UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
 Washington, D.C. 20549
SCHEDULE 13G
Under the Securities Exchange Act of 1934
(Amendment No. 4)*
ARC DOCUMENT SOLUTIONS, INC.

(Name of Issuer)

Common Stock, par value $0.001 per share

(Title of Class of Securities)

00191G103

(CUSIP Number)

December 31, 2020

(Date of Event Which Requires Filing of this Statement)
Check the appropriate box to designate the rule pursuant to which this
Schedule is filed:
[X] Rule 13d-1(b)
[_] Rule 13d-1(c)
[_] Rule 13d-1(d)
*The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.
The information required in the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

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CUSIP NO.  00191G103                    13G                     Page 2 of 8 Pages
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(1)   NAMES OF REPORTING PERSONS.
       I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (entities only).

      Renaissance Technologies LLC      26-0385758
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(2)  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS):
      (a) [_]
      (b) [_]
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(3)  SEC USE ONLY

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(4) CITIZENSHIP OR PLACE OF ORGANIZATION

      Delaware
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                                                (5) SOLE VOTING POWER

     NUMBER OF SHARES                                    3,500,043
     BENEFICIALLY OWNED                         _____________________________
     BY EACH REPORTING
     PERSON WITH:                               (6) SHARED VOTING POWER

                                                           0
                                                _____________________________

                                                (7)  SOLE DISPOSITIVE POWER

                                                           3,847,523
                                                _____________________________

                                                (8)  SHARED DISPOSITIVE POWER

                                                          0
                                                ______________________________

(9)  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                              3,847,523
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(10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
      (SEE INSTRUCTIONS)
                                                                    [_]
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(11)  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                              8.77 %
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(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)
                      IA

                                Page 2 of 8 pages
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                                Page 3 of 8 pages
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 CUSIP NO.  00191G103                   13G                     Page 3 of 8 Pages
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 (1) NAMES OF REPORTING PERSONS.
      I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).

     RENAISSANCE TECHNOLOGIES HOLDINGS CORPORATION    13-3127734

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(2)  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)
      (a) [_]
      (b) [_]
-----------------------------------------------------------------------------
(3)  SEC USE ONLY

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(4) CITIZENSHIP OR PLACE OF ORGANIZATION

      Delaware
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                                                (5) SOLE VOTING POWER

     NUMBER OF SHARES                                    3,500,043
     BENEFICIALLY OWNED                         _____________________________
     BY EACH REPORTING
     PERSON WITH:                               (6) SHARED VOTING POWER

                                                           0
                                                _____________________________

                                                (7)  SOLE DISPOSITIVE POWER

                                                           3,847,523
                                                _____________________________
                                                (8)  SHARED DISPOSITIVE POWER

                                                           0
                                                _____________________________

(9)  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                              3,847,523
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(10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
      (SEE INSTRUCTIONS)
                            [_]
-----------------------------------------------------------------------------
(11)  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                              8.77 %
-----------------------------------------------------------------------------
(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)
                              HC

                                Page 3 of 8 pages
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 CUSIP NO.  00191G103                   13G                   Page 4 of 8 Pages
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Item 1.

    (a) Name of Issuer

        ARC DOCUMENT SOLUTIONS, INC.

    (b) Address of Issuer's Principal Executive Offices.

         12657 Alcosta Blvd, Suite 200, San Ramon, California 94583

Item 2.

    (a) Name of Person Filing:

         This Schedule 13G is being filed by Renaissance Technologies LLC
         ("RTC") and Renaissance Technologies Holdings Corporation ("RTHC").

     (b) Address of Principal Business Office or, if none, Residence.

         The principal business address of the reporting persons is:

                 800 Third Avenue
                 New York, New York  10022

     (c) Citizenship.

        RTC is a Delaware limited liability company, and
        RTHC is a Delaware corporation.

     (d) Title of Class of Securities.

         Common Stock, par value $0.001 per share

     (e) CUSIP Number.

