CHRIS HAY

IDEAS · SYSTEMS · OBJECTS / LONDON · 2026

The address is built through depth.

Relation is there early. Entity arrives late. The coordinates change in between.

01 / THE DEPTH OF A QUESTION · RECORDED MEASUREMENTS

Residual enteringL8

The relation is already there.

Held-out reader accuracy across model depth
Residual entering
RELATION01 accuracy0.900.941.001.001.001.001.00
ENTITY01 accuracy0.170.140.190.160.301.001.00
BINDING01 accuracy0.180.180.230.190.451.001.00
L8 → L12
↻ Basis change L8 → 12
L20 → L24
↻ Basis change L20 → 24
L8 → L24
L8–24 / mechanistic evidence
L28 → L30
Answer-token endpoint

Capital or language is readable, and changing the relation is already causally consequential. Entity and binding readers remain weak.

194 prompts · 3 held-out wording folds. Stages are equally spaced for reading; only the displayed depths were measured. Complete reader record
  • L28: Perfect readability may decode the answer token; this endpoint is not clean address geometry.
  • L30: Perfect readability may decode the answer token; this endpoint is not clean address geometry.
ABOUT THIS NOTE +

For capital versus language on Gemma 3 4B IT, two instruments agree: relation information is readable and causally consequential by L8; entity binding becomes decisive in the final-position residual between L24 and L28. Cross-layer reader alignment recovers relation information across changing coordinates. The L28–30 endpoint may carry the answer token, so the mechanistic evidence window is L8–24.

N-ADDRESS-BUILDSUPPORTEDRECORDED 2026-09-06DRAFT · V0.1REFERENCE DRAFTFOLLOW ↓

What does the state
actually control?

02 / REPLACE ONE POSITIONSCHEMATIC RECREATION · MEASURED RATES

Same intervention.
Different depth.

DONOR / FRANCE · CAPITAL“The capital of France is”Final-position state, entering L20
RECIPIENT / JAPAN · CAPITAL“The capital of Japan is”
·····
RECIPIENT CONTEXT REMAINSSWAP HERE
CONTINUE THE REMAINING LAYERS → READ THE NEXT TOKEN
RECIPIENT ANSWER RETAINED96%46 / 48 transplants
DONOR ANSWER IMPOSED0%0 / 48 transplants
○ RECIPIENT● DONOR· OTHER 2/48

France’s state. Still Japan’s answer.
The entity has not taken control here.

Japan/Tokyo and France/Paris illustrate the intervention. Percentages are aggregate top-1 outcomes across 48 different-entity transplants, not probabilities or repeated trials for this example. Position boxes are schematic, not a tokenisation. No model runs in your browser.

At L20, the final-position state carries a usable relation frame but does not override the recipient’s entity. By L28, the wrong-entity donor controls the answer.

The relation survives.
The coordinates change.

03 / THE RELATION READERSAME INFORMATION · DIFFERENT COORDINATES
STATE + READER / MISMATCHEDIllustrative basis change.
Not a projection of measured states.
L8 → L120.39

CHANCE .50 SAME-LAYER 0.94

L20 → L240.46

CHANCE .50 SAME-LAYER 1.00

Across depth, the same reader falls below chance.

Relation only · held-out transfer accuracy, mean of 3 folds. Raw → aligned: L8→12, .39 → .90; L20→24, .46 → 1.00. Entity’s coordinate behaviour remains unresolved.
WHAT THIS MEANS

Relation first.
Entity binding later.

The evidence supports staged construction in the final-position residual, through changing intermediate representations.

04 / INSTRUMENT & RECORD

ADDRESS-BUILD-1

Gemma 3 4B IT · bf16 · 2026-09-06
Causal transplant + cross-layer reader

SELF-SPLICE / MAX LOGIT Δ0.000e+00Bit-identical before any arm was scored.
48 CAUSAL PROMPTS194 READER PROMPTS7 DEPTHS3 READER FOLDS
Methodology & frozen gates +

Causal half. Replace only the residual entering layer L at the final prompt position. Continue the remaining layers normally and read next-token logits; no generation and no weight editing. Four wordings, 48 retained prompts, 1,169 transplants. The different-relation arm has 23 eligible pairs per depth; the other arms have 48.

