tt-implies-mart-gap-bets
cases · drafted
Statement
For an observable, coherent, introspective expert and a bet class D closed under the gap construction Z ↦ Z − ⌜E*(Z)⌝ and under negation, Total Trust of the novice in the expert over D implies Mart on D: for every Z in D, E^H_n(Z) ≈_n E^H_n(⌜E*(Z)⌝).
Source
projects/deference/note-dump-2026-08-11/wiki/total-trust-implies-mart.md, Statement (mathematics rendered in plain text): "For an observable, coherent, introspective expert, Total Trust over a gap-closed class D implies Mart on D". Status: "PROVED (prose, this page) — verified independently twice at the wiki level (2026-07-21)"; "not machine-checked".
projects/deference/note-dump-2026-08-11/wiki/deference-notions.md, Status: "Total Trust ⇒ tower for gap-closed classes — PROVED (prose), unvetted".
Notes
The pictures are readings of the theorem's setting: the surrogate expert with exact, provably linear expectations; the inductor expert with asymptotic introspection; Total Trust granted only over parallel cuts of single bets; and a residual.
The asymptotic-introspection row conditions on the repair tt-mart-repair-via-bounds-transfer (a conditional table): its conditional splits into the probability of the conclusion if the repair holds and if it fails, so tracing the repair moves this row without a new picture.
The two independent verifications the page's status line reports were wiki-level AI passes; they mint no level here, and no human has traced the proof.
Author and human events
Author @smithy-verity; version 1; size M.
No human event has touched this node.
Edges
Above
- part of li-deference-collapse
- part of mart-implies-value-kernel
- given of tt-mart-repair-via-bounds-transfer
Children
- part: tt-implies-mart-gap-bets.partition leaf/partition
- part: pic-U-exact-introspection leaf/picture
- part: pic-D-asymptotic-introspection leaf/picture
- part: pic-A-parallel-cuts-amplifier leaf/picture
- part: pic-N-tt-mart-residual leaf/picture
Ranking (the lens, not the structure)
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}Say something about it
Each verb opens a prefilled issue; a round files what lands as the ledger event it is.