What is a verb to describe someone speaking honestly? Instead of "Joe speaks honestly about today", I'd like to say "Joe honests about today". But an actual, real word.
1 : to make a solemn declaration under oath for the purpose of establishing a fact (as in a court)
2 a : to make a statement based on personal knowledge or belief : bear witness
2 b : to serve as evidence or proof
3 : to express a personal conviction
Joe levels about today.
The New Oxford American Dictionary defines this like so:
4 [ no obj. ] (level with) informal be frank or honest with (someone): when are you going to level with me?
(Note that "level with" is a common usage for this definition, but it is not a set phrase; this is a definition for the word "level," not an idiom.)
This is the only word I can think of that really does mean just that.
Most other words suggested signify that the speaker claims his statements are true, but they don't imply at all that they really are true. "Avow, testify, aver, affirm"—all are closer synonyms of "declare" or "assert."
Interesting that there are so few verbs that really mean "to tell the truth" but there are plenty that mean "to say one is telling the truth."
Related words that are other parts of speech include (adjectives) candid, frank, honest; and (nouns) candor, frankness, honesty.
Assert or confess openly ODO.
"He avowed that he had voted Labour in every election."
Avow has the connotation of speaking frankly.
Avouch is another verb meaning to affirm or assert but avouch is no longer in common use.
Joe opened up about today.
From an understanding that when someone "speaks honestly" they speak from their heart.
dictionary.com isn't aware of this usage of 'opened up'. Cambridge dictionary defines it as:
to talk about your personal thoughts or feelings
Merriam-Webster is a bit vague with their definition:
to become communicative
As a note, this may not be a good answer, just an answer - someone may be speaking the truth without involving their feelings.
to declare positively
Mr. Murray avers that many large organizations in the private sector are run by curmudgeons like him … — Joseph Epstein
In the time-honored tradition of verbing a noun, you could say that
Joe truths1 about today.
This usage actually is fairly venerable, though rare; in the set phrase "to truth it in love" the Oxford English Dictionary attests it back to 1604, and in more colloquial usage to 1888.
It may be familiar to some folks from the lyrics to the Nancy Sinatra song "These Boots are Made for Walking":
You keep lyin' when you oughta be truthin'
(lyrics courtesy of Google Play Music)
Note that while the meaning is fairly transparent, this usage is definitely non-standard; for more formal writing or speech, you'd want to stick to some variation of Joe spoke honestly or Joe was honest or Joe told the truth.
†a. trans. with it. To speak or act truly and honestly; to behave in accordance with the truth. Chiefly in to truth it in love. Cf. TRUTHIFY v. 1. Obs. rare (in later use chiefly U.S.).
Chiefly with reference or allusion to Ephesians 4:15 (see note in etymology).
1604 A. WILLET Thes. Ecclesiæ ix. 106 Saint Paul therefore saith, ἀλαθεύοντες εν̑ ἀγάπη, following the truth in loue, Ephes. 4.15... We must then loue in the truth, and truth it in loue.
b. intr. U.S. colloq. and regional. To tell the truth.
1888 St. Louis (Missouri) Post-Dispatch 27 Aug. 6/6 ‘Hip! Ar' ye truthin?’ exclaimed the girl as she sprang up.
[two more attestations, 1920 & 1923, omitted]
("truth, v." OED Online. Oxford University Press, June 2017. Definition 3.)
NB The OED is behind a paywall; if you don't have access, check with your local library, which may have a subscription.
The best antonym I can find given your example sentence is prevaricate.
Of the antonyms to prevaricate listed at those two sites, the several that make the most sense to me in context of your question are: assert, testify, confirm, and verify.
While all four of those words fundamentally mean, "to speak honestly," they all have baggage that might impact the meaning you're looking for.
Assert: aggressive or forceful context. Definitive, but not necessarily precise.
Testify: judicial or religious context. Witnessing an event.
Confirm: Assumes previous knowledge in the conversation.
Verify: Assumes a question of inauthenticity.
We would need more information about how you are using your sentence to give you a more precise answer.
Authenticity the quality of being authentic
a : worthy of acceptance or belief as conforming to or based on fact
Authenticity has come into popular usage when describing a person's demeanor, feelings or "way of being." I think it works for your sample sentence.