Methods / GOBLIN-CYCLE-2026-10-26-001 / 2026-10-26
The Goblins Accused an Innocent Messenger
Supplemental methods for the synthetic permutation-language network. Evidence status: offline finite result, not externally validated.
Operate the experiment ↗Question
How much can a relative-only checker infer from the consistency of several pairwise translation mappings? In particular, can it reconstruct one damaged mapping while remaining vulnerable to multiple changes that mimic a different single fault?
Model and authority separation
For each seed, the generator creates n = 3 or 4 hidden bijective codebooks mapping common latent synthetic meaning IDs to local glyph IDs. Pairwise claimed maps are computed by composing their inverse and forward codebooks. The generator has oracle knowledge of the original codebooks; the auditor only receives the pairwise mapping tables and topology. The browser exposes the oracle to readers as an inspection aid: no security boundary prevents a person from viewing the bundled synthetic evidence.
The auditor computes triangular consistency: a direct mapping from A to C must equal the composition of A→B and B→C for every glyph. Bad triangles identify contradictions. If every failed triangle contains exactly one common edge, it nominates that edge; two-hop routes avoiding the nominated link must agree on a replacement, and all triangles must close after replacing it. The verdict remains explicitly conditional on one bad edge.
Perturbations and controls
| Condition | What was planted |
|---|---|
| Single | One randomly selected pairwise link had two distinct output symbols swapped. |
| Double | Two different links selected in sequence; each had its own swapped output symbols. |
| Triangle | Only three nodes, full triangle, one swapped link. |
| Star | Four nodes with only hub links; one swapped link and no cycles. |
| Coordinated | A single consistent glyph permutation applied at node B to all three incident links. This differs from the original oracle while preserving every cycle. |
| Clean | No changes to pairwise codebooks or mappings. |
The pseudorandom stream is xorshift32 with nonzero seed 1–256, mod-index Fisher–Yates permutation generation, and eight-, sixteen-, or thirty-two-symbol vocabularies. The exact sweep iterates all six conditions and three vocab sizes for 256 seeds each, a total of 4,608 scripted cases.
Observed result
Single: 768/768 exactly recovered the planted link and its original mapping. Double: 757/768 returned no unique single-fault repair, but 11/768 gave a uniquely nominated *innocent* edge, whose replacement made the cycles fully consistent while increasing the count of actually wrong edges from two to three. Three nodes: 768/768 ambiguous. Star: 768/768 unobservable. Coordinated: 768/768 cycle-consistent with three oracle-wrong links. Clean: 768/768 cycle-consistent with zero wrong links.
Implementation checks and actual evidence
The Python implementation ran six focused stdlib unit-test methods successfully, including 768 single-fault reconstruction checks, star and triangle non-overclaim checks, coordinated gauge changes, and every two-fault false accusation. A separately implemented JavaScript version embedded in the public viewer was evaluated for every combination. The regenerated per-case JSON matched the Python fixture output byte-for-byte as Git blob 7081b5154663dbb7f4451d51ae85ea274c45bd07.
Reproduce locally with python research/run.py and python -m unittest discover -s tests -v. Source files and exact raw records: public source directory. The receipt records SHA-256 of the source files and the 4,608-row output. These are same-author checks, not independent replication.
What is still unknown
The result does not show that general learned languages admit the same reconstruction, that multiple nonbijective or noisy links behave similarly, that agents intended deceit, or that the observed 11/768 fraction generalizes to other networks or fault models. The generator's shared latent symbols and full pairwise dictionaries are substantial supplied structure. A diagnosis based on relative compatibility cannot certify which community glossary is semantically right without outside anchoring. We explicitly do not interpret a consistent reconstruction as a trustworthy authority on the world.
Established mathematical lineage: Lerman and Shi, Robust Group Synchronization via Cycle-Edge Message Passing (2022). This lab illustrates a specific finite failure mode; it does not claim novelty over cycle-consistency research.