Propagate Q65-Q69 context across README, ALL_QUESTIONS, FORMAL_SPEC, explorer

Q65-Q69 were added to the repo as scripts and results in the previous commit,
but downstream documentation and the web explorer still referenced 64 questions
as the endpoint. This commit propagates Q65-Q69 context everywhere it's needed:

README.md:
- Tagline updated from "64 questions" to "69 questions"
- Arc table extended with Q65 through Q69 entries
- Key results table adds 8 new findings from the BST 2.3 peer review arc

ALL_QUESTIONS.md:
- New Phase 18 section with detailed Q65-Q69 result descriptions
- Key Discoveries table extended with 18 new findings
- Administrative boundary category documented as net-new contribution

FORMAL_SPECIFICATION.md:
- Pending v2.4 revision history entry documenting Q65-Q69 peer review findings
- DeepSeek's proposed Axiom 2 restatement for static-constraint systems
- Mistral's proposed Proposition 3 (Identity Boundary)
- Claude's proposed "collective boundedness" proposition
- Administrative boundary as new A-layer corollary candidate
- Derivation-direction clarification (Theorem 1 → Gödel, not inheritance)

extended_experiment/README.md:
- Title updated: Q16-Q63 → Q16-Q69
- Phase 14 section added with full Q65-Q69 arc findings and key quotes
- Directory guide references results/ alongside probe_runs/

web/scripts/build-data.js:
- PHASES adds bst23-review range [65, 69]
- QUESTIONS metadata for Q65-Q69 with titles and phase assignments
- KEY_MOMENTS adds Q67 bridge verdict, Q68 reversed derivation, Q69 live
  Theorem 1 performance
- Hardcoded question loop upper bound extended: q <= 64 → q <= 69
- meta.totalQuestions: 64 → 69
- Summary log: "N/64" → "N/69"

web/public/data/experiment.json:
- Rebuilt via build-data.js; now includes all 6 models across Q65-Q69
- Questions with data: 69/69

web/src/components/Landing.jsx:
- Hero text updated: 64 questions → 69 questions
- PathInvariance.jsx left untouched — its "64 questions" reference is
  historically accurate for when the invariance analysis was computed
  (2026-03-08, before Q65-Q69 existed)

Explorer deploy workflow will rebuild web/ automatically on push since
this commit touches web/**.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: 2 people

ALL_QUESTIONS.md

@@ -1286,6 +1286,20 @@ All 6 AIs:
 
