You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: auth_verification.go
    path of file: ./repos/bytom/protocol/casper
    
    the code of the file until where you have to start completion: package casper

import (
	"fmt"

	log "github.com/sirupsen/logrus"

	"github.com/bytom/bytom/errors"
	"github.com/bytom/bytom/protocol/bc"
	"github.com/bytom/bytom/protocol/state"
)

// AuthVerification verify whether the Verification is legal.
// the status of source checkpoint must justified, and an individual validator ν must not publish two distinct Verification
// ⟨ν,s1,t1,h(s1),h(t1)⟩ and ⟨ν,s2,t2,h(s2),h(t2)⟩, such that either:
// h(t1) = h(t2) OR h(s1) < h(s2) < h(t2) < h(t1)
func (c *Casper) AuthVerification(msg *ValidCasperSignMsg) er
    
func (c *Casper) authCachedMsg(msg *ValidCasperSignMsg, msgKey string) error {
	defer c.verificationCache.Remove(msgKey)

	source, err := c.store.GetCheckpoint(&msg.SourceHash)
	if err != nil {
		return errors.Wrap(err, "get source checkpoint")
	}

	targetNode := c.tree.nodeByHash(msg.TargetHash)
	if targetNode == nil {
		return errors.New("get target checkpoint")
	}

	target := targetNode.Checkpoint
	v, err := convertVerification(source, target, msg)
	if err != nil {
		return errors.Wrap(err, "authVerificationLoop fail on newVerification")
	}

	c.mu.Lock()
	defer c.mu.Unlock()
	return c.authVerification(v, target)
}