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                                                                   Exhibit 10.58

                            Pledge Security Agreement
                      (Instruments, Stock, Possessed Goods)

      THIS AGREEMENT is made between FLEET NATIONAL BANK, its successors and
assigns ("Bank") and NYSERNet.net, Inc. ("Grantor") with an address of 100
Elwood Davis Road, Syracuse, New York 13212.

      1.    DEFINITIONS.  Unless otherwise indicated in this Agreement,
all terms shall have the same meanings as given to them in the Uniform
Commercial Code as amended from time to time in the State of New York.

      (a)   "Debtor" means: (choose and complete ONE of the following
            choices for Section a)

            ----------
                  x     AppliedTheory Corporation. with an address of:
            ----------  1500 Broadway, New York, NY 10036

      (b)   "Collateral" means the personal property described in the Schedule A
            attached to this Security Agreement which is made part hereof
            together with all additions, replacements, and proceeds in any form
            thereof. The Schedule may be supplemented from time to time by
            additional Schedules signed by both Grantor and Bank and attached to
            or which specifically reference this Agreement.

      (c)   "Liabilities" shall have the meaning provided in Schedule "B"
            attached hereto.

      (d)   "Required Value" means the fair market value of Collateral which the
            Bank requires must be maintained at all times, as follows (and as
            shown on any supplemental schedules attached to this Agreement from
            time to time): See Attached Schedule "A".

      2. SECURITY INTEREST. The Grantor hereby pledges, assigns, and grants to
Bank a security interest in the Collateral to secure the payment and performance
of the Liabilities. This security interest is specifically intended to be a
continuing interest and shall cover Collateral in which the Grantor acquires an
interest after the date of this Agreement as well as Collateral in which Grantor
now has an interest. This security interest shall continue until terminated as
described in this Agreement even if all Liabilities are paid in full from time
to time. Bank shall have the right to apply Collateral and any proceeds
therefrom to all or any part of the Liabilities as and in the order Bank may
elect, whether such Liabilities are otherwise secured and whether due or not.

      3. FIRST LIEN/COLLATERAL STATUS. Except for the pledge and security
interest granted hereby and any other interests to which the Bank has consented
in writing, Grantor is the owner of the Collateral free from all liens,
encumbrances, and security interests. Grantor will not sell or transfer the
Collateral or any interest therein (including, without limitation, a security
interest) without the prior written consent of the Bank. Grantor will defend the
Collateral against the claims and demands of all persons, and will cause the
immediate removal and termination of any levy, execution, judgment or other
lien, or similar claim of third persons to the Collateral.

      Grantor represents and warrants that each instrument or evidence
constituting a part of the Collateral is genuine and in all respects what it
purports to be. Grantor will deliver to the Bank upon its request information
regarding any restrictions on transferability or marketability of the
Collateral, including without limitation information regarding holding periods
and affiliate relationships.

      4. PERFECTION OF SECURITY INTEREST. The Grantor will deliver the
certificates, instruments, or other evidence of the Collateral to the Bank or to
its designee or bailee. Grantor will execute and deliver to Bank such financing
statements, security agreements, assignments, and other papers, as Bank may at
any time or from time to time reasonably request. Grantor hereby authorizes Bank
to execute and file financing statements with or without the
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signature of the Grantor from time to time as Bank may deem necessary or
desirable. Grantor hereby appoints Bank as its attorney in fact to execute and
deliver notices of lien, financing statements, assignments, and any other
documents, notices, and agreements necessary for the perfection of the Bank's
security interests in the Collateral. Grantor agrees to pay the costs of filing
or perfection of the Bank's security interests, searches of the public records,
and releases or assignments of the Banks interests.

      5. TAXES. Grantor will pay promptly, when due, all taxes and assessments
upon the Collateral or its use or operation, or upon this Agreement.

      6. PROTECTION OF BANK'S INTEREST. Seven or more days after the day the
Bank mails the Grantor notice, upon failure of the Grantor to (i) remove liens
or interests prohibited by Section 3 of this Agreement, or (ii) pay taxes or
assessments as required by Section 5 of this Agreement, the Bank in its
discretion may discharge any such liens or interests or, pay taxes or
assessments. Bank also may pay any costs of perfection, searches, releases, or
assignments pursuant to Section 4 of this Agreement. Grantor agrees to reimburse
Bank on demand for any and all expenditures so made, and until paid the amount
thereof also shall be part of the Liabilities secured by the Collateral. Bank
shall have no obligation to Grantor or Debtor to make any such expenditures nor
shall the making thereof relieve any default hereunder.

      7. REQUIRED VALUE OF COLLATERAL. The Grantor will assure that the fair
market value of the Collateral is at least the Required Value at all times. Upon
request of the Bank, the Grantor will provide evidence of the value of the
Collateral. Grantor will deliver to the Bank, in form acceptable to the Bank,
such additional Collateral as may be required to maintain Collateral of the
Required Value.

