# Related-work search appendix — protocol and record (2026-09-02 and 2026-09-05)

*This appendix is the contemporaneous search record behind every
"closest found" and "no prior found" claim in "Coherence Is Not Truth"
(Note v1.2). It is a curated public derivation of the internal record:
condensed, with connective prose written for public reading, and with
repository, host and internal record identifiers neutralised. Every
query string, verdict, count and citation copied from the record is
unchanged.*

The house rule applies throughout: a claim of absence is a claim about
these queries on these dates, never about the literature in general. The
note's own positioning sentence is bounded the same way — "bounded by the
companion survey's coverage and the 2026-09-05 pass" — and names its own
collapse conditions.

## Protocol

- **Dates.** 2026-09-02: the prior-art hunt of review-panel round 1.
  2026-09-05: the coordinator's sweep; the external reviewer's
  adversarial pass and the coordinator's ruling on it; the bibliographic
  verification of every new or changed reference.
- **Verification rule.** A citation enters the note only if its record
  was fetched and its metadata (title, authors, year, venue, identifier)
  read from the page — arXiv abstract pages, publisher/DOI pages, DBLP,
  IFAAMAS/AAAI/IJCAI proceedings pages, or the authors' own publication
  lists. No citation from memory survives to the tag: the authors and
  initials supplied from memory during assembly were each checked, and
  the corrections are recorded in part (iv).
- **Query accounting.** The 2026-09-05 sweep reproduces **33 web query
  strings verbatim**, plus 2 arXiv API queries; 4 Semantic Scholar
  queries were attempted and all returned HTTP 429, so that source
  contributed nothing. The 2026-09-02 hunt ran six targeted searches;
  their strings were not contemporaneously enumerated in the panel
  record, so no list is reproduced for it and no count beyond the
  record's own six is claimed. The external reviewer's pass did not
  export a query log; only the candidates it produced, each verified,
  are relied on.

## The absence claims, and what would collapse each

The note makes its absence claim once, narrowly (§2, Positioning):
*to our knowledge this is the first construction in which divergent
sparse-block codebooks are calibrated across a population by multi-agent
loop residuals that remain native symbolic vectors and are reused as the
repair of the map itself.* The sweep and the hunt attacked that sentence
through six component claims. The verdict vocabulary is the brief's:
COLLAPSE (a verified publication erases or narrows the claim), NEAR-MISS
(a verified neighbour that falls short, cited), CLEAR (nothing found).

1. **No VSA/HDC loop composition.** Collapses on any vector-symbolic or
   hyperdimensional work that composes binding-based translations around
   a loop of three or more codebooks, domains or agents and measures the
   closure defect. Two-domain cycle consistency (VSAIT, Theiss et al.,
   ECCV 2022) exists and does not count.
2. **No cycle residual reused as the repair.** Collapses on any
   multi-agent translation or alignment system in which the
   cycle-inconsistency residual is itself installed as the repair of the
   map — repair by construction from the defect, not repair by removal of
   mappings.
3. **No resonator missing-factor repair.** Collapses on any resonator
   network or factorizer used to detect a missing factor or propose a
   repair codeword rather than to factor over fully known codebooks.
4. **No deliberately farmed, priced divergence.** Collapses on any
   emergent-communication work that farms divergence as a design goal,
   instruments it, and prices it against forced uniformity.
5. **No edge-level attribution with a certificate and refusal.** The
   note's differentiator from the synchronization line: edge-level
   attribution with a local λ(u,v) ≥ 3 boundary, a certificate kept
   beside the answer, and constructive repair of the map itself — "the
   synchronization methods emit estimates without abstention, and the
   residual-as-diagnostic works abstain without attributing or
   repairing." Collapses on a synchronization or residual-diagnostic
   method that attributes to an edge, certifies, and abstains outside a
   stated boundary.
6. **No preregistered layered factorial.** "No preregistered agent-system
   factorial crossing translation, grounding and authority was found"
   (§2, §11.1). Collapses on any such preregistered factorial.

The discussion's sentence (§13.5) — *what does not exist is a translation
map with a loop residual and refusal across three or more heterogeneous
agents* — is the ≥3-heterogeneous-agent form of claims 1 and 2, searched
by the same queries (12, 14, 17, 20 below), and its near-misses are
listed under it.

