption cost, because the alternative is not always free either. Reaching zero attack-success with a formal-isolation defense means restructuring your agent; reaching it with fak means a wrapper. Same number on the axis, very different load — and that difference, not the ASR, is the actual reason to switch. Conversely, an alternative that costs more than the segment’s entire tolerance is not available to that buyer, so it cannot be their next-best option: the engine refuses it (ALT_UNAFFORDABLE) rather than let fak win against something nobody would deploy.

Three anchor shapes the naive form gets wrong

mode	when	what changes
`pure_tax`	the alternative is the ceiling — you already run the best thing and fak can only take a cut	`β = (F−N)/│N│`, so the cell can never score positive on the axis. That is the honest shape of a tax.
`parity_at_ceiling`	fak and the next-best both sit at the limit	`β = 0`. No advantage on the axis; any reason to switch must come from the differential adoption cost.
ceiling override	the ceiling is per-hardware (a bandwidth roofline)	the cell states its own `c` and derivation.

Claim caps — you cannot outrun your own evidence

condition	cap
`MODELED` / `PROJECTED` provenance	at most `CRUISE`
`OBSERVED` provenance	at most `RELATIVISTIC`
`lower-bound` ceiling	at most `RELATIVISTIC`

w_net (raw) is always reported; w_eff is the capped value decisions use. You cannot claim a category-defining lead on a simulated corpus, and you cannot claim to be near light-speed when all you know is where the current record sits.

Why there is no overall score

A mean over the sphere is precisely the lie this scorecard exists to avoid: it lets a spike on one axis pay for a dent on another that a given buyer actually cares about. So each use case reports its pull (best cell — the real reason to adopt) and its drag (worst cell — what you eat to get it). A material axis that is REGRESSIVE blocks adoption regardless of pull. And a use case whose deciding comparison has never been run comes back UNDECIDABLE instead of being quietly scored on whichever cells happen to exist.

Honesty gates (`lightgap_debt`)

code	refuses
`NO_FAK_SOURCE`	a fak value with no committed artifact
`NO_ALT_SOURCE` / `NO_ALT_NAMED`	a next-best value that is a guess
`NAIVE_BASELINE`	a win measured against a strawman
`NO_COST_BASIS`	an adoption cost with no measured basis
`CEILING_BREACHED`	`β > 1` — the ceiling is wrong, not the result
`DEGENERATE_CEILING`	the ceiling equals the alternative and the cell did not declare `pure_tax`
`ALT_UNAFFORDABLE`	an alternative this buyer could never deploy
`NO_DERIVATION`	a ceiling asserted without a derivation
`UNFENCED_MODELED_LEAD`	a large win on `MODELED`/`PROJECTED` evidence, no fence
`UNCOVERED`	a facet a buyer materially weights, with no cell — the work-list
`IMMATERIAL_CELL`	a cell scored for a facet the segment weights 0