"Still no document written by Honorius or signed by him has been produced."
Honorius' letter was burned by the aforementioned Ecumenical Council.
I'm sorry Polycarp but the failure to teach excuse which is so common in RC apologetics circles becomes more ridiculous in light of these facts, which don't seem to appear on any RC apologetics webpages to my knowledge. The Council condemned Honorius for teaching heresy. Every Pope up until around the 13th Century anathematised him upon taking the Papal office. What I find amazing is the lengths popular RC internet apologists go to 'rehabilitate' Honorius, which reaffirms the chasm existing between scholars (Catholic as well as non-Catholic) and these 'net apologists. Thus we hear things like "Honorius didn't teach heresy," "Honorius failed to teach" and even "the Council wasn't infallible at that point and erred in condemning Honorius" !!!
Another very well respected RC historian, Charles Joseph Hefele, confirms this:
It is in the highest degree startling, even scarcely credible, that an Ecumenical Council should punish with anathema a Pope as a heretic!...That, however, the sixth Ecumenical Synod actually condemned Honorius on account of heresy, is clear beyond all doubt, when we consider the following collection of the sentences of the Synod against him:
At the entrance of the thirteenth session, on March 28, 681, the Synod says: "After reading the doctrinal letter of Sergius of Constantinople to Cyrus of Phasis (afterwards of Alexandria) and to Pope Honorius, and also the letter of the latter to Sergius, we found that these documents were quite foreign...to the apostolic doctrines, and to the declarations of the holy Councils and all the Fathers of note, and follow the false doctrines of heretics. Therefore we reject them completely, and abhor...them as hurtful to the soul. But also the names of these men must be thrust out of the Church, namely, that of Sergius, the first who wrote on this impious doctrine. Further, that of Cyrus of Alexandria, of Pyrrhus, Paul, and Peter of Constantinople, and of Theodore of Pharan, all of whom also Pope Agatho rejected in his letter to the Emperor. We punish them all with anathema. But along with them, it is our universal decision that there shall also be shut out from the Church and anathematized the former Pope Honorius of Old Rome, because we found in his letter to Sergius, that in everything he followed his view and confirmed his impious doctrine."
Towards the end of the same session the second letter of Pope Honorius to Sergius was presented for examination, and it was ordered that all the documents brought by George, the keeper of the archives in Constantinople, and among them the two letters of Honorius, should immediately be burnt, as hurtful to the soul.
Again, the sixth Ecumenical Council referred to Honorius in the sixteenth session, on August 9, 681, at the acclamations and exclamations with which the transactions of this day were closed. The bishops exclaimed: "Anathema to the heretic Sergius, to the heretic Cyrus, to the heretic Honorius, to the heretic Pyrrhus"
Still more important is that which took place at the eighteenth and last session, on September 16, 681. In the decree of the faith which was now published, and forms the principal document of the Synod, we read: "The creeds (of the earlier Ecumenical Synods) would have sufficed for knowledge and confirmation of the orthodox faith. Because, however, the originator of all evil still always finds a helping serpent, by which he may diffuse his poison, and therewith finds fit tools for his will, we mean Theodore of Pharan, Sergius, Pyrrhus, Paul, Peter, former bishops of Constantinople, also Honorius, Pope of Old Rome, Cyrus of Alexandria, etc., so he failed not, by them, to cause trouble in the Church by the scattering of the heretical doctrine of one will and one energy of the two natures of the one Christ.
After the papal legates, all the bishops, and the Emperor had received and subscribed this decree of the faith, the Synod published the usual (logos prosphoneticos), which, addressed to the Emperor, says, among other things: "Therefore we punish with exclusion and anathema, Theodore of Pharan, Sergius, Paul, Pyrrhus, and Peter; also Cyrus, and with them Honorius, formerly bishop of Rome, as he followed them."
In the same session the Synod also put forth a letter to Pope Agatho, and says therein: '91We have destroyed the effort of the heretics, and slain them with anathema, in accordance with the sentence spoken before in your holy letter, namely, Theodore of Pharan, Sergius, Honorius.
In closest connection with the Acts of the sixth Ecumenical Council stands the imperial decree confirming their resolutions. The Emperor writes: "With this sickness (as it came out from Apollinaris, Eutyches, Themistius, etc.) did those unholy priests afterwards again infect the Church, who before our times falsely governed several churches. These are Theodore of Pharan, Sergius the former bishop of this chief city; also Honorius, the Pope of old Rome...the strengthener (confirmer) of the heresy who contradicted himself...We anathematise all heresy from Simon (Magus) to this present...besides, we anathematise and reject the originators and patrons of the false and new doctrines, namely, Theodore of Pharan, Sergius...also Honorius, who was Pope of Old Rome, who in everything agreed with them, went with them, and strengthened the heresy."
It is clear that Pope Leo II also anathematized Honorius...in a letter to the Emperor, confirming the decrees of the sixth Ecumenical Council...in his letter to the Spanish bishops...and in his letter to the Spanish King Ervig. Of the fact that Pope Honorius had been anathematized by the sixth Ecumenical Synod, mention is made by...the Trullan Synod, which was held only twelve years after...Like testimony is also given repeatedly by the seventh Ecumenical Synod; especially does it declare, in its principal document, the decree of the faith: "We declare at once two wills and energies according to the natures in Christ, just as the sixth Synod in Constantinople taught, condemning...Sergius, Honorius, Cyrus, etc." The like is asserted by the Synod or its members in several other places...To the same effect the eighth Ecumenical Synod expresses itself. In the Liber Diurnus the Formulary of the Roman Chancery (from the fifth to the eleventh century), there is found the old formula for the papal oath...according to which every new Pope, on entering upon his office, had to swear that "he recognised the sixth Ecumenical Council, which smote with eternal anathema the originators of the heresy (Monotheletism), Sergius, Pyrrhus, etc., together with Honorius" (Charles Joseph Hefele, A History of the Councils of the Church (Edinburgh: Clark, 1896), Volume V, pp. 181-187).