3.1 KiB
Logogram Chirality Route Gate
Purpose
Promote logogram chirality into the active FAMM equation stack only where it is beneficial.
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.
Canonical rule
chirality is display metadata by default;
chirality becomes a route coordinate only when it changes admissibility.
Chirality witness
\chi_{\mathrm{logo}}
=
(d,\;h,\;\phi,\;p,\;m)
Where:
| Term | Meaning |
|---|---|
d |
direction |
h |
handedness / chirality |
phi |
phase |
p |
placement |
m |
mode / modifier family |
Logogram atom
L_i
=
(
\mathrm{id}_i,
\mathrm{payloadHash}_i,
\chi_{\mathrm{logo},i},
\mathrm{residualPolicy}_i,
\mathrm{receiptHash}_i
)
Packet primitive upgrade
Current broad packet form:
\Gamma_i
=
\gamma_i
\otimes
\chi_i
\otimes
\kappa_i
\otimes
\tau_i
\otimes
U_i\Lambda_i a_i
\otimes
\theta_i
\otimes
\epsilon_i
Upgrade:
\boldsymbol{\chi}_i
=
[
\chi^{\mathrm{geom}},
\chi^{\mathrm{logo}},
\chi^{\mathrm{braid}},
\chi^{\mathrm{op}}
]_i
Then:
\Gamma_i
=
\gamma_i
\otimes
\boldsymbol{\chi}_i
\otimes
\kappa_i
\otimes
\tau_i
\otimes
U_i\Lambda_i a_i
\otimes
\theta_i
\otimes
\epsilon_i
Route probability upgrade
P(\sigma_t=i\mid X_t)
\propto
\exp[
-\alpha d_i
-\beta\Omega_i
+\gamma I_i
-\eta C_i
+\lambda\mu_i
+\rho R_i
+\chi H_i
]
where:
H_i
=
\operatorname{compat}
(
\chi_{\mathrm{state}},
\chi_{\mathrm{op}},
\chi_{\mathrm{logo}},
\chi_{\mathrm{surface}}
)
Where it plugs in
| Layer | Use |
|---|---|
| FAMM | route score / scar class / invariant overlap |
| PIST | wrong-handed transition prevention |
| PIST-Chaos | operator sampling bias |
| NUVMAP DAG | projected node identity when chirality changes future legal moves |
| Delta stream | replayable orientation-changing event |
| GCCL-Rep | packet witness |
| AVM | deterministic replay input |
Add-only-if-beneficial gate
Promote chi_logo to active routing only if at least one condition holds:
1. It disambiguates two same-payload atoms.
2. It prevents a wrong-handed PIST transition.
3. It reduces NUVMAP false merges.
4. It improves replay determinism.
5. It yields a measurable route-shortening or residual reduction.
Otherwise keep it as metadata/receipt only.
No-drift boundary
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.
Project sentence
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.