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165 lines
3.1 KiB
Markdown
165 lines
3.1 KiB
Markdown
# Logogram Chirality Route Gate
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## Purpose
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Promote logogram chirality into the active FAMM equation stack **only where it is beneficial**.
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The existing logogram/symbology design already requires direction, chirality, phase, placement, residual policy, and receipt hash for lawful atomization. This document adds the missing operational layer: chirality can become a route coordinate when orientation changes admissibility, transition legality, replay, or DAG identity.
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## Canonical rule
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```text
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chirality is display metadata by default;
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chirality becomes a route coordinate only when it changes admissibility.
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```
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## Chirality witness
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```math
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\chi_{\mathrm{logo}}
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=
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(d,\;h,\;\phi,\;p,\;m)
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```
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Where:
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| Term | Meaning |
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|---|---|
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| `d` | direction |
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| `h` | handedness / chirality |
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| `phi` | phase |
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| `p` | placement |
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| `m` | mode / modifier family |
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## Logogram atom
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```math
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L_i
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=
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(
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\mathrm{id}_i,
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\mathrm{payloadHash}_i,
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\chi_{\mathrm{logo},i},
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\mathrm{residualPolicy}_i,
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\mathrm{receiptHash}_i
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)
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```
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## Packet primitive upgrade
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Current broad packet form:
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```math
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\Gamma_i
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=
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\gamma_i
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\otimes
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\chi_i
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\otimes
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\kappa_i
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\otimes
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\tau_i
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\otimes
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U_i\Lambda_i a_i
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\otimes
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\theta_i
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\otimes
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\epsilon_i
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```
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Upgrade:
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```math
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\boldsymbol{\chi}_i
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=
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[
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\chi^{\mathrm{geom}},
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\chi^{\mathrm{logo}},
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\chi^{\mathrm{braid}},
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\chi^{\mathrm{op}}
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]_i
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```
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Then:
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```math
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\Gamma_i
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=
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\gamma_i
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\otimes
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\boldsymbol{\chi}_i
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\otimes
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\kappa_i
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\otimes
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\tau_i
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\otimes
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U_i\Lambda_i a_i
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\otimes
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\theta_i
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\otimes
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\epsilon_i
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```
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## Route probability upgrade
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```math
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P(\sigma_t=i\mid X_t)
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\propto
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\exp[
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-\alpha d_i
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-\beta\Omega_i
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+\gamma I_i
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-\eta C_i
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+\lambda\mu_i
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+\rho R_i
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+\chi H_i
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]
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```
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where:
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```math
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H_i
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=
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\operatorname{compat}
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(
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\chi_{\mathrm{state}},
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\chi_{\mathrm{op}},
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\chi_{\mathrm{logo}},
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\chi_{\mathrm{surface}}
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)
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```
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## Where it plugs in
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| Layer | Use |
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|---|---|
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| FAMM | route score / scar class / invariant overlap |
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| PIST | wrong-handed transition prevention |
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| PIST-Chaos | operator sampling bias |
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| NUVMAP DAG | projected node identity when chirality changes future legal moves |
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| Delta stream | replayable orientation-changing event |
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| GCCL-Rep | packet witness |
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| AVM | deterministic replay input |
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## Add-only-if-beneficial gate
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Promote `chi_logo` to active routing only if at least one condition holds:
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```text
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1. It disambiguates two same-payload atoms.
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2. It prevents a wrong-handed PIST transition.
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3. It reduces NUVMAP false merges.
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4. It improves replay determinism.
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5. It yields a measurable route-shortening or residual reduction.
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```
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Otherwise keep it as metadata/receipt only.
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## No-drift boundary
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This is not a claim that glyph orientation has universal semantic meaning. The payload remains the canonical object. Chirality only participates when its receipt changes route legality, replay, admissibility, or compression outcome.
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## Project sentence
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Logogram chirality becomes beneficial when orientation changes admissibility: the same payload with different handedness can produce a different PIST transition, NUVMAP address, scar class, or replay receipt, so chirality must be promoted from glyph metadata into a first-class route witness.
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