How can I use the sgtk API to generate a path and publish it?

Below is a snippet of code using the sgtk API to get a context, resolve a template path into an absolute path, and then publish that path.
The code doesn’t actually create a file at the generated path, so you would need to implement that part. For example to tell Maya to export a file to the generated path.

import sgtk

# Get the engine we are currently running in.
# (This assumes the code is running in an environment where an engine has already been started.)
current_engine = sgtk.platform.current_engine()

# Grab the sgtk API instance.
tk = current_engine.sgtk

# grab the current context from the engine.
ctx = current_engine.context

# Or alternatively create a new context representing the task we want to publish to.
# ctx = tk.context_from_entity("Task",13153)

# Create the folders just in case they haven't already been created.
tk.create_filesystem_structure("Task",ctx.task["id"])

#### Resolving the path ####

# Get a template instance for for the template we want to resolve into a path.
template = tk.templates["maya_shot_publish"]

# Use the context to resolve as many of the template fields as possible.
fields = ctx.as_template_fields(template)

# Manually fill in the remaining fields that can't be figured out automatically from context.
fields["name"] = "mypublish"
fields["version"] = 2

# Resolve the template path using the field values.
publish_path = template.apply_fields(fields)

#### Registering the Publish File ####

publish_name = fields["name"]
version = fields["version"]

# Register the path as a publish.
sgtk.util.register_publish(tk,
                           ctx,
                           publish_path,
                           publish_name,
                           version,
                           published_file_type = "Maya Scene")