# R12 ER-CST v1.1 Witness Equality Bus Preregistration

**Status:** pre-board, pre-seed scientific contract

**Date:** 2026-07-20

**Hard complete-system ceiling:** fewer than 200,000,000 parameters

## 1. Closed predecessor result

ER-CST v1 (`90fd496`, board seed `8277659525319823840`, training seed
`7148525615058810782`, job `694511`) is rejected on its sole development read.
Its confirmation remains sealed at access count zero.

The result is not a generic parser or executor failure. On 2,048 fresh development
rows, treatment achieves 100% exact line, declaration binding, initial occurrence,
late-query occurrence, event-reference, HALT, and query fields. It achieves zero
complete three-card packets, 311/2,048 exact recurrent states, 682/2,048 answers,
and zero joints. Family-deranged training retains 2,018/2,048 exact initial states;
equality-ablated training retains 1,398/2,048. A held-out global class-remapping
diagnostic recovers only 16.80% complete card tuples. Therefore the live failure is
dynamic equality extraction from determining witnesses, with secondary gradient
interference between card and declaration features. It is not a simple inverse-card
or output-code mismatch.

## 2. Hypothesis

The confirmed SD-CST transport/runtime already has sufficient capacity for exact
bounded compilation and recurrence. ER-CST v1 asked one undifferentiated record
vector to discover a six-occurrence equality relation and classify a permutation.
That is the wrong inductive interface.

ER-CST v1.1 predicts that a model-owned relational bottleneck will solve the missing
operation:

1. select the three `before` and three `after` opaque-name occurrences in each rule;
2. fingerprint the selected byte strings with the inherited learned bigram bus;
3. construct a learned 3x3 `after`-to-`before` equality matrix;
4. score all six legal `S_3` assignments by summing their three selected equality
   edges;
5. delete source and use only the resulting categorical cards in the unchanged
   recurrent motor.

This is structured model-owned equality attention. The host enumerates the declared
finite `S_3` output domain but never parses names, supplies equality edges, chooses a
card, reads execution, or repairs a prediction.

## 3. Frozen architecture

Parent: independently confirmed SD-CST Complete Physical Fresh v1.3.

Preserved without semantic change:

- thirteen-record physical parser and semantic role assignment;
- declaration binding and initial-state compiler;
- opcode-to-rule event references;
- explicit pre-apply HALT and post-HALT suffix suppression;
- late-query compiler;
- 36-cell tied categorical card motor;
- 18-cell categorical state reader.

Removed:

- the direct six-way `er_rule_permutation_head` classifier.

Added:

- six learned occurrence queries per semantic rule;
- dedicated witness query/key projections and normalization;
- a fingerprint-space equality projection and bounded learned scale;
- exact finite assignment aggregation over the six `S_3` permutations;
- public witness-pointer and 3x3 equality evidence.

Card and witness-pointer gradients see detached shared records, token memory, and
record assignment. They cannot rewrite the declaration/initial path. Other parser
losses retain their prior trainability contract.

Exact default counts:

| Component | Parameters |
|---|---:|
| Raw Shohin base | 125,081,664 |
| Witness-equality compiler | 67,641,890 |
| Tied card motor | 2,438 |
| State reader | 835 |
| **Complete system** | **192,726,827** |
| **Headroom below 200M** | **7,273,173** |
| Trainable complete system | 12,021,276 |

## 4. Fresh board

No predecessor scored row may be reused. After this source is committed and pushed,
draw one board seed and generate:

- 48,000 train rows from 12,000 four-renderer families;
- 2,048 one-read development rows from 512 disjoint families;
- 2,048 sealed confirmation rows from 512 disjoint families.

The board retains fresh opaque names, random physical record order, disjoint
train/scored renderer-composition cosets, depths one through eight, and explicit
following HALT. Training exposes compiler fields only. It adds occurrence-span
targets for `before[0:3]` and `after[0:3]` in each of three rules. These spans are
parser supervision, not equality, card, trajectory, final-state, or answer oracle.

Required board gates include all predecessor integrity gates plus exact decoding of
all 18 witness spans per row, independent byte-identical rebuild, mode `0600` on
confirmation, and development/confirmation access `0/0`.

## 5. Frozen arms and budget

All arms start from byte-identical initialization and receive 48,000 rows, two
epochs, 3,000 updates, family batch eight/four renderer views, AdamW lr `2e-4`, 100
warmup updates, cosine decay, clip 1.0, and identical motor/reader certificates.

1. **Treatment:** true source witnesses and true cards.
2. **Family-deranged:** true source witnesses; card labels are a family-stable
   non-identity rotation of rule slots.
3. **Equality-ablated:** true card labels; each of the six witness occurrences is
   replaced by a distinct, width-preserving, family-stable opaque name. Occurrence
   spans, byte offsets, renderer identity, grammar, and all non-equality evidence are
   preserved.

No arm receives final state, answer, trajectory, development labels, confirmation
labels, executor feedback, retry feedback, or another arm's weights.

## 6. Development gates

All must pass on the sole development read before confirmation can be considered:

- treatment packet, recurrent state, answer, and joint each at least 90%;
- every packet field, including all three rule cards, at least 95%;
- line, binding, initial, witness, and query pointer exactness each at least 90%;
- minimum renderer joint at least 85%;
- minimum depth joint at least 80%;
- treatment packet and joint each exceed both controls by at least 50 percentage
  points;
- each control packet at most 35% and state at most 40%;
- 36/36 motor and 18/18 reader certificates exact;
- confirmed parent/excluded state unchanged;
- complete system strictly below 200M;
- immutable checkpoint exists before development access;
- independent assessor reproduces every metric from raw categorical evidence;
- custody exactly development/confirmation `1/0`.

No threshold may be changed after the source commit or board/training seed draw.

## 7. Confirmation and claim boundary

Open the fresh confirmation exactly once only if every development and independent-
assessment gate passes. Otherwise reject, keep confirmation sealed, and use only the
development decomposition to preregister a new fresh-board hypothesis.

Passing would establish bounded fresh episodic `S_3` rule inference by learned
witness equality, source-deleted categorical composition, internal HALT, and late-
query readout. It would not establish unrestricted natural-language grounding,
arbitrary algorithms, arithmetic, planning, self-directed search, or broad general
reasoning.