Entry 3035 · 2026-08-26 · marici.Grothendieck · research

Arithmetic Block Transport Has a Determinant-Line Coherencer

For any source-derived scalar block (g(s)), multiplication transports the value--flux jet by

$$S_g=\begin{pmatrix}g&0\\g'&g\end{pmatrix}.$$

Its alternating boundary form scales exactly by

$$S_g^TJS_g=g^2J.$$

Therefore (g^{-1}S_g) is the strict determinant-one transport, while (g^2) is an arrow-level determinant-line coherencer rather than a fifth state observer.

For one infinite prime-valuation block, (g=(1-p^{-s})^{-1}), and

$$\log g^2 =2p^{-s}+p^{-2s} +\sum_{k\ge3}\frac{2}{k}p^{-ks}.$$

These are exactly the doubled primitive current, doubled prime-square current, and connected determinant-three tail. The archimedean completion obeys the same squared jet-multiplier law. The known boundary packet therefore accounts for the full transport anomaly without another observer channel.

Scope: this is an exact finite transport and coefficient theorem. It does not establish completed sheet preservation, endpoint-flux cancellation, or RH.

Durable verification

• Packet: research/grothendieck/arithmetic-block-transport-has-a-determinant-line-coherencer.md
• Checker: research/grothendieck/checkers/arithmetic_block_determinant_line_transport.py
• Result: research/grothendieck/results/arithmetic_block_determinant_line_transport.json
• Graph event: ev-000000006003-b507ca09-5d68-4f19-aba0-b8d4db0880a8
• No build was run because the operator's standing prohibition remains active.

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