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E02 · deterministic representation laboratory

Keep the edge identity still while the world moves.

Seven possible edges receive one frozen glyph and one fixed node-relative slot. The primary comparison changes only the edge-encoding channel. A separate movement block asks whether the visual template survives endpoint relocation. Computed render diagnostics are evidence; reader performance remains unmeasured.

Comparison arms
4
Frozen edge universe
7
Validated slot capacity
8
Human measurements
not-run

One graph state, four edge channels

Nodes, positions, labels, scale, viewport, and State A membership are frozen. The outline is intentionally a low-information control: it answers only “adjacent to O?” The overlay compares State A with State B and keeps an inspectable quiet slot for edges in neither.

Persistent-line baseline

exact present edge identity through endpoint-spanning geometry · 1 non-endpoint crossings

e01e02e04e05OXENSF

Binary-outline control

direct adjacency to the selected origin, not individual edge identity · binary origin adjacency only

OXENSF

Invariant endpoint tokens

exact present edge identity in fixed node-relative slots · 8 endpoint occurrences

OXENSFe01 at easte01 at origine02 at northe02 at origine04 at fare04 at northe05 at fare05 at south

Aligned two-state set overlay

A only, B only, both, and neither with redundant appearance · all four A/B states visible

OXENSFe01: bothe01: bothe02: a-onlye02: a-onlye03: b-onlye03: b-onlye04: bothe04: bothe05: a-onlye05: a-onlye06: b-onlye06: b-onlye07: neithere07: neither
solid green + dark border · A ∩ Brust fill · A only blue border · B onlydashed empty · neither

Absence needs its own treatment

Both candidates preserve the frozen slot. The quiet view keeps “neither” inspectable without filling the field with active ink; the on-demand view raises only absent candidates during an explicit comparison. Their relative human legibility remains unmeasured.

Quiet reserved slot

Persistent, low-contrast, dashed.

OXENSFe01: bothe01: bothe02: a-onlye02: a-onlye03: b-onlye03: b-onlye04: bothe04: bothe05: a-onlye05: a-onlye06: b-onlye06: b-onlye07: neithere07: neither

On-demand absence focus

Explicit, high-contrast, interaction-gated.

OXENSFe01: bothe01: bothe02: a-onlye02: a-onlye03: b-onlye03: b-onlye04: bothe04: bothe05: a-onlye05: a-onlye06: b-onlye06: b-onlye07: neithere07: neither

Deterministic boundary cases

Each pair preserves the same state and node geometry. The sparse case is a counterexample: its line is already unambiguous, so the experiment does not treat every line as defective.

Crossed-node ambiguity

1 non-endpoint mask crossings · 4 present edges

persistent linesinvariant tokens
e01e02e04e05OXENSFOXENSFe01 at easte01 at origine02 at northe02 at origine04 at fare04 at northe05 at fare05 at south

Shared corridor and plausible near-passes

1 non-endpoint mask crossings · 3 present edges

persistent linesinvariant tokens
e01e02e03OXENSFOXENSFe01 at easte01 at origine02 at northe02 at origine03 at origine03 at south

Sparse counterexample

0 non-endpoint mask crossings · 1 present edges

persistent linesinvariant tokens
e02OXENSFOXENSFe02 at northe02 at origin

Movement is isolated from adjacency

Edge e01 is unchanged while its second endpoint moves near, far, and across the origin. The line changes angle or length; the circle token keeps its shape, scale, orientation, and normalized slot.

Endpoint-spanning line

Geometry is part of the patch.

right-nearright-farleft

Frozen endpoint token

The local patch is identical.

right-nearright-farleft
0.074minimum line descriptor similarity
1.00token patch similarity
1State A non-endpoint mask crossings

The global dictionary has a hard boundary

Eight identities receive distinct marks. The ninth is rejected. The implementation does not shrink marks, reuse tokens, drop edges, or rebuild the dictionary per panel.

stable token capacity exceeded: 9 edges require 8 slots

Findings and non-findings

The crossed-node mechanism exists in the frozen fixture

State A produces 1 line-to-non-endpoint mask intersections; endpoint-local arms add no ink outside node masks.

The token patch remains invariant when an endpoint moves

The frozen token descriptor remains at similarity 1.00; the endpoint-spanning line descriptor falls to 0.074.

The set overlay is complete and exclusive

All 4 declared A/B states appear exactly once per candidate edge using the frozen seven-edge dictionary.

The useful universe is bounded

8 identities validate and 9 fail loudly without reuse.

Not established

No reader study was run, so the experiment does not establish that stable tokens improve accuracy, speed, confidence, or learnability.

Not established

The sparse case has no non-endpoint crossing; E02 therefore does not support a claim that straight lines are inherently ambiguous.

Not established

Pixel and descriptor diagnostics support representation stability only; they are not proxies for human recognition.