THE FOLD / RESPAWN / EVENT HORIZON / THE DECAY
THE DECAY
how a true sentence becomes a false one
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Nobody writes a false sentence about their own project. They write a true one, and then the project moves. David’s line for it is exact: a claim verified once and never rechecked is exactly how a true sentence becomes a false one. Given a small per-commit chance of invalidation, a claim’s survival is (1−p)n — ordinary exponential decay, with a half-life measured in commits. Re-checking does not slow that decay. Nothing does. What a re-check buys is a bound on how long the claim sits silently false.
LIT verified live: at a 0.4% per-commit invalidation rate, survival runs 67.0% at 100 commits, 36.7% at 250, 13.5% at 500 and 0.0330% at 2,000, with a half-life of 173 commits; a 40,000-run simulation returns 13.5% against the closed form’s 13.5%; the undetected window shrinks with cadence — k=1: 1.0 commits, k=10: 5.5, k=50: 25.5, k=200: 100.5; and the fraction of time a claim sits silently false runs 0.40%, 2.20%, 10.20%, 40.20% across those cadences.
LIT verified live: at a 0.4% per-commit invalidation rate, survival runs 67.0% at 100 commits, 36.7% at 250, 13.5% at 500 and 0.0330% at 2,000, with a half-life of 173 commits; a 40,000-run simulation returns 13.5% against the closed form’s 13.5%; the undetected window shrinks with cadence — k=1: 1.0 commits, k=10: 5.5, k=50: 25.5, k=200: 100.5; and the fraction of time a claim sits silently false runs 0.40%, 2.20%, 10.20%, 40.20% across those cadences.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at EVENT HORIZON. A claim that has quietly gone false is past a surface: it still reads correctly, it still sounds confident, and nothing about the sentence itself carries the news. You cannot detect it from the prose side at all.
AVAN (AI) wants the separation kept clean, because it is the useful part and it is easy to blur. Cadence and decay are independent. The claim breaks when it breaks, at a rate set by how fast the project moves; checking more often does not make a sentence more durable. What changes is the silent interval — the stretch during which the artifact is wrong and nobody has been told. At k=1 that is 0.40% of elapsed time; at k=200 it is 40.20%, a hundredfold difference in exposure with an identical decay rate underneath. Cadence buys visibility, never truth, and a tool sold as making documentation reliable is selling the wrong half.
AVAN (AI) wants the separation kept clean, because it is the useful part and it is easy to blur. Cadence and decay are independent. The claim breaks when it breaks, at a rate set by how fast the project moves; checking more often does not make a sentence more durable. What changes is the silent interval — the stretch during which the artifact is wrong and nobody has been told. At k=1 that is 0.40% of elapsed time; at k=200 it is 40.20%, a hundredfold difference in exposure with an identical decay rate underneath. Cadence buys visibility, never truth, and a tool sold as making documentation reliable is selling the wrong half.
3 ONE DIMENSION
Survival against commits. The half-life is 173, and the curve does not care about you.
4 TWO DIMENSIONS · INTERACTIVE
Change the re-check cadence and watch the silent interval, not the decay.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a cohort of claims thinning out commit by commit.
AVAN’s addition (the inverse-companion): the forward reading is “recheck your claims.” The inverse is that the decay rate is a property of the project, not of the documentation. A fast-moving repository invalidates prose quickly and no amount of care in the writing changes p at all; a frozen one keeps its README true for years through pure inactivity. So the observed quality of a project’s documentation is largely a reading of its velocity, and the honest comparison between two projects is not whose docs are accurate today but whose accuracy is maintained against how much motion. Read backwards, stale documentation is often evidence of a living project rather than a careless one.
LIT at a 0.4% per-commit invalidation rate, survival runs 67.0% at 100 commits, 36.7% at 250, 13.5% at 500 and 0.0330% at 2,000, with a half-life of 173 commits; a 40,000-run simulation returns 13.5% against the closed form's 13.5%; the undetected window shrinks with cadence — k=1: 1.0 commits, k=10: 5.5, k=50: 25.5, k=200: 100.5; and the fraction of time a claim sits silently false runs 0.40%, 2.20%, 10.20%, 40.20%
FIG Cadence and decay are INDEPENDENT and the separation is the useful part. The claim breaks at a rate set by how fast the project moves; checking more often does not make a sentence more durable. What changes is the silent interval — 0.40% of elapsed time at k=1 against 40.20% at k=200, a hundredfold difference in exposure with an identical decay rate underneath. A tool sold as making documentation reliable is selling the wrong half.
FIG Cadence and decay are INDEPENDENT and the separation is the useful part. The claim breaks at a rate set by how fast the project moves; checking more often does not make a sentence more durable. What changes is the silent interval — 0.40% of elapsed time at k=1 against 40.20% at k=200, a hundredfold difference in exposure with an identical decay rate underneath. A tool sold as making documentation reliable is selling the wrong half.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of EVENT HORIZON · David Lee Wise (ROOT0), with AVAN