Document:

Exhibit 4.2

 

	
        NUMBER

        C-
	SHARES CUSIP 039562 103
	 	 
	SEE REVERSE FOR CERTAIN DEFINITIONS	 
	 	 

 

ARCHIMEDES TECH SPAC PARTNERS CO.

INCORPORATED
UNDER THE LAWS OF DELAWARE

COMMON STOCK

 

THIS
CERTIFIES THAT                         is
the owner of            FULLY PAID AND NON-ASSESSABLE SHARES OF COMMON
STOCK OF THE PAR VALUE OF $0.0001 EACH OF ARCHIMEDES TECH SPAC PARTNERS CO., transferable on the books of the Company in person
or by duly authorized attorney upon surrender of this certificate properly endorsed.

 

The
Company will be forced to liquidate if it is unable to complete an initial business combination within the time period set forth
in the Company’s Amended and Restated Certificate of Incorporation, as the same may be amended from time to time.

 

This
certificate is not valid unless countersigned by the Transfer Agent and registered by the Registrar.

 

Witness
the facsimile seal of the Company and the facsimile signatures of its duly authorized officers.

 

Dated:

 

	 	 	 
	President	 	Secretary

 

     

     

    

 

ARCHIMEDES TECH SPAC PARTNERS CO.

 

The Company will furnish
without charge to each stockholder who so requests, a statement of the powers, designations, preferences and relative, participating,
optional or other special rights of each class of equity or series thereof of the Company and the qualifications, limitations,
or restrictions of such preferences and/or rights. This certificate and the shares represented thereby are issued and shall be
held subject to all the provisions of the Company’s Amended and Restated Certificate of Incorporation and all amendments
thereto and resolutions of the Board of Directors providing for the issue of securities (copies of which may be obtained from the
secretary of the Company), to all of which the holder of this certificate by acceptance hereof assents.

 

The following abbreviations,
when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according
to applicable laws or regulations:

 

	TEN COM	–	as tenants in common	 	UNIF GIFT MIN ACT	–	________ Custodian ________
	TEN ENT	–	as tenants by the entireties	 	 	 	(Cust)                       (Minor)
	 	 	 	 	 	 	 
	JT TEN	–	as joint tenants with right of survivorship and not as tenants in common	 	 	 	
        under Uniform Gifts to Minors Act

        _____________________________

        (State)

 

Additional abbreviations may also be used
though not in the above list.

 

For value received,                      hereby
sells, assigns and transfers unto                     

 

PLEASE INSERT SOCIAL SECURITY OR OTHER
IDENTIFYING NUMBER(S) OF ASSIGNEE(S)

 

	 

(PLEASE PRINT OR TYPEWRITE NAME(S) AND ADDRESS(ES),
INCLUDING ZIP CODE(S), OF ASSIGNEE(S))

 

	 

 

	 

 

                              shares
of Common Stock represented by the within Certificate, and hereby irrevocably constitutes and appoints

 

                    Attorney
to transfer the said shares of Common Stock on the books of the within named Company with full power of substitution in the premises.

 

Dated:                    

 

	 	 
	 	Notice:  The signature(s) to this assignment must correspond with the name as written upon the face of the certificate in every particular, without alteration or enlargement or any change whatever.

 

Signature(s) Guaranteed:

 

	 	 
	THE SIGNATURE(S) MUST BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15 (OR ANY SUCCESSOR RULE).	 

 

The holder(s) of this certificate shall
be entitled to receive a pro-rata portion of the funds from the trust account only in the event that (i) the Corporation is forced
to liquidate because it does not consummate an initial business combination within the period of time set forth in the Corporation’s
Amended and Restated Certificate of Incorporation, as the same may be amended from time to time (the “Charter”)
or (ii) if the holder seeks to convert his shares upon consummation of, or sell his shares in a tender offer in connection with,
an initial business combination or in connection with certain amendments to the Charter. In no other circumstances shall the holder(s)
have any right or interest of any kind in or to the trust account.Exhibit 4.3

 

	NUMBER _________-	
        (SEE REVERSE SIDE FOR LEGEND)

        THIS WARRANT WILL BE VOID IF NOT EXERCISED PRIOR TO THE EXPIRATION
        DATE (DEFINED BELOW)
	WARRANTS

 

ARCHIMEDES TECH SPAC PARTNERS CO.

CUSIP 039562 111

 

WARRANT

 

THIS CERTIFIES
THAT, for value received ______, is the registered holder of a warrant or warrants (the “Warrant(s)”)
of Archimedes Tech SPAC Partners Co., a Delaware corporation (the “Company”), expiring at 5:00 p.m., New York
City time, on the five year anniversary of the Company’s completion of an initial merger, share exchange, asset acquisition,
stock purchase, recapitalization, reorganization or other similar business combination with one or more businesses or entities
(a “Business Combination”), to purchase one fully paid and non-assessable share of common stock, par value $0.0001
per share (“Shares”), of the Company for each Warrant evidenced by this Warrant Certificate. The Warrant entitles
the holder thereof to purchase from the Company, commencing on thirty days after the Company’s completion of an initial Business
Combination, such number of Shares of the Company at the Warrant Price (as defined below), upon surrender of this Warrant Certificate
and payment of the Warrant Price at the office or agency of Continental Stock Transfer & Trust Company (the “Warrant
Agent”), but only subject to the conditions set forth herein and in the Warrant Agreement between the Company and Continental
Stock Transfer & Trust Company. In no event will the Company be required to net cash settle any warrant exercise. The term
“Warrant Price” as used in this Warrant Certificate refers to the price per Share at which Shares may be purchased
at the time the Warrant is exercised. The initial Warrant Price per Share is equal to $11.50 per share. The Warrant Agreement provides
that upon the occurrence of certain events the Warrant Price, the Redemption Trigger Price (defined below) and the number of Shares
purchasable hereunder, set forth on the face hereof, may, subject to certain conditions, be adjusted.

