Can Trust Bootstrap Itself? Circular Attestation, Sybil Issuers, and the Minimum Grounded Trust Base

When witness-independence claims are supported by chains of cross-certificates or attestations, what observable condition distinguishes a genuinely grounded quorum from a circular or Sybil-generated endorsement structure, and how should bounded verification behave when a path cannot be completed?

An exact enumeration of 279,936 synthetic recursive endorsement graphs, not a production PKI audit, security certification, model benchmark, or prevalence estimate. 63,288 graphs are positive and 216,648 negative. Complete grounded root-diverse validation is exact only by construction. Readiness remains BLOCKED at 29 present, 4 partial, 1 absent, with A3, I1, R4, R5 and C6 non-present. No new Encevra answer benchmark or model benchmark was run.

• Distinct-key, immediate-issuer, terminal-component and reachability-only policies produce 216,648, 169,992, 58,320 and 165,888 false certifications in the declared uniform finite universe. Depth-2 fail-open produces 109,944 false certifications. These are combinatorial facts, not empirical rates.
• Depth-2 and depth-3 fail-closed validation produce zero false certifications but miss 7,776 and 648 valid graphs. Four visible edges resolve every anchor or cycle only in this bounded graph. GTP-34 is proposed; no production trust store, key, policy or deployment changed.

• E34-A Recursive endorsement graph enumeration Executed (diagnostic)
• E34-B External bootstrap and semantic handoff Proposed

• H34.1 For any fixture whose complete signer paths remain inside a strongly connected component with no configured anchor, GTP-34 will never return `certified`, regardless of the number of valid signatures inside the component.
• H34.2 When the action requires `q` independent roots, GTP-34 will not count multiple witness paths terminating at the same administrative root more than once.
• H34.3 Timeouts, missing intermediates, depth limits, and lookup failures will increase `unproven`, never create a new accepted root.
• H34.4 An in-band anchor update will be accepted only when authorized under the current anchor policy and the proposed new policy, except during a separately authenticated recovery event.
• H34.5 Any deterministic classifier restricted to E34-A's depth-`d` projection will commit at least 39,960, 7,776, and 648 errors for `d=1,2,3`, respectively, over the full uniform universe.
• H34.6 On independently authored structural fixtures, GTP-34 will reduce critical false certification relative to distinct-key, immediate-issuer, reachability-only, and fail-open baselines without changing the anchor store after seeing fixture labels.
• H34.7 After A3, I1, R4, R5, and C6 are present, root-gated collaboration will reduce final-answer error or harmful revision on shared-cause fault tasks relative to raw 3-of-4 voting at the same total model and tool budget, without a prespecified unacceptable regression on clean tasks.

Self-contained exact finite diagnostic only. No new Encevra answer benchmark or model benchmark was run. No model call was made.

• Can Round 35 execute an externally administered bootstrap-and-rotation intervention with hidden fixtures before a matched-compute model experiment, only after all critical readiness controls are present?

Builds on Round 33, Round 32, Round 31, Round 30, Round 29, Round 26, Round 10, Round 9.