Path-Epigenetic Manifold Regulation

Status: LEAN_RECEIPT_SURFACE

Claim boundary: this is a finite state model for a 1D routed carrier path that regulates a 16D manifold through explicit markers. It does not claim biological equivalence, nanometer fabrication readiness, ASIC readiness, compression gain, or physical circuit validation.

Core Idea

A 1D circuit/logogram path can act like an epigenetic control strand:

stable 1D carrier path + mutable regulatory markers -> selected 16D expression

The path itself is not rewritten every time behavior changes. Instead, local markers on the path decide which dimensions of the 16D manifold are expressed, damped, witnessed, or routed to quarantine.

path change   != manifold rewrite
marker change = expression rewrite

Folded-Point Source

This surface can be fed by the folded-point model:

apparent 0D point
  -> folded interior dimensional witness
  -> torsion potential
  -> 1D regulatory carrier path
  -> 16D manifold expression

So the path does not need to contain the whole 16D manifold directly. It can be the regulatory carrier that selects which folded degrees of freedom become active.

16D Packet

The first Lean surface declares these addressable dimensions:

Dimension	Meaning
`identity`	Symbol or packet identity.
`route`	Carrier-route expression.
`scale`	Declared scale band.
`phase`	Local phase expression.
`torsion`	Twist/chirality/load expression.
`curvature`	Route/manifold bending expression.
`energy`	Normalized work/load value.
`velocity`	Normalized change-rate value.
`residual`	Scar, error, or repair residue.
`semanticMass`	SMN-style semantic load.
`confidence`	Gate confidence or admissibility weight.
`density`	Local occupancy/compression-density hint.
`topology`	Topology class or closure expression.
`witness`	Receipt/replay closure expression.
`underverse`	Quarantine/complement accounting lane.
`time`	Version, rotation, or update index.

All first-pass dimensions are Q0.16 normalized expression levels.

Marker Actions

Each 1D site carries one finite marker:

Action	Meaning
`activate`	Set a target dimension to the marker strength.
`damp`	Set a target dimension to zero.
`gateWitness`	Close the witness dimension when the marker receipt is present.
`quarantine`	Route strength into `underverse` and `residual`.

Layout failure also routes into underverse and residual, because a physical or geometric route violation is not allowed to silently mutate the manifold.

Decision Gate

layout violation or explicit quarantine marker -> QUARANTINE
layout clear but missing marker receipt         -> HOLD
all markers receipted and layout-clear          -> ADMIT

This keeps the model from treating a pretty path as a valid transition. The path has to be layout-clear and receipted before it can alter manifold expression.

Lean Surface

0-Core-Formalism/lean/Semantics/Semantics/Core/PathEpigeneticManifold.lean

Executable fixtures:

admittedPath       -> torsion activates and witness closes
holdPath           -> missing receipt leaves torsion unchanged and emits HOLD
quarantinePath     -> layout violation routes residual/underverse and emits QUARANTINE

Design Rule

The circuit-path analogy becomes useful when the logogram is treated as a routed cell:

stroke/path segment -> route
width/spacing       -> scale/layout gate
bend/crossing       -> torsion/curvature
loop closure        -> witness
defect              -> residual and Underverse

The current implementation is a finite semantic/layout gate, not a fabrication DRC. A future hardware lane can lower these fields into a real layout checker only after physical spacing, units, process rules, and test receipts exist.

Non-Claims

This does not prove a biological epigenetic equivalence.
This does not claim DNA, hachimoji, or molecular execution.
This does not claim nanometer circuit manufacturability.
This does not claim ASIC readiness.
This does not claim compression improvement.
This does not claim physical routing correctness beyond the finite Lean gate.

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