A חתיכה הראויה להתכבד — a (whole) piece fit to be served before guests — has, like a בריה, a status of חשיבות and is not nullified, even in a thousand; it must be forbidden in itself (נבילה, בשר בחלב) and not through an absorbed taste, it must be whole (a cut or crushed piece is nullified), and one does not attribute the cut to the forbidden piece (Shulchan Aruch, Yoreh De'ah 101 — 9 se'ifim)
חֲתִיכָה הָרְאוּיָה לְהִתְכַּבֵּד בָּהּ לִפְנֵי הָאוֹרְחִים — כְּמוֹ בְּרִיָּה, אֲפִלּוּ בְּאֶלֶף לֹא בְּטֵלָה, וַאֲפִלּוּ הִיא אֲסוּרָה בַּהֲנָאָה, וַאֲפִלּוּ אֵין אִסּוּרָהּ אֶלָּא מִדְּרַבָּנָן. אֲבָל אִם נוֹלַד סָפֵק בַּדָּבָר — מְקִלִּין, מִשּׁוּם דַּהֲוֵי סְפֵקָא דְּרַבָּנָן.
A piece fit to be served before the guests — like a beriah — is not nullified even in a thousand, even if it is forbidden in benefit, and even if its prohibition is only rabbinic. But if a doubt arises about it, one is lenient, since it is a rabbinic doubt.
Shulchan Aruch, Yoreh De'ah 101:1LEVEL 01
Hebrew text of the 9 se'ifim with a fluent English translation. The piece fit to be served (חהל״ה), a prohibition מחמת עצמה, an unplucked fowl and a gizzard according to custom, the whole piece that is nullified once cut, and identifying a טריפה explained with practical cases.
📖 StudyLEVEL 02
In-depth pilpul: the sugya of Chullin and Beitzah, whether 'not nullified' is by Torah law or rabbinic (Taz sk1-2), the חשיבות of the חהל״ה compared to a בריה, the yesod of מחמת עצמה against טעם בלוע, the debate on שלם / נחתך, the מִמַּה נַּפְשָׁךְ of se'if 7, חקירות and נפקא מינות.
📖 StudyLEVEL 03
Comparative tables (מחמת עצמה / טעם בלוע, שלם / נחתך-נתרסק, what is 'fit' or not according to custom), golden rules, classic pitfalls (ספק להקל, כדי קליפה, אין מבטלין, אין תולין) and memorization of the 9 se'ifim.
📖 StudyLEVEL 04
The practical halacha according to the Shach, Taz, Pri Megadim and Pitchei Teshuva (the Torah-law / rabbinic debate, the Radbaz on a טריפה that became חהל״ה, the Chatam Sofer), then the Sephardic poskim (Yabia Omer, Yalkut Yosef, Or LeTzion) and Ashkenazi poskim. Note: the Shulchan Aruch HaRav does not deal with this siman — this is a level of psak, not "Daat HaRav".
📖 StudyAccording to the Shulchan Aruch (YD 101:1), a piece fit to be served before guests (חתיכה הראויה להתכבד) has, like a בריה, a status of חשיבות (importance) and is not nullified, even in a thousand (אפילו באלף לא בטלה), even if it is forbidden in benefit and even if its prohibition is only rabbinic. The Taz (sk1-2) explains that this very 'not nullified' is itself rabbinic (by Torah law it is nullified); practical consequence: in a case of doubt one is lenient (a rabbinic doubt). For practical halacha, consult your Rav.
Only a prohibition in itself (מחמת עצמה) — such as a נבילה or meat that became בשר בחלב — confers the 'not nullified' status (se'if 2). But a permitted piece that became forbidden only through an absorbed taste (טעם שבלעה מאיסור), or a piece forbidden only כדי קליפה (the thickness of a peel), is nullified and is not a חתיכה הראויה להתכבד. The Taz (sk4) explains that an absorbed taste is not 'fit to be served'. For practical halacha, consult your Rav.
The piece keeps this status only while it is whole (שלם): if it was cut (נחתכה) or crushed (נתרסקה), it is nullified by majority — even after the mixture and even if still recognizable (se'if 6) — except if it was cut deliberately in order to nullify it (אין מבטלין איסור לכתחילה). And when a forbidden fit piece became mixed with permitted ones and one of them was cut, one does not attribute the cut to the forbidden piece (אין תולין) to permit everything: מִמַּה נַּפְשָׁךְ — if the forbidden one was cut it is nullified, but if a permitted one was cut, the forbidden one is still whole and not nullified (se'if 7). For practical halacha, consult your Rav.