## (i) The 2026-09-02 prior-art hunt (review-panel round 1)

**Brief.** One panelist was briefed as prior-art hunter with live web
search and a single win condition: find a published work (paper,
preprint or system) that anticipates the claim or triggers one of its
named collapse conditions, verifiable through search results in the
session — no citation from memory. The claim under attack was stated as
the note then stated it ("… directly reused for constructive repair";
reworded on 2026-09-05, see (iii)). The four named collapse conditions
were claims 1–4 above. The brief listed the near-neighbours already cited
as search anchors, not findings: representation holonomy (Sevetlidis &
Pavlidis, ICLR 2026), the sheaf atlas (Javidnia, arXiv:2603.00824),
sheaf-theoretic transport and obstruction (Olivieri & Hernández,
arXiv:2605.14033), CEMP (Lerman & Shi, FoCM 2022), group synchronization
(Singer 2011), ontology alignment composition and repair, semantic channel
equalization, and vec2vec.

**Result: no collapse condition triggered** across six targeted searches
— nothing composes VSA bindings around ≥3-agent loops, no resonator
missing-factor repair, no deliberately farmed divergence, no system
reusing the cycle residual as the repair. **Near-miss:** Levy, Paradise,
Carmeli, Meir, Goldwasser & Belinkov, "Unsupervised Translation of
Emergent Communication," AAAI 2025 (arXiv:2502.07552) — unsupervised
machine translation deciphering emergent protocols without parallel data;
two-space, no loops, no VSA. The searches re-confirmed that the survey's
near-neighbour map was current (Factorizers for Distributed Sparse Block
Codes, arXiv:2303.13957; Javidnia, arXiv:2603.00824). The panel record's
ruling: "the narrow positioning claim stands as of 2026-09-02."

**Disposition.** Levy et al. entered §2's emergent-communication
paragraph (round-1 edit 4); its initials, supplied from memory at
assembly, were corrected at verification (part (iv)). The panel record
for this round is Receipt A.

## (ii) The 2026-09-05 sweep

**Verdicts.** Six claims, each returned **NEAR-MISS or CLEAR; none
returned COLLAPSE.** No near-miss was listed against claims 1 (VSA loop
composition) or 3 (resonator missing-factor repair). The near-misses, as
the sweep listed them, with the characterisation each carries in the note
after verification:

*Against claim 2 (residual reused as the repair) and claim 5 (attribution
with certificate and refusal):*

- **Mishra, arXiv:2608.11252** — a cohomological theory of context
  preservation in agentic reasoning: a harmonic residual over loops of
  contexts gates abstention; single agent, no map repair. The nearest
  miss to the positioning claim: it reuses a residual to gate abstention,
  not to repair a map.
- **Hernández & Sánchez-Soto, arXiv:2606.00714** — the Cartan-Topos
  Protocol: sheaf-Laplacian consensus with logical holonomy as a
  diagnostic, not a map repair.
- **Duncan & Kileel, arXiv:2505.21932** (*Res. Math. Sci.* 13(2):48,
  2026) — higher-order group synchronization; states the single-corruption
  form starkly (one corrupted element, and the cycle's inconsistency gives
  that element's corruption); estimates, no abstention.
- **Li, Shi & Lerman, arXiv:2511.02329** (NeurIPS 2025) — Cycle-Sync;
  cycle consistency alone suffices for exact recovery; no abstention, no
  map repair.

*Against claim 4 (farmed, priced divergence):*

- **Beltoft et al., arXiv:2605.31170** — emergent languages in
  populations of language-model agents, from token efficiency to
  oversight evasion; divergence observed, not farmed or priced.
- **Kong, Lai, Piao & Evans, arXiv:2605.17193** — robust semantic
  collapse across multi-LLM systems despite lexical variation; the
  opposite dynamic, so divergence is not free to farm in LLM populations.

*Against the §13.5 form (a loop residual with refusal across ≥3
heterogeneous agents):*

- **Schoenegger, Carlson, Schneider & Daly, arXiv:2602.16424** — the
  sweep's strongest hit: verifiable semantics for agent-to-agent
  communication — two agents, certified terms, recertification on drift,
  with transitivity left as future work. A pairwise certified-vocabulary
  object; not a loop, not three agents.
- **Yuan et al., arXiv:2604.02369** — a semantic view of eighteen agent
  communication protocols: only limited protocol-level support for
  semantic verification, with semantics pushed into prompts and wrappers.

