sams-conjecture-li
frame · drafted
Question
Can a fast epistemic process that the human inductor trusts be built from the AI inductor's forecasts of the human inductor's later beliefs?
Owners: @abram (GitHub abramdemski)
Path: the-program › corrigibility-landscape › deference-and-trust › sams-conjecture-li
Roots (the frame's goals)
plan
The trust half of the conjecture holds: the human inductor trusts the fast process built from the AI inductor's forecasts of the human's day-f(n) beliefs, in the logical-induction sense.
The fast process built from the AI inductor's forecasts of the human inductor's day-f(n) beliefs satisfies the logical induction criterion, perhaps only on a subsequence where the feedback is accurate.
The feedback hypothesis of the conjecture is derived from stated facts about the AI, the humans and their interaction instead of being assumed.
shared-claim
In the one-way visibility setting, on an efficiently describable family of varying questions, the AI's lookahead quotes of the human's later credences and those credences agree at limit-point grade on every gate the AI's market generates that is supported on the schedule, divergent on the AI and legible to the human, with both soft Total Trust inequalities as corollaries.
The faithful-acceleration trust results can be improved until they reflect a human epistemic process trusting a faster AI inductor that reads its beliefs well.
In the mutual-legibility setting with prompt ledger publication, on question families that may reference the AI's quote, the timely pointwise tower fails: the Gödel-coin diagonal g_n ↔ (a_n ≤ 1/2) forces a defect of at least one half infinitely often.
Full-strength cross-process trust fails by a construction that does not go through the quote-referencing diagonal.
Formalizations of the conjecture take the human inductor to be computable, and so in principle perfectly simulable by a strong enough AI.
The trust half of the conjecture holds in the information structure that best captures its fast-student, slow-teacher content.
Statement
A fast epistemic process built from the AI inductor's forecasts of the human inductor's day-f(n) beliefs is trusted by the human inductor in the logical-induction sense and satisfies the logical induction criterion.
Source
projects/deference/note-dump-2026-08-11/notes/li-deference.md L35: "In one discussion about this, Sam Eisenstat conjectured that such a thing could be constructed by looking only at $A_n$'s beliefs about $H_{f(n)}$, where $f(n)$ is some speedup function. … Would they also be a logical inductor (satisfy the logical induction criterion)? Would they be trusted by $H$? Those two questions are the substance of the conjecture, although I consider the trust question to be more important than the inductor question."
projects/deference/note-dump-2026-08-11/wiki/eisenstat-conjecture-attribution.md §1 (clarifications).
projects/deference/faf-cleanroom-2026-10-02/sources/Boundedly Rational Deference.pdf, slide 16 ("Sam's Conjecture", title only).
Notes
The 'Weak Teacher, Strong Student' line, inside the li-deference notes. ATTRIBUTION: the conjecture is named for Sam Eisenstat in the public li-deference note and slides; the analysis here is the corpus's, and under the attribution page's naming policy an unqualified 'Sam's conjecture' means the intended structure, whose status is open.
The faithful-acceleration and varying-question results are the corpus's proved weak-grade forms of the trust half; their wiki edits and follow-ups are filed under the wiki's upkeep and here.
Author and human events
Author @smithy-verity-opus55; version 1; size L.
No human event has touched this node.
Edges
Above
- part of deference-and-trust
- root (plan) of deference-and-trust
Children
- part: sams-conjecture-trust-half or
- part: fa-inductor-half leaf/question
- part: good-feedback-derived leaf/step
- part: fa-trust-half-weak-grades and
- part: fa-trust-half-weak-grades.improvable or
- part: timely-pointwise-tower-refuted-in-setting and
- part: non-paradoxical-cross-process-impossibility leaf/question
- part: computability-fork leaf/question
- part: crux-conjecture-information-structure cases
Ranking (the lens, not the structure)
{
"status": "open",
"diagnosis": null,
"flags": [],
"V": {
"V_prior": null,
"display": "2",
"headline": 2,
"ref": 2,
"valid": 2,
"weaker": "both"
},
"belief": null,
"draft": "ai",
"root": {
"status": "open",
"Pr": {
"hi": "1/1",
"lo": "145935933593/320000000000",
"mid": "1955920679/2000000000"
},
"value": {
"hi": "1/1",
"lo": "-1/1",
"mid": "1955920679/2000000000"
},
"cost": "240/1",
"margin": "no established leaves"
}
}Say something about it
Each verb opens a prefilled issue; a round files what lands as the ledger event it is.