         00191G103

                                        Page 4 of 8 pages
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Item 3. If this statement is filed pursuant to Rule 13d-1(b) or 13-d-2(b)
        or (c),check whether the person filing is a:

(a) [_]  Broker or dealer registered under section 15 of the Act.
(b) [_]  Bank as defined in section 3(a)(6) of the Act.
(c) [_]  Insurance Company as defined in section 3(a)(19) of the Act.
(d) [_]  Investment Company registered under section 8 of the Investment
         Company Act.
(e) [x]  Investment Adviser in accordance with Sec.240.13d-1(b)(1)(ii)(E).
(f) [_]  Employee Benefit Plan or Endowment Fund in accordance with
         Sec. 240.13d-1(b)(1)(ii)(F).
(g) [_]  Parent holding company, in accordance with Sec.240.13d-1(b)(1)(ii)(G).
(h) [_]  A savings associations as defined in Section 3(b) of the Federal
         Deposit Insurance Act.
(i) [_]  A church plan that is excluded from the definition of an investment
         company under section 3(c)(14) of the Investment Company Act of 1940.
(j) [_]  Group, in accordance with Sec.240.13d-1(b)(1)(ii)(J).

Item 4. Ownership.

    (a) Amount beneficially owned.

        RTC:     3,847,523      shares
        RTHC:    3,847,523      shares, comprising the shares beneficially owned
                        by RTHC, because of RTHC's majority ownership of RTC.

    (b) Percent of Class.

        RTC:    8.77 %
        RTHC:   8.77 %

    (c)  Number of shares as to which the person has:

         (i) sole power to vote or to direct the vote:

             RTC:    3,500,043
             RTHC:   3,500,043

         (ii) Shared power to vote or to direct the vote:       0

         (iii) sole power to dispose or to direct the disposition of:
                RTC:    3,847,523
                RTHC:   3,847,523

          (iv)  Shared power to dispose or to direct the disposition of:

                RTC:    0
                RTHC:   0

                                        Page 5 of 8 pages
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Item 5. Ownership of Five Percent or Less of a Class.

        If this statement is being filed to report the fact that as of the
        date hereof the reporting person has ceased to be the beneficial
        owner of more than five percent of the class of securities,
        check the following:  [_]

Item 6. Ownership of More than Five Percent on Behalf of Another Person.

        Certain funds and accounts managed by RTC have the right to receive
        dividends and proceeds from the sale of the securities which are
        the subject of this report.

Item 7. Identification and Classification of the Subsidiary Which Acquired
        the Security Being Reported on by the Parent Holding Company.

             Not applicable

Item 8. Identification and Classification of Members of the Group.

             Not applicable

Item 9. Notice of Dissolution of a Group.

             Not applicable

                                        Page 6 of 8 pages
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Item 10. Certification

By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were acquired and are held in the ordinary
course of business and not acquired and are not held for the purpose of or
with the effect of changing or influencing the control of the issuer of the
securities and were not acquired and are not held in connection with or as
a participant in any transaction having that purpose or effect.

                                   SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete
and correct.

Date:  February 10, 2021

                              Renaissance Technologies LLC

                              By: /s/ James S. Rowen
                                  Chief Operating Officer

                              Renaissance Technologies Holdings Corporation

                              By: /s/ James S. Rowen
                                  Vice President

Attention: Intentional misstatements or omissions of fact constitute
Federal criminal violations (See 18 U.S.C. 1001).

                                        Page 7 of 8 Pages
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                                EXHIBIT 99.1

                AGREEMENT REGARDING JOINT FILING

                UNDER RULE 13D-1(K) OF THE EXCHANGE ACT

In accordance with Rule 13d-1(k) under the Securities Exchange Act of 1934,
as amended, each of the undersigned agrees to the filing on behalf of each
of a Statement on Schedule 13G, and all amendments thereto, with respect to
the shares of Common Stock, par value $0.001 per share of
ARC DOCUMENT SOLUTIONS, INC.

Date:  February 10, 2021

                                      Renaissance Technologies LLC

                                      By:  /s/ James S. Rowen
                                           Chief Operating Officer

                                        Renaissance Technologies Holdings Corporation

                                          By: /s/ James S. Rowen
                                              Vice President

                                        Page 8 of 8 Pages