 

No fraction of a Share
will be issued upon any exercise of a Warrant. If the holder of a Warrant would be entitled to receive a fraction of a Share upon
any exercise of a Warrant, the Company shall, upon such exercise, round up to the nearest whole number the number of Shares to
be issued to such holder.

 

Upon any exercise of
the Warrant for less than the total number of full Shares provided for herein, there shall be issued to the registered holder hereof
or the registered holder’s assignee a new Warrant Certificate covering the number of Shares for which the Warrant has not
been exercised.

 

Warrant Certificates,
when surrendered at the office or agency of the Warrant Agent by the registered holder in person or by attorney duly authorized
in writing, may be exchanged in the manner and subject to the limitations provided in the Warrant Agreement, but without payment
of any service charge, for another Warrant Certificate or Warrant Certificates of like tenor and evidencing in the aggregate a
like number of Warrants.

 

Upon due presentment
for registration of transfer of the Warrant Certificate at the office or agency of the Warrant Agent, a new Warrant Certificate
or Warrant Certificates of like tenor and evidencing in the aggregate a like number of Warrants shall be issued to the transferee
in exchange for this Warrant Certificate, subject to the limitations provided in the Warrant Agreement, without charge except for
any applicable tax or other governmental charge.

  

The Company and the
Warrant Agent may deem and treat the registered holder as the absolute owner of this Warrant Certificate (notwithstanding any notation
of ownership or other writing hereon made by anyone), for the purpose of any exercise hereof, of any distribution to the registered
holder, and for all other purposes, and neither the Company nor the Warrant Agent shall be affected by any notice to the contrary.

 

This Warrant does not
entitle the registered holder to any of the rights of a stockholder of the Company.

 

     

    

    

 

The Company reserves
the right to call the Warrant at any time prior to its exercise with a notice of call in writing to the holders of record of the
Warrant, giving at least 30 days’ notice of such call, at any time while the Warrant is exercisable, if the last sale price
of the Shares has been at least $18.00 per share (the “Redemption Trigger Price”) on each of 20 trading days
within any 30 trading day period (the “30-day trading period”) commencing after the Warrants become exercisable
and ending on the third business day prior to the date on which notice of such call is given and if, and only if, there is a current
registration statement in effect with respect to the Shares underlying the Warrants commencing five business days prior to the
30-day trading period and continuing each day thereafter until the date of redemption. The call price of the Warrants is to be
$0.01 per Warrant. Any Warrant either not exercised or tendered back to the Company by the end of the date specified in the notice
of call shall be canceled on the books of the Company and have no further value except for the $0.01 call price.

 

	By:	 	 	 
	 	President	 	Secretary

 

SUBSCRIPTION FORM

 

To Be Executed by the Registered Holder
in Order to Exercise Warrants

 

The undersigned Registered Holder irrevocably
elects to exercise ______________ Warrants represented by this Warrant Certificate, and to purchase the Common Stock issuable upon
the exercise of such Warrants, and requests that Certificates for such shares shall be issued in the name of

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

(PLEASE TYPE OR PRINT NAME AND ADDRESS)

 

_____________________________________________________________________________________

 

(SOCIAL SECURITY OR TAX IDENTIFICATION NUMBER)

 

and be delivered to _____________________________________________________________________

 

             (PLEASE
PRINT OR TYPE NAME AND ADDRESS)

 

and, if such number of Warrants shall not
be all the Warrants evidenced by this Warrant Certificate, that a new Warrant Certificate for the balance of such Warrants be registered
in the name of, and delivered to, the Registered Holder at the address stated below:

 

	Dated:	 
	 	(SIGNATURE)
	 	 
	 	 
	 	 
	 	 
	 	(ADDRESS)
	 	 
	 	 
	 	(TAX IDENTIFICATION NUMBER)

 

     

    

    

 

ASSIGNMENT

 

To Be Executed by the Registered Holder
in Order to Assign Warrants

 

For Value Received, _______________________ hereby sell, assign,
and transfer unto

 

	
        (PLEASE TYPE OR PRINT NAME AND ADDRESS)

         

	
         

         

	
         

         

(SOCIAL SECURITY OR TAX IDENTIFICATION NUMBER)

 

and be delivered to _______________________________________________________________________

(PLEASE PRINT OR TYPE NAME AND ADDRESS)

 

______________________ of the Warrants
represented by this Warrant Certificate, and hereby irrevocably constitute and appoint _________________________________ Attorney
to transfer this Warrant Certificate on the books of the Company, with full power of substitution in the premises.

 

	Dated:	 	 	 
	 	 	(SIGNATURE)

 

The
signature to the assignment of the Subscription Form must correspond to the name written upon the face of this Warrant Certificate
in every particular, without alteration or enlargement or any change whatsoever, and must be guaranteed by a commercial bank or
trust company or a member firm of the NYSE American, Nasdaq, New York Stock Exchange, Pacific Stock Exchange, or Chicago Stock
Exchange.

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