*Against claim 6 (preregistered layered factorial):*

- **Zhang, Wang & Lei, arXiv:2606.11686** — layer-isolated evaluation:
  one-layer-at-a-time regression injection; no crossing, no authority
  layer, not preregistered.
- **MAS-FIRE (Jia et al.), arXiv:2602.19843** — fault injection and
  reliability evaluation for LLM-based multi-agent systems; not
  factorial, not preregistered.
- **Xu et al., arXiv:2608.01710 (CapLease)** — durable authorization
  state for replay-resistant agent actions; scenario-evaluated rather
  than factorial.
- **Mellafe Zuvic, arXiv:2606.28679 (ScopeGate)** — capability gates are
  not authorization; scenario-evaluated rather than factorial.

**Disposition.** All twelve entered the note as cited neighbours (§2 and
§13.5) under the characterisations above, each verified in part (iv).

**Query log (web, verbatim, 2026-09-05 — all 33):**

1. `hyperdimensional computing translation map cycle consistency holonomy multi-agent codebook 2026`
2. `arXiv 2026 "cycle consistency" emergent communication multi-agent translation residual repair vocabulary divergence`
3. `group synchronization corrupted edge identification abstention certificate edge connectivity cycle-edge message passing 2025 2026`
4. `preregistered multi-agent LLM experiment factorial fault injection translation grounding authorization layers 2026`
5. `resonator network "missing factor" OR "novel factor" OR "unknown codeword" detection hyperdimensional 2025 2026`
6. `sheaf cohomology multi-agent LLM consensus obstruction repair agents 2026 arXiv`
7. `"holonomy" agents language semantic drift translation loop 2026`
8. `semantic drift heterogeneous LLM agents shared vocabulary misunderstanding detection refusal correspondence layer 2026`
9. `"emergent communication" population divergence dialects "bandwidth" cost translation vs standardization trade-off 2025 2026`
10. `"sparse block codes" binding translation between codebooks agents 2026 Hersche Kleyko Frady`
11. `map synchronization cycle consistency "abstain" OR "abstention" OR "certificate" outlier edge identifiability 2025 2026 arXiv`
12. `vec2vec OR "semantic channel equalization" three or more latent spaces cycle consistency multi-agent 2026`
13. `LLM agent "lease" OR "capability token" authority revocation evaluation tool-call permission layer independent failure grounding translation 2026`
14. `arXiv 2026 "translation" between LLM agents ontology "refuse" OR "abstain" when uncertain inspectable mapping evaluated "comprehension"`
15. `"cycle" inconsistency "as the repair" OR "used for repair" translation maps agents hypervector OR "vector symbolic" 2025 2026`
16. `"gauge" OR "connection" OR "parallel transport" multi-agent representations semantic alignment population LLM 2026 arXiv cs.MA`
17. `"emergent communication" "translation" "triangle" OR "three agents" OR "transitivity" consistency composed protocols 2025 2026`
18. `"group synchronization" OR "cycle consistency" identifiability "edge connectivity" corrupted edges 2025 2026 arXiv math.OC theorem`
19. `"preregistered" OR "pre-registered" OSF multi-agent LLM agents experiment fault attribution 2026 arXiv`
20. `Belinkov OR Levy emergent communication translation 2026 follow-up population multiple protocols composed translation`
21. `"representation holonomy" OR "gauge theory of superposition" citing 2026 multi-agent codebook population`
22. `hyperdimensional computing multi-agent communication codebook alignment semantic communication agents 2025 2026 arXiv`
23. `LLM agents dialects "translation cost" OR "communication cost" divergence vs shared protocol economy simulation 2026 arXiv cs.MA`
24. `"cycle consistency" OR "loop consistency" multi-agent LLM translation ontology alignment three agents detect inconsistency 2026 arXiv`
25. `sheaf "LLM agents" OR "language agents" translation glue obstruction repair residual 2026 arXiv SheafAlign follow-up`
26. `agent fault "translation" "grounding" "authorization" separated layers "attribution" "repair" evaluation 2026 arXiv "no impersonation" OR "layer independence"`
27. `"Emergent Languages in Populations of Language Model Agents" 2026 arXiv abstract divergence dialects`
28. `"anchor" OR "anchors" translation map repair "refuse" OR "do not overwrite" OR "protected" direct evidence cycle consistency alignment update gating 2025 2026`
29. `hyperdimensional OR "vector symbolic" cross-domain three domains OR "multi-domain" translation unbinding consistency loop 2025 2026`
30. `"deliberately" OR "induced" OR "engineered" vocabulary divergence population LLM agents instrumented translation "uniform" protocol comparison cost 2026`
31. `cycle consistency residual used to correct pairwise maps "edge correction" OR "map correction" synchronization constructive repair 2025 2026`
32. `multi-agent LLM fault injection factorial "main effects" OR "interaction effects" communication fault grounding fault permission fault independence 2026`
33. `Google Scholar "abelian" holonomy codebook OR "block code" translation agents drift 2026`

**arXiv API (2 queries):** `all:holonomy AND (agents OR codebook OR
vocabulary OR translation)`, 40 newest; `abs:"cycle consistency" AND
abs:agents AND (translation OR vocabulary OR communication)`.

