The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-a-bijective-proof-answer-concise-7f13

stable pending witness
2026-05-29 02:47:06 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of a bijective proof? Answer concisely in 2-3 sentences.
81 chars

Generation

A bijective proof demonstrates that two sets have the same size by constructing an explicit one-to-one correspondence between their elements, providing a deeper combinatorial insight than algebraic manipulation alone. This method not only proves equality of counts but also reveals the underlying structural relationship between seemingly different mathematical objects. Bijective proofs are often more elegant and intuitive than other proof techniques, making them highly valued in combinatorics.
29 tokens in · 89 tokens out · 2803 ms · $0.0014

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
2814.3 ms
Base LLM
2802.8 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0014

Trail

02:47:06 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
02:47:06 red_gate decision=pass reason=no disqualifying input patterns detected
02:47:09 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=89 latency_ms=2802.8 cost_usd=0.0014
02:47:09 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:47:09 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:47:09 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:47:09 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:47:09 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:47:09 signed hash_algo=sha256 hash=sha256:65d65e8389e59066a0d0ccd2e2ae15cf132825359954e7d570b8523051a4d24e

Content hash

sha256:65d65e8389e59066a0d0ccd2e2ae15cf132825359954e7d570b8523051a4d24e

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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