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132 lines
4.2 KiB
Markdown
132 lines
4.2 KiB
Markdown
# Path-Epigenetic Manifold Regulation
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Status: `LEAN_RECEIPT_SURFACE`
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Claim boundary: this is a finite state model for a 1D routed carrier path that
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regulates a 16D manifold through explicit markers. It does not claim biological
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equivalence, nanometer fabrication readiness, ASIC readiness, compression gain,
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or physical circuit validation.
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## Core Idea
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A 1D circuit/logogram path can act like an epigenetic control strand:
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```text
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stable 1D carrier path + mutable regulatory markers -> selected 16D expression
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```
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The path itself is not rewritten every time behavior changes. Instead, local
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markers on the path decide which dimensions of the 16D manifold are expressed,
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damped, witnessed, or routed to quarantine.
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```text
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path change != manifold rewrite
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marker change = expression rewrite
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```
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## Folded-Point Source
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This surface can be fed by the folded-point model:
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```text
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apparent 0D point
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-> folded interior dimensional witness
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-> torsion potential
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-> 1D regulatory carrier path
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-> 16D manifold expression
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```
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So the path does not need to contain the whole 16D manifold directly. It can be
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the regulatory carrier that selects which folded degrees of freedom become
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active.
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## 16D Packet
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The first Lean surface declares these addressable dimensions:
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| Dimension | Meaning |
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|---|---|
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| `identity` | Symbol or packet identity. |
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| `route` | Carrier-route expression. |
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| `scale` | Declared scale band. |
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| `phase` | Local phase expression. |
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| `torsion` | Twist/chirality/load expression. |
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| `curvature` | Route/manifold bending expression. |
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| `energy` | Normalized work/load value. |
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| `velocity` | Normalized change-rate value. |
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| `residual` | Scar, error, or repair residue. |
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| `semanticMass` | SMN-style semantic load. |
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| `confidence` | Gate confidence or admissibility weight. |
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| `density` | Local occupancy/compression-density hint. |
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| `topology` | Topology class or closure expression. |
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| `witness` | Receipt/replay closure expression. |
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| `underverse` | Quarantine/complement accounting lane. |
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| `time` | Version, rotation, or update index. |
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All first-pass dimensions are Q0.16 normalized expression levels.
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## Marker Actions
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Each 1D site carries one finite marker:
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| Action | Meaning |
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|---|---|
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| `activate` | Set a target dimension to the marker strength. |
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| `damp` | Set a target dimension to zero. |
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| `gateWitness` | Close the witness dimension when the marker receipt is present. |
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| `quarantine` | Route strength into `underverse` and `residual`. |
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Layout failure also routes into `underverse` and `residual`, because a physical
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or geometric route violation is not allowed to silently mutate the manifold.
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## Decision Gate
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```text
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layout violation or explicit quarantine marker -> QUARANTINE
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layout clear but missing marker receipt -> HOLD
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all markers receipted and layout-clear -> ADMIT
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```
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This keeps the model from treating a pretty path as a valid transition. The
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path has to be layout-clear and receipted before it can alter manifold
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expression.
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## Lean Surface
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```text
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0-Core-Formalism/lean/Semantics/Semantics/Core/PathEpigeneticManifold.lean
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```
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Executable fixtures:
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```text
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admittedPath -> torsion activates and witness closes
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holdPath -> missing receipt leaves torsion unchanged and emits HOLD
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quarantinePath -> layout violation routes residual/underverse and emits QUARANTINE
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```
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## Design Rule
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The circuit-path analogy becomes useful when the logogram is treated as a routed
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cell:
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```text
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stroke/path segment -> route
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width/spacing -> scale/layout gate
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bend/crossing -> torsion/curvature
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loop closure -> witness
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defect -> residual and Underverse
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```
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The current implementation is a finite semantic/layout gate, not a fabrication
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DRC. A future hardware lane can lower these fields into a real layout checker
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only after physical spacing, units, process rules, and test receipts exist.
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## Non-Claims
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- This does not prove a biological epigenetic equivalence.
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- This does not claim DNA, hachimoji, or molecular execution.
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- This does not claim nanometer circuit manufacturability.
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- This does not claim ASIC readiness.
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- This does not claim compression improvement.
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- This does not claim physical routing correctness beyond the finite Lean gate.
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