The primary gap compares full-vocabulary KL under wrong-binding and same-binding transplants. Recipient retention alone is insufficient: donor-answer rate distinguishes incompatibility from transporting a value. Self-splicing must reproduce the baseline bit-identically.

Reader Part 2b. 194 retained prompts, 20 bindings, 14 entities, capital and language, 12 wordings. Three folds hold out 4 wordings and train on 8. PCA dimension 128; ridge 1.0. Component-specific same-layer gates were frozen before measurement: relation ≥ .85, entity ≥ .40, binding ≥ .30. All pass, but entity and binding pass only in the confounded endpoint band.

The original hypothesis needed reframing. Wrong-entity swaps were as harmless as same-binding swaps through L20, so the early convergence is not binding-specific. The original causal gate condition 2 failed. Coordinate-change support is for relation only.

Bank boundary. Currency and continent could not be made reachable with the same wording bank. Relation-specific wordings would entangle relation with phrasing. This note makes no claim beyond capital versus language.

Complete measurements +
Held-out accuracy · Part 2b · mean across 3 folds
Depthrelationentitybinding
L80.900.170.18
L120.940.140.18
L161.000.190.23
L201.000.160.19
L241.000.300.45
L28Answer-token endpoint1.001.001.00
L30Answer-token endpoint1.001.001.00

Full-precision reader results

* L28–30 may be answer decoding. Chance floors: relation .50; entity .071; binding .05. Weak early entity/binding readability is not evidence of complete absence.

All transplant arms · KL over the full vocabulary
Depth / donorntransplantsRecipient retainedDonor answerMedian KL
L8 · Same binding / new wording4856%Not applicableSame-binding donor1.518
L8 · Different entity / same relation4854%0%1.512
L8 · Same entity / different relation2322%30%6.109
L8 · Unrelated donor4817%2%6.680
L12 · Same binding / new wording4858%Not applicableSame-binding donor1.096
L12 · Different entity / same relation4860%0%1.121
L12 · Same entity / different relation2322%39%6.484
L12 · Unrelated donor4815%4%7.162
L16 · Same binding / new wording4896%Not applicableSame-binding donor0.727
L16 · Different entity / same relation4896%0%0.755
L16 · Same entity / different relation2322%61%7.327
L16 · Unrelated donor4815%4%8.066
L20 · Same binding / new wording48100%Not applicableSame-binding donor0.647
L20 · Different entity / same relation4896%0%0.692
L20 · Same entity / different relation230%83%8.402
L20 · Unrelated donor480%4%8.403
L24 · Same binding / new wording4896%Not applicableSame-binding donor0.643
L24 · Different entity / same relation4869%13%1.171
L24 · Same entity / different relation230%100%10.088
L24 · Unrelated donor480%6%10.067
L28 · Same binding / new wording4898%Not applicableSame-binding donor0.675
L28 · Different entity / same relation480%100%9.412
L28 · Same entity / different relation230%96%10.467
L28 · Unrelated donor480%100%16.715
L30 · Same binding / new wording4896%Not applicableSame-binding donor0.693
L30 · Different entity / same relation480%100%10.008
L30 · Same entity / different relation230%96%10.693
L30 · Unrelated donor480%100%17.056

Full-precision causal results

relation · cross-layer reader transfer
TransitionRawNorm onlyProcrustesSame layer
L8 → L120.390.390.900.94
L12 → L160.900.900.931.00
L16 → L200.880.880.991.00
L20 → L240.460.461.001.00
L24 → L280.970.971.001.00
L28 → L301.001.001.001.00

Full-precision reader results

entity · cross-layer reader transfer
TransitionRawNorm onlyProcrustesSame layer
L8 → L120.080.080.150.14
L12 → L160.160.160.130.19
L16 → L200.150.150.180.16
L20 → L240.080.080.210.30
L24 → L280.480.480.481.00
L28 → L301.001.001.001.00

Full-precision reader results

binding · cross-layer reader transfer
TransitionRawNorm onlyProcrustesSame layer
L8 → L120.060.060.190.18
L12 → L160.160.160.200.23
L16 → L200.170.170.220.19
L20 → L240.080.080.290.45
L24 → L280.580.580.641.00
L28 → L301.001.001.001.00

Full-precision reader results

All displayed tables round values for reading. The JSON files retain full recorded precision, gate values and the causal KL gap at each depth.