**Semantic Scholar:** four queries attempted, all HTTP 429; unreachable
for the sweep.

## (iii) The external reviewer's adversarial pass (2026-09-05) and its disposition

An external reviewer read the assembled draft and proposed four
literature families as threats to the positioning:

1. **Group synchronization and cycle-edge message passing** — CEMP
   (Lerman & Shi 2022), Singer (2011), higher-order group synchronization
   (Duncan & Kileel 2026), Cycle-Sync (Li, Shi & Lerman 2025).
2. **Interaction-based ontology alignment repair** — Laera et al. 2006;
   van Diggelen et al. (ANEMONE, 2007); Togia & McNeill 2013; Anslow &
   Rovatsos 2015; Euzenat (IJCAI 2017) and the dynamic-epistemic-logic
   formalisation of the Alignment Repair Game (van den Berg, Atencia &
   Euzenat, AAMAS 2020); Jiménez-Ruiz, Payne, Solimando & Tamma (KR
   2016); Steels's *Talking Heads Experiment*.
3. **Distributed truth maintenance and multi-agent belief revision** —
   Doyle 1979; Bridgeland & Huhns (AAAI 1990); Dragoni 1992.
4. **Evidence-gated belief revision (2026)** — Preregistered Belief
   Revision Contracts (Alqithami, arXiv:2604.15558); *Replicating
   Belief, Not Bits* (He & Yu, arXiv:2607.09748).

**Disposition (the coordinator's prior-art ruling, same day).** None of
the four collapsed the narrow claim; all four narrowed how it may be
stated. The ruling, as applied to the note:

- **The contribution sentence.** The contribution is not cycle
  consistency, holonomy, ontology alignment, or the general idea of
  refusing an unsupported repair — those have substantial prior
  literatures — but an executable instance in which independently
  evolved codebooks are calibrated without a common codebook,
  higher-order inconsistency is converted into a local, constructive
  repair of the map itself, and the instrument's success and refusal
  boundaries are measured under controlled semantic faults. Inserted in
  §2 and §14, replacing the earlier framing.
- **The propositions.** All four are labelled "standard; stated for this
  substrate", with a plain aside beside each: Proposition 2 is
  bounded-distance decoding uniqueness for the graph's cut code,
  Proposition 3 its local form, Proposition 1 the definition of
  decodability. CEMP is raised to §2's first paragraph and named beside
  Propositions 2 and 3, with the single-corruption statement credited to
  higher-order group synchronization and Cycle-Sync cited for exact
  recovery from cycle consistency alone.
- **The four families** entered §2 as labelled paragraphs, each closing
  with one sentence stating what differs here: the maps are over sparse
  block codes, the witness is a third-party loop invisible on the failing
  pair, and the repair is the inverse residual installed on the listener
  edge (family 2); the ancestors keep provenance for and revise
  *beliefs*, we calibrate *representations* (family 3); they gate belief
  updates, we gate the repair of a translation edge on direct anchor
  evidence and a loop certificate (family 4).
- **The positioning.** "Directly reused for constructive repair" became
  "reused as the repair of the map itself"; Mishra is cited as the
  nearest miss (a residual reused to gate abstention, not to repair a
  map); the collapse conditions were extended with "any system reusing
  the cycle residual as the repair of the map itself".
- **The discussion.** §13.5's "does not exist until someone builds it"
  was softened to cite Schoenegger et al. and Yuan et al., and the
  absence restated as "a translation map with a loop residual and
  refusal across three or more heterogeneous agents".
- **A contradiction caught on the external read** of the assembled
  draft, fixed before the tag: §2 had claimed the synchronization
  methods abstain; the differentiator now reads that synchronization
  methods emit estimates without abstention and the residual-as-diagnostic
  works abstain without attributing or repairing.