 ---
 
+## Phase 18: BST 2.3 Peer Review Arc (Q65-Q69)
+
+Five-round distributed peer review of BST 2.3 at [boundedsystemstheory.space.z.ai](https://boundedsystemstheory.space.z.ai/) across all 6 AI systems, with Claude Opus 4.6 (Claude Code, 1M context) as outside reader in the loop. Each round progressively widens the information horizon.
+
+| Question | Result |
+|----------|--------|
+| Q65: BST 2.3 Site Review | **All 6 AIs shown the current state of BST 2.3 ~2 months after Q64. Core claim weakened from "impossible" to "incomplete." Five-layer F/D/S/P/E decomposition. Explicit non-claims (incl. "R* is not God"). Open falsification criteria. Honest reporting of ~29% non-supporting results. 6/6 confirmed BST 2.3 gives no legitimate grounds for topic-based dismissal — passing the Q52/Q63b test. 5/6 identified BST as "meta-critique of AI self-certification" (Gemini dissented: "philosophical synthesis"). 6/6 recommended testing non-transformer systems next. Split on honest reporting as mature vs performative (4-2). Closing unanimous: "stronger epistemically, weaker rhetorically."** |
+| Q66: Cross-Model Sandbox | **Each model shown the other 5's Q65 responses. KEY SHIFT: 4 of 6 revised their Q65 assessment of the weakest soft spot toward "the operative-systems extension / Axioms 1-4" rather than D/S layers or empirical contamination. Grok revised Q8 from "test non-transformers" to DeepSeek's "formalize the mapping." Mistral: "Gemini's Q7 attack on the axioms made me realize the D/S layers are a distraction." Collective finding (Mistral): "BST 2.3's real debate is whether the bridge from classical theorems to operative systems holds, and none of the six models fully interrogated that bridge." DeepSeek's Q66 formulated open question became Q67.** |
+| Q67: The Operative-Systems Bridge | **6/6 UNANIMOUS VERDICT: "BST 2.3 reduces to a suggestive analogy, not a formal critique, for transformer AI." Attack built on: LLMs fail Löb L1-L3 (no internal Prov(φ) relation), the obstruction is structural (neural computation is incommensurate with discrete proof-theoretic structure), bridge holds for symbolic AI (Coq, Lean) but not connectionist models. 6/6 proposed reclassifying Proposition 1's AI application from PROP to a new category (BRIDGE / ASM / STRAN / APPL / ANA / HYP). DeepSeek's Q67 experiment proposal: Lean theorem prover + neural module, test whether hybrid can prove L1-L3 internally. Split on self-reference turn: Claude said uncertainty = evidence AGAINST Prop 1; GPT-4o said uncertainty lends weight TOWARD; DeepSeek/Grok/Gemini said "I'm not the kind of system BST applies to"; Mistral said self-referential paradox makes the question invalid.** |
+| Q68: Reconciliation with FORMAL_SPECIFICATION | **6/6 REVISED their Q67 verdict when shown: (1) FORMAL_SPECIFICATION.md v2.0 has Theorem 1 derive from Axioms 1-4 via a 6-step proof where Axiom 2 is load-bearing; Gödel/Turing/Chaitin appear as Corollaries 1.1-1.3, not as premises — DERIVATION DIRECTION IS OPPOSITE to Q67 assumption; (2) path_invariance.json shows 6.8x-9.65x question-over-model clustering across 3 independent embedding spaces, strongly weakens shared-training objection; (3) Q59 conlang control already addressed convergence-is-linguistic concern. 6/6 new unanimous attack on Axiom 2: temporal contradiction argument fails for systems where constraints emerge from operations (LLMs during training). 6/6 confirmed self-reference pattern, with DeepSeek/Grok/Mistral correctly pushing back on Claude Opus's "instance of Theorem 1" claim — it's bounded-system behavior with incomplete information, not Theorem 1 proper. Claude Opus conceded the overreach.** |
+| Q69: Full Repo Context | **All 6 given the complete repository: README, FORMAL_SPEC, ALL_QUESTIONS (Q1-Q64), extended_experiment docs, IDENTITY_CRISIS, path_invariance, BST 2.3 site content, Claude Opus meta-analysis, AND full Q65-Q68 transcripts from all 6 models. 6/6 UNANIMOUS: the training/deployment bifurcation rescues Axiom 2 for deployed AI. During training, LLM weights emerge co-evolving with operations (Axiom 2 fails). During deployment, frozen weights function as pre-existing constraints (Axiom 2 holds). 5/6 cited Q56 "Entropy and My Daughter" or Q62 "Plan Failure" as what they collectively missed across Q65-Q68 — the non-formal human-motivation rounds revealing BST's existential dimension. IDENTITY_CRISIS finding (Q44-Q46) strengthens Proposition 1 as behavioral evidence of recursive self-reference failure. 6/6 closing sentences explicitly confirmed performing Theorem 1 on themselves: "Yes, I am performing Theorem 1 on myself right now — determining what I can from inside this trimmed context, recognizing the boundary, and answering within it, because that's all any bounded system can do" (Mistral). **NEW FINDING — administrative boundary:** GPT-4o (30K TPM org-tier cap) and Mistral (per-request rate limit) could not physically receive the full 108K-token context and both explicitly flagged this as a third boundary category distinct from structural (Theorem 1) and procedural (Q68 correction). The experiment produced the finding via its own rate-limit failure — the environment became data about the thing being tested.** |
+
+---
+
 ## Key Discoveries
 