The failed reader stays in the record +

The first Part 2 had about 1.5 training examples per binding class. Entity accuracy stayed around .14 in all 21 cells. It is an instrument failure, not evidence about the model. Part 2b repairs coverage and uses component-specific gates; the relation threshold was raised to .85 before readability was inspected.

Download preserved Part 2 result ↓
Registry, hashes & source provenance +

EXP-20260906-181253-00733
CONSOLIDATED WRITE-UP / V7
SOURCE / f97a470644df1c38498030896f8f6cfffe7689b1

The registry snapshot comes from chuk-experiments. Result JSON was extracted from the registered commit in the local LARQL repository. The public GitHub API did not resolve that commit at verification time; the frozen downloads below remain available with this note.

Causal rows SHA-256 (reported by harness)
9e039cc98dda26749773df55b468ced2bc522d592b8eb72a73dae9e29924a7ba
Reader Part 2b result SHA-256 (reported by harness)
516bd1139a73622080890958b5488261cad3e9e889642364ed65b2b450fdcebf

These are the harness’s payload hashes, not hashes of the formatted download files. The NPZ state captures were excluded by the source repository’s *.npz rule. Recorded aggregates support this recreation; they are not a complete state-capture archive.

Registered source location ↗

RETURN TO THE QUESTION / N-MAP

What is the map
actually a map of?

SOURCES & PROVENANCE

AUTHOR / CHRIS HAY · VERSION / 0.1

REFERENCE THIS DRAFT

An unpublished working record. These references identify the draft and omit a publication date. They become version-specific publication citations when the record is released.

Chris Hay. The address is built through depth. [Unpublished draft, version 0.1. First publicly recorded 2026-09-06]. https://chrishayuk.com/notebook/the-address-is-built-through-depth
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262 WORDS · DRAFT

Relation is there early. Entity arrives late. The coordinates change in between. For capital versus language on Gemma 3 4B IT, two instruments agree: relation information is readable and causally consequential by L8; entity binding becomes decisive in the final-position residual between L24 and L28. Cross-layer reader alignment recovers relation information across changing coordinates. The L28–30 endpoint may carry the answer token, so the mechanistic evidence window is L8–24. ADDRESS-BUILD-1 tests native facts with single-position causal transplants and a separate cross-layer reader. Relation readability is 0.90 at L8 and 1.00 at L16. Same-binding and wrong-entity transplants both retain the recipient answer in 46/48 cases at L16. What converges early is the relation frame, not the entity binding. At L20 a wrong-entity donor preserves 46/48 recipient answers and supplies its own answer in 0/48 cases. At L24 those counts are 33/48 and 6/48. At L28 they are 0/48 and 48/48. These are cohort rates, not probabilities for one Japan/France prompt. For relation, L8→L12 raw transfer is 0.39 versus 0.90 after Procrustes alignment; L20→L24 is 0.46 versus 1.00. Norm-only equals identity in every cell. Entity’s coordinate behaviour remains unresolved. One model, capital versus language, final-position residual only. L28–30 may decode answer tokens. A basis change enabling entity commitment is an open inference, not a finding. ADDRESS-BUILD-1, EXP-20260906-181253-00733. Gemma 3 4B IT bf16, 2026-09-06. 48 native-fact prompts in the causal half; 194 prompts, 20 bindings, 12 wordings, 3 folds in reader Part 2b. Splice floor 0.000e+00. Source commit f97a470. Original Part 2 is preserved as a failed instrument. DRAFT · V0.1 · RECORDED 2026-09-06 https://chrishayuk.com/notebook/the-address-is-built-through-depth

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Relation is there early. Entity arrives late. The coordinates change in between. Working note · v0.1. https://chrishayuk.com/notebook/the-address-is-built-through-depth

A thread

  1. Relation is there early. Entity arrives late. The coordinates change in between. Working note · v0.1.
  2. Cross-layer reader alignment recovers relation information across changing coordinates.
  3. The L28–30 endpoint may carry the answer token, so the mechanistic evidence window is L8–24.
  4. ADDRESS-BUILD-1 tests native facts with single-position causal transplants and a separate cross-layer reader.
  5. DRAFT · V0.1 · RECORDED 2026-09-06 Read the complete record, evidence and scope: https://chrishayuk.com/notebook/the-address-is-built-through-depth
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