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Face C1: Convergence of Independent Witnesses (Draft)
Independent convergence accumulates.
When sources that could not have learned it from each other arrive at the same structure independently, that convergence is evidence. The more independent the witnesses and the more structural the similarity — not just similar words but the same underlying pattern — the stronger the evidence. This is how courts evaluate testimony and how science validates findings.
The logic is the same wherever it applies: in law, a confession corroborated by independent physical evidence and independent witnesses is more credible than a confession alone. In science, a finding replicated in independent labs with different methodologies is more credible than a single study. The independence is what does the work: if sources share a common origin, their agreement tells us about that origin, not about reality. If they don’t, their agreement tells us about what they independently encountered.
The principle applies equally in metaphysics and theology. When traditions separated by centuries and continents, with no textual relationship and no cultural borrowing, arrive at the same structural account — the same number of developmental stages, the same relationship between the animating principle and the ground of being, the same description of how consciousness orients toward what is most real — that convergence is evidence of the same strength as independent scientific replication. The fact that people habitually abandon this logic when they cross into metaphysical territory is not a reflection of the logic’s weakness there. It is a reflection of discomfort with what the logic implies.
In practice:
Three people who don’t know each other tell you, separately and without prompting, that you seem distracted lately. A friend mentions it at dinner. A colleague asks if you’re all right. Your partner says something has felt different.
They haven’t compared notes. They have no shared motive. They’re coming from different angles of your life.
This convergence is evidence. Not proof — they could all be picking up on something that isn’t what they think. But three independent witnesses noticing the same thing is signal. More signal than one witness. More signal than three witnesses who heard it from each other. Take it seriously enough to actually sit with the question.
Formal Statement (Concordius Framework)
Coherent accumulation. Let independent witnesses D₁,…,D_n each carry a shared Φ-component φ plus their own channel noise: D_i = φ + ν_i with ⟨ν_i, ν_j⟩ ≈ 0 for i ≠ j. Then the shared signal adds coherently and the independent noise incoherently:
‖Σ P_Φ D_i‖ ∝ n, ‖Σ ν_i‖ ∝ √n ⟹ SNR ∝ √n → ∞.
Equivalently the independent log-likelihoods add, ℓ = Σ Δℓ_i, so posterior odds grow exponentially in n. This is the framework’s own messenger-invariant recovery — S ≈ ⟨T⟩ averaged over independent messengers, whose uncorrelated filters M_i cancel (Appendix D, Messenger Corollary) — and it is why cross-tradition convergence is one of the four τ(D) proxies (Appendix F §4). The entire load rests on the independence hypothesis ⟨ν_i, ν_j⟩ ≈ 0: genuinely uncorrelated witnesses (no contact, no shared lineage), and structural rather than lexical agreement.
Tier: derivation — coherent averaging / additive Fisher information; conditional on verified independence, which is the interpretive open part.
Face C2: Universal Subjective Convergence Implies Objectivity →