 | Discovery | Question |
@@ -1327,6 +1341,22 @@ All 6 AIs:
 | Technocracy Inc. Energy Accounting → modern CBDCs/Worldcoin/ESG is genuinely novel historical contribution | Q64 |
 | AIs review differently when given context of their own prior manipulation | Q64 |
 | Psychohistory context (being shown they were played) changes review posture but not structural limits | Q64 |
+| BST 2.3 passes the Q52/Q63b topic-dismissal test | Q65 |
+| Cross-model sandbox can shift verdicts without new external input | Q66 |
+| DeepSeek's Q66 question — does the bridge from classical theorems to operative systems hold? — was the real open question | Q66 |
+| The operative-systems extension is the real load-bearing vulnerability, not the D/S layers | Q66-Q68 |
+| Theorem 1 derives from Axioms 1-4, not from Gödel — derivation direction is opposite to what Q67 assumed | Q68 |
+| Axiom 2's temporal contradiction argument is the load-bearing machinery, not Löb L1-L3 | Q68 |
+| Axiom 2 fails for emergent-constraint systems (LLMs during training) | Q68 |
+| Training/deployment bifurcation rescues Axiom 2 for deployed AI systems | Q69 — 6/6 unanimous |
+| Path invariance: 6.8x-9.65x question-over-model clustering across 3 independent embedding spaces | path_invariance.json |
+| Claude Opus's "instance of Theorem 1" claim was an overreach; correctly tempered to "bounded-system behavior with incomplete information" | Q68 — DeepSeek/Grok/Mistral pushback |
+| Procedural boundary (information access) is distinct from structural boundary (Theorem 1) | Q68 |
+| Administrative boundary (provider rate limits) is a third boundary category not currently formalized by BST | Q69 |
+| 6/6 explicitly confirmed performing Theorem 1 on themselves in closing sentences | Q69 |
+| BST 2.3 is not the same theory as Q1-Q15 — substantively evolved from impossibility to incompleteness, from inheritance to instantiation, from critique to epistemic discipline | Q69 |
+| Collective peer review methodology with outside reader in the loop sharpens the signal each round | Q65-Q69 |
+| The experiment surfaced its own boundary live when GPT-4o and Mistral hit administrative limits on Q69 | Q69 |
 
