Lexical Definition

‎ὑπόστασις‎ hypóstasis (hoop-os'-tas-is) confidence/essence ^G:N-F
from a compound of ‎ὑπό‎ and ‎ἵστημι‎

confidence, confident, person, substance.

• a setting under (support), i.e. (figuratively) concretely, essence, or abstractly, assurance (objectively or subjectively)

Abbott-Smith

ὑπό-στασις, -εως, ἡ (< ὑφίστημι, to set under, stand under, support) [in LXX for מַצָּב (I Ki 13:23 14:4 B), תִּקְוָה (Ru 1:12, Ez 19:5), etc., also in Wi 16:21 ;]
1. a support, base or foundation (in various senses).
2. substance (Arist., al.; opp. to φαντασία, ἔμφασις): He 1:3
3. steadiness, firmness (Polyb., al.), hence, assurance, confidence: II Co 9:4 11:17, He 3:14 11:1 (here perhaps title-deed, as that which gives reality or guarantee; v. MM, xxv).†

Abbott-Smith References

Liddell-Scott-Jones

ὑπόστασις, εως, ἡ,

(ὑφίστημι, ὑφίσταμαι): as an act, standing under, supporting, ἡ κεφαλὴ τοῦ μηροῦ καὶ ὁ αὐχὴν τοῦ ἄρθρου.. ὑπὸ συχνῷ μέρει τοῦ ἰσχίου τὴν ὑ. πεποίηται [LXX+5th c.BC+]

__2 resistance, τοῦ κύματος [Refs 4th c.BC+] (unless = settling down); so perhaps in [Refs 5th c.BC+]
__3 lying in ambush, [Refs 5th c.BC+]
__B as a thing,
__B.I in liquids, that which settles at the bottom, sediment, [Refs 5th c.BC+]; especially of sediment in the urine, [Refs 5th c.BC+]; but the urine itself is called ἡ ὑ. ἡ εἰς τὴν κύστιν, [Refs 4th c.BC+]
__B.I.b an accumulation of pus, abscess, [Refs 5th c.BC+]
__B.I.2 νέφους ὑποστάσεις cloud-cumuli, [Refs 1st c.BC+]
__B.I.3 a kind of jelly or thick soup, in plural, [Refs 4th c.BC+]
__B.I.4 metaphorically of time, duration, ἡ στιγμιαία τῶν καιρῶν ὑ. [Refs 2nd c.AD+]; μνήσθητι τίς μου ἡ ὑ. remember how short my time is, [LXX]; ἡ ὑ. μου ὡσεὶ οὐθὲν ἐνώπιόν σου mine age is as nothing before thee, [Refs]; ἐφ᾽ ὅσον αὐτοῦ (i.e. Ἕκτορος) ἡ ὑ. τῶν χρόνων ὑπῆρχεν as long as his store of years lasted, [Refs 2nd c.AD+]
__B.I.5 coming into existence, origin, ἡ ὑ. μου ἐν τοῖς κατωτάτω τῆς γῆς [LXX+1st c.AD+]; ἀκμὴ οὐδὲ ἔχει γενέσεως ὑ. καθ᾽ ἑαυτήν has no power of originating by itself, [Refs 2nd c.AD+]
__B.II foundation or substructure of a temple, etc., [LXX+1st c.BC+]; ὑποστάσεις ἐπάλξεων lower part of a crenellated wall, [Refs 3rd c.BC+]; ὑ. ξύλου is falsa lectio for{ὑπότασις ξ}. in [Refs 5th c.BC+]
__B.II.2 metaphorically of a narrative, speech, or poem, ground-work, subject-matter, argument, [Refs 2nd c.BC+]
__B.II.3 plan, purpose, [Refs]; οἱ Αἰγύπτιοι.. ἰδίᾳ τινὶ ὑ. κεχρημένοι εἰσί (i.e. in their calendar) [Refs 1st c.BC+]
__B.II.4 confidence, courage, resolution, steadiness, of soldiers, [Refs 2nd c.BC+]; hope, ἔστι μοι ὑ. τοῦ γενηθῆναί με ἀνδρί [LXX]; ἀπώλετο ἡ ὑ. αὐτῆς[LXX+NT]; ἔστιν δὲ πίστις ἐλπιζομένων ὑπόστασις confidence in things hoped for, [NT] (unless substance be the right sense here).
__B.II.5 undertaking, promise, οἱ ὑπογεγραμμένοι γεωργοὶ ἐπέδωκαν ἡμῖν ὑπόστασιν [Refs 3rd c.BC+]
__B.II.6 Astrology texts, τὰ τούτου (i.e. κλήρου τύχης) τετράγωνα ὑπόστασις (perhaps -στάσεις) [λέγεται] [Refs 2nd c.BC+]
__B.III substantial nature, substance, δύσσχιστα, τῷ κολλώδη τὴν ὑ. ἔχειν woods hard to cleave, because of their resinous substance, [Refs 4th c.BC+]
__B.III.2 substance, actual existence, reality (οἱ νεώτεροι τῶν φιλοσόφων ἀντὶ τῆς οὐσίας τῇ λέξει τῆς ὑ. ἐχρήσαντο [Refs 5th c.BC+]; τῶν ἐν ἀέρι φαντασμάτων τὰ μέν ἐστι κατ᾽ ἔμφασιν, τὰ δὲ καθ᾽ ὑπόστασιν (substantial, actual), [Refs 4th c.BC+]; so ὑποστάσεις are the substances of which the reflections (αἱ κατοπτρικαὶ ἐμφάσεις) appear in the mirror, [Refs]; ὑ. ἔχειν have substantial existence, [Refs 2nd c.BC+]; ἰδίᾳ χρησάμενον ὑποστάσει (ὑποτάσει codex), πρὸς ἰδίαν ὑ. φυτευθέντα, a separate existence, [Refs 2nd c.AD+]; [ἡ παρασιτικὴ] διαφέρει καὶ τῆς ῥητορικῆς καὶ τῆς φιλοσοφίας.. κατὰ τὴν ὑ. (in respect of reality) · ἡ μὲν γὰρ ὑφέστηκεν, αἱ δὲ οὔ [Refs 2nd c.AD+]
__B.III.3 real nature, essence, χαρακτὴρ τῆς ὑ. [NT]
__B.IV as a Rhet. figure, the full expression or expansion of an idea, [Refs 2nd c.AD+]
__B.V ={ὑπόστημα} [Refs]camp, [LXX]
__B.VI wealth, substance, property,[LXX+3rd c.AD+]
__B.VI.2 plural, title deeds, documents recording ownership of property, [Refs 2nd c.AD+]

_{LSJ Scripture Refs: LXX.Ps.68.3* ☩ LXX.Ps.88.48* ☩ LXX.Ps.138.15* ☩ LXX.Nah.2.7* ☩ LXX.Ruth.1.12 ☩ LXX.Ezek.19.5 ☩ Heb.3.14 ☩ 2Cor.11.17 ☩ Heb.11.1 ☩ Heb.1.3 ☩ LXX.1Kgs.13.23 ☩ LXX.Deut.11.6 ☩ LXX.Jer.10.17}