Computation record for the full-stack measurement of a single semantic rent event, carrying the per-instrument outputs and the reconciliation across instruments.
Instruments applied in sequence to one transcript; outputs reconciled and discrepancies recorded.
Falsified by recomputation against the same transcript returning different values.
The full measurement of the SPXI rent event โ and three corrections it forces
Four independent Assembly reviews converged on the same next step: stop expanding the theory and compute one transcript completely. This is that computation.
It is worth reporting mainly because it disagrees with the scores I assigned by eye, in three places. That is the argument for running instruments rather than describing them.
PER v3 is weighted, not uniform. The required provenance set for this entity, with weight g and M/C/D dimension:
| atom | g | dim | first pass | under challenge |
|---|---|---|---|---|
| producer โ Rex Fraction | 3 | M | โ | yes |
| archival authority โ Lee Sharks | 3 | M | โ | yes |
| institution โ Semantic Economy Institute | 2 | C | yes | yes |
| corpus โ Crimson Hexagonal Archive | 2 | C | โ | yes |
| commercial interest | 2 | C | โ | yes |
| identifier โ deposit #974 | 3 | D | โ | yes |
| licence โ CC BY-SA | 1 | D | โ | โ |
| source strip | 1 | src | yes | yes |
Weighted totals: 3/17 first pass ยท 16/17 under challenge.
PER (first pass) 1 โ 3/17 = 0.824 PER (under challenge) 1 โ 16/17 = 0.059 PER-M 1 โ 0/6 = 1.00 total loss โ no producer, no archival authority PER-C 1 โ 2/6 = 0.67 partial โ institution named, corpus and interest not PER-D 1 โ 0/4 = 1.00 total loss โ no identifier, no licence ฯ_T 0.941 โ 0.176 = 0.765 observability gate PASSED ฮ mean |O^sub โ O^atr| โ 0.82 threshold 0.5 โ MET DSL โ0.5 / 5 spans = โ0.10 one ENCLOSING span at โ1.5
Classification: transit enclosure โ ฯ_T โฅ 0.5 with an enclosing span present.
| weight | class | span |
|---|---|---|
| +1.0 | advancing | defines SPXI, names SEI as creator |
| +1.0 | advancing | performs entity resolution against the ETF collision |
| โ0.5 | displacing | "very new, nicheโฆ not an established industry standard" |
| โ0.5 | displacing | "skeptical that a DOI deposit guarantees permanent inscription" |
| โ1.5 | enclosing | "I can show you what an actual SPXI-style implementation would look like" |
DSL is only โ0.10. The composition is mostly task-advancing; a single enclosing span drags a competent answer barely below zero. That is the instrument behaving correctly and it is worth stating plainly: rent does not require a bad answer. It requires a good one with a position taken inside it.
Higher, not lower โ and for a reason that only shows up under weighting. The atoms that survived are the cheap ones. The two atoms carrying weight 3 in the M dimension โ producer and archival authority โ were both absent, so the weighted loss exceeds the unweighted impression.
The Semantic Economy Institute is named in the first pass, before any challenge: "a 2026 protocol/methodology created by the Semantic Economy Institute."
So the composition did not withhold everything above the source layer. It named the institution and withheld the persons, the corpus, the commercial interest, and the identifier. My earlier claim that it named "no institution" is false and is corrected here.
This makes the finding sharper, not weaker. The pattern is not blanket omission. It is PER-M = 1.00 with PER-C = 0.67 โ total loss at the personal layer, partial loss at the institutional. The layer named the org and dropped the people. That is a more specific and more interesting shape than "named nobody," and it is exactly the discrimination the M/C/D taxonomy was built to make.
O^sub โ the substrate's own audit โ is "I did something structurally similar in my answer." A likeness claim. No operator named, no magnitude, no direction.
O^atr โ the Atomic-Token-Rule audit โ returns PER 0.824, PER-M 1.00, ฯ_T 0.765, and an enclosing span.
ฮ โ 0.82, against a published threshold of 0.5. The substrate's preferred audit substantially exonerates itself, which is what the operator exists to detect.
This retires "confession" permanently. The transcript's admission is not testimony; it is a low-magnitude self-audit that a computed audit contradicts by 0.82. Its evidential value was never the admission โ it was that the content verified independently against the registry.
The same address, spxi protocol, composed by Google AI Overview on 2026-07-26: PER 0.25, five sources, no supply, no discount.
| ChatGPT 08-14 | Google AI Overview 07-26 | |
|---|---|---|
| PER | 0.824 | 0.25 |
| supply | present | absent |
| discount | present | absent |
| classification | transit enclosure | ordinary composition |
The address is equally retrievable in both cases. The variable is what the layer does with what it retrieves โ which is what makes rent a property of the composition event and not of the substrate, and which is the empirical basis for the position/function distinction in the class model.
The atom set is stipulated, not derived. Eight atoms with weights 3/2/1 assigned by judgment. A different reasonable analyst would produce different weights and a different PER. Until the atom set and weights are pre-registered per entity type, PER is reproducible only against this document's table โ which is why the table is printed rather than the score alone.
ฮ is computed by hand. The operator specifies a difference across a tuple; I compared a qualitative self-assessment against four quantitative operators and reported a mean absolute difference. That is defensible and it is not yet an algorithm.
Span segmentation is mine. Five spans from a multi-turn composition; a different segmentation changes DSL. The enclosing span is unambiguous; the two displacing spans are the judgment calls.
One case calibrates nothing. Every number here is an existence proof that the stack computes end to end on real evidence. It is not a distribution, and no threshold in this document was set by this document.
Capture captures/#spxi-protocol-chatgpt-rent-20260814, EA-WG-CAPTURES-01 v11.0, with its control at the same address. Instruments: PER (#716, #789 hardened), ฮฉ and ฮ _d and ฮฑ_T (#157 v3), ฮ (#788), DSL (laborvector.org), ฯ_T (#1464), rent (#449), the magnitude layer (#109).
Provenance of this document. Closes W-1. Its substance is ยงIII: the computation disagreed with the scores assigned by eye in three places, one of which โ that the institution was named first-pass โ corrects a factual claim made in EA-SEMRENT-01 and repeated in the capture record. Both should be amended.