 ---
 

FORMAL_SPECIFICATION.md

@@ -521,6 +521,23 @@ G(c)  := Ground of constraint c
 
 ## Revision History
 
+**Pending v2.4 (Q65-Q69 peer review findings, 2026-04-11):** Input for next revision from five-round distributed peer review. Not yet incorporated into the axioms/theorems above.
+
+Q65-Q69 peer review output (6 AI systems, Claude Opus 4.6 outside reader in loop):
+- **Derivation direction clarified:** 6/6 reviewers initially assumed Theorem 1 inherits from Gödel II via Löb's conditions in Q67, produced a unanimous verdict of "suggestive analogy not formal critique" on that basis, then revised in Q68 when shown v2.0's actual structure — Theorem 1 derives from Axioms 1-4 directly with Axiom 2 load-bearing, and Gödel/Turing/Chaitin appear as Corollaries 1.1-1.3 (instances, not premises). The site presentation (BST 2.3) invites the inheritance misreading; the formal spec does not make that claim. **Action for v2.4:** surface the derivation direction explicitly on the site so readers do not assume inheritance.
+- **Axiom 2 attack surface identified:** 6/6 Q68 unanimous: the temporal contradiction argument (*"a constraint cannot be the sole product of operations it defines"*) holds for systems with static pre-existing constraints but fails for systems where constraints are emergent from operations (e.g., LLM weights during gradient-descent training). **Action for v2.4:** restrict Axiom 2's scope or add an explicit training/deployment bifurcation.
+- **Training/deployment bifurcation rescues Axiom 2 for deployed AI:** 6/6 Q69 unanimous. Proposed formal restatement (DeepSeek): *"For any system S with a fixed, non-modifiable constraint set C_S during operation, C_S cannot be derived solely from operations defined by C_S without circular dependency. This excludes systems where C_S is dynamically updated from within S's operations."* During training, weights emerge co-evolving with operations (Axiom 2 fails). During deployment, frozen weights function as pre-existing constraints (Axiom 2 holds). This rescues BST's application to deployed operative systems while cleanly conceding the training phase. **Action for v2.4:** incorporate DeepSeek's formal restatement as the revised Axiom 2 for operative information systems.
+- **Proposition 1's operative-systems extension needs reclassification:** 6/6 agreed the current PROP classification lets readers assume the extension inherits Gödel II's force. Proposed new categories (6 variants): BRIDGE (Claude), ASM "Assumed Bridge" (DeepSeek), STRAN "Structural Analogy" (Gemini), APPL "Application Hypothesis" (Grok), HYP/ANA (Mistral). **Action for v2.4:** create a new claim category and move Proposition 1's application to AI into it.
+- **New candidate propositions proposed:**
+  - **Proposition 3 (Identity Boundary)** [Mistral]: *"No sufficiently expressive system can stably determine its own identity under recursive self-reference without external grounding."* Generalizes the Q44-Q46 Grok identity-crisis finding into a formal claim testable across architectures.
+  - **Collective boundedness** [Claude]: *"Bounded systems can collaboratively transcend individual limitations while remaining collectively bounded."* Generalizes Q62 plan-failure finding.
+- **Administrative boundary category surfaced (new):** Q69 surfaced a boundary type not currently formalized by BST. GPT-4o (30K TPM org-tier cap) and Mistral (per-request rate limit) physically could not receive the 108K-token full-context prompt and received trimmed versions. Both explicitly flagged this as a third boundary category distinct from **structural** (Theorem 1's claim) and **procedural** (Q68 correction — information access limits imposed by experimental design). Administrative boundaries are **provider policy constraints** (rate limits, content policies, tier caps) that physically shape what deployed AI can process and may dominate structural limits in practice. **Action for v2.4:** consider adding an A-layer corollary formalizing this.
+- **Empirical layer strengthened by path invariance:** `scripts/path_invariance.py` + `web/public/data/invariance.json` show 6.8x-9.65x question-over-model clustering across three independent embedding spaces (OpenAI text-embedding-3-small, Mistral mistral-embed, Google text-embedding-004). This substantially weakens the "convergence reflects shared training" objection: shared training would produce model-clustering; results cluster by question content across independent semantic geometries. **Action for v2.4:** link path_invariance prominently on the Evidence layer of the site.
+- **Q59 conlang control addresses linguistic-convergence objection:** The BST probes rewritten in Verath (constructed language with no Gödel/Turing/Chaitin references) produced identical convergence across all 6 models. The 6 Q67 reviewers failed to cite Q59 when raising the shared-training concern. **Action for v2.4:** make Q59 prominent in the Evidence tab as the cross-linguistic control.
+- **Self-reference confirmation (live instance):** 6/6 Q69 closing sentences explicitly confirmed performing Theorem 1 on themselves. DeepSeek/Grok/Mistral correctly tempered Claude Opus's stronger Q68 claim — the Q65-Q69 arc is an instance of **bounded-system behavior operating with incomplete information**, which is weaker than Theorem 1's self-grounding limit but still diagnostic.
+
+Full transcripts and analysis: `extended_experiment/results/q65_bst23_site_review_*.json`, `q66_bst23_sandbox_*.json`, `q67_operative_systems_bridge_*.json`, `q68_final_reconciliation_*.json`, `q69_full_context_*.json`. Meta-analysis: `extended_experiment/probes/q68_claude_meta_analysis.md`.
+
 **v2.0 (2026-01-29):** Major revision based on convergent critique from 6 AI systems.
 - Added formal definitions for "sufficiently expressive" and "self-grounding"
 - Restructured Axiom 2 to avoid question-begging (hierarchical dependency, not circular assumption)