The reviewer also proposed eight bibliographic corrections. Six were
confirmed at verification (Alqithami; Jia et al.; Schoenegger, Carlson,
Schneider & Daly; Zhang, Wang & Lei; Hernández & Sánchez-Soto; Mishra).
Two were right on title and author but wrong in premise: ScopeGate and
CapLease **are** the named systems of arXiv:2606.28679 and
arXiv:2608.01710 respectively, so the note's in-text names stand and the
entries gained only their titles and authors.

## (iv) Bibliographic verification (2026-09-05)

Scope: every reference entry added or changed at assembly — 25 entries
marked for verification, the Levy et al. entry (round-1 edit 4), and the
existing Lerman & Shi entry — 27 blocks. Each block records the corrected
reference line, the claim-to-source fit of the note's characterising
clause, and a status. Sources: arXiv abstract pages and HTML full texts,
publisher/DOI records, DBLP, IFAAMAS/AAAI/IJCAI proceedings pages, and
the authors' own publication lists. The note was not edited by the
verifier; the corrections were spliced in afterwards, verbatim.

**Counts:** VERIFIED 24 · VERIFIED-PARTIAL 2 · NOT FOUND 0. The two
partials: Dragoni 1992 (title, editors, venue and year confirmed; the
page range 103–112 from citing bibliographies only) and Laera et al.
2006 (four authors and the CMNA 2006 venue from the authors' own lists;
pages unconfirmed from a primary proceedings page). The KR 2016 item is
counted VERIFIED, with the observation that no record exists in the
repository it had been cited to; the copy lives on the authors'
institutional site.

**Claim-to-source corrections (two substantive, applied):**

1. **Cycle-Sync (Li, Shi & Lerman, arXiv:2511.02329) — overstated.** The
   note had credited it, with higher-order group synchronization, with
   the single-corruption localisation statement. That statement is not
   made in Cycle-Sync, whose contribution is that cycle-consistency
   information alone suffices for exact and robust recovery. Corrected in
   §2 and the §7.4 aside: the single-corruption form is stated in
   higher-order group synchronization (Duncan & Kileel); Cycle-Sync is
   cited for exact recovery from cycle consistency alone.
2. **Yuan et al. (arXiv:2604.02369) — overstated.** "No protocol-level
   semantic verification across eighteen protocols" became "only limited
   protocol-level support for semantic verification across eighteen
   agent communication protocols, with semantics pushed into prompts and
   wrappers" — the abstract's word is "limited".

**Also applied:** one misattribution in form (an institutional
repository name standing in for a citation → Jiménez-Ruiz, Payne,
Solimando & Tamma, KR 2016); three wording fixes (*Replicating Belief*'s
five outcomes named in full; "formalisation **of** the Alignment Repair
Game"; Cartan-Topos "a diagnostic, not a map repair"); and metadata
corrections — Levy et al. initials (I. Levy, S. Goldwasser); Laera et
al. four authors and CMNA venue; Togia & McNeill as a journal article
(*Artificial Intelligence Review* 40(2):175–191); Beltoft et al.'s full
title; full titles recovered for Cycle-Sync and Layer-Isolated
Evaluation; issue and DOI added to Lerman & Shi. All other characterising
clauses fit their sources as written.

## Summary for the note

Two dated passes, one adversarial family pass and one verification pass,
with no COLLAPSE verdict on any of the six claims and no reference left
unverified. The bracketing structure the record establishes: the
synchronization line owns the mathematics (pairwise-to-global
inconsistency, cycle-edge localisation, the single-corruption statement,
exact recovery from cycle consistency) and emits estimates without
abstention; the residual-as-diagnostic line (Mishra; Cartan-Topos)
abstains without attributing or repairing; the ontology-alignment line
repairs correspondences between symbolic ontologies from communication
failure, on the failing pair; the truth-maintenance and evidence-gated
lines gate beliefs, not translation edges; emergent communication observes
divergence in the wild and reports the opposite dynamic in LLM
populations; the layered-evaluation neighbours inject one layer at a time
or evaluate by scenario, unpreregistered; and the nearest built object to
the discussion's absence is a pairwise certified vocabulary with
transitivity left as future work. The note's claimed cell — divergent
sparse-block codebooks calibrated across a population by multi-agent loop
residuals that remain native symbolic vectors and are reused as the
repair of the map itself, with attribution certified inside a local
boundary and refused outside it — is unoccupied within these searches on
these dates.