      8. INCOME AND DISTRIBUTIONS. Until the occurrence of an Event of Default,
Grantor shall have the right to receive all cash income from the Collateral.
Whether or not such an Event of Default has occurred, Bank shall have the right,
and Grantor authorizes the Bank: (i) to receive and hold as part of the
Collateral any new or additional securities issued by the issuer of any
Collateral which have been issued to Grantor with respect to the Collateral, and
any income from (except cash,) increases in or profits on the Collateral
including stock or other dividends, and (ii) to receive any distribution upon
dissolution and liquidation of the Issuer of any Collateral, upon surrender of
such Collateral or any part thereof in exchange therefore and to hold the net
cash receipts from any such distributions as part of the Collateral. If Grantor
receives any of the items to which Bank has the right under this paragraph,
Grantor shall hold the same in trust for Bank and shall deliver the same
immediately to Bank.

      9. CERTAIN BANK RIGHTS. The Bank may (without any obligation to do so),
after an Event of Default, without notice to the Grantor and whether or not the
Liabilities shall then become due and payable: (i) transfer Collateral into its
name or that of its nominee and may receive the income and any distributions
thereon and hold the same as Collateral for the Obligations, (ii) notify parties
obligated on any of the Collateral of Bank's rights hereunder; (iii) enforce
collection of any of the Collateral by suit or otherwise; (iv) release, exchange
or surrender any part of the Collateral; (v) compromise, extend, increase or
renew for any period or change the time of payment of any indebtedness evidenced
by the Collateral; (vi) take control of any proceeds of the Collateral; (vii)
perform any obligations of the Grantor hereunder; and (viii) upon an Event of
Default direct the order or manner of the disposition of the Collateral and any
and all other Collateral and the enforcement of any and all endorsements and
guaranties relating to the Liabilities or any part thereof as the Bank may, in
its sole discretion, determine.

      10. DEFAULT. The following events or conditions shall be an "Event of
Default" under this Agreement: (a) any default with respect to any of the
Liabilities and the expiration of any applicable grace period, (b) any failure
to comply with any term of this Agreement, (c) any representation or warranty
made to Bank by Grantor in this Agreement proving false or misleading in any
material respect as of the date made, (d) loss, theft, material damage or
destruction of the Collateral, or (e) the Collateral declines in value below the
Required Value and the Collateral is not restored to its Required Value within
two (2) business days of notice (which notice may be by telephone or telecopy)
from the Bank to the Grantor. These Events of Default are not intended to affect
in any way the Liabilities payable on demand and shall not prejudice the Bank's
rights to demand payment of any such Liabilities at any time


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      11. REMEDIES. Upon the occurrence of an Event of Default, the Bank may
declare all of the Liabilities to be immediately due and payable and Bank shall
have the rights and remedies of a secured party under the Uniform Commercial
Code of the State of New York as amended from time to time in any jurisdiction
where enforcement of this Agreement is sought in addition to all other rights
and remedies at law or in equity, Grantor and Debtor agree that notice of the
time and place of public sale of any of the Collateral or of the time after
which any private sale thereof is to be made or of other disposition of the
Collateral shall be deemed reasonable notice seven days after such notice is
deposited in the mail, certified or registered mail, return receipt requested,
postage prepaid or otherwise delivered to Grantor and Debtor at the addresses
shown in the preamble and Section 1 of this Agreement respectively.

      In addition to its other rights, the Bank may but shall not be obligated
to notify any parties, which are obligated to pay Grantor any Collateral or
proceeds thereof, to make all payments directly to Bank, Grantor authorizes such
parties to make such payments directly to Bank and to rely on notice from the
Bank without further inquiry, Bank may demand and take all necessary or
desirable steps to collect such Collateral in either Bank's or Grantor's name,
with the right to enforce, compromise, settle, or discharge any of the
foregoing. Bank may endorse Grantor's name on any checks, commercial paper,
instruments, and the like pertaining to the foregoing.

      Other than for its gross negligence or willful misconduct, the Bank shall
not be responsible to Grantor for loss or damage resulting from the Bank's
failure to enforce or collect any Collateral or any monies due or to become due
thereunder. Bank shall have no obligation to take, and Grantor shall have the
sole responsibility for taking, any and all steps to preserve rights against any
and all prior parties to any Collateral, whether or not in Bank's possession.

      After an Event of Default, the Grantor shall receive as the sole property
of the Bank and hold in trust for the Bank all monies, checks, notes, drafts,
and other property (collectively called "items of payment") representing the
proceeds of any Collateral.

      The rights of the Bank are cumulative, and the Bank may enforce its rights
under this Agreement irrespective of any other collateral, guaranty, right, or
remedy it may have. The exercise of all or a part of its rights or remedies
hereunder shall not prevent the Bank from exercising at the same or any other
time any other right or remedy with respect to the Liabilities. The Grantor
authorizes the Bank in its sole discretion to direct the order or manner of the
disposition of the Collateral.

      From the proceeds realized from the Collateral, the Bank shall be entitled
to retain all sums secured hereby as well as its reasonable expenses of
collection including without limitation those of retaking, holding,
safeguarding, accounting for, preparing for sale, selling and reasonable
attorneys' fees and legal expenses. If the proceeds realized from the Collateral
are not sufficient to defray said expenses and to satisfy the balance due on the
Liabilities, the Grantor shall remain liable for such expenses and Debtor shall
remain liable for such expenses and any deficiency with respect to the
Liabilities. Any payments or proceeds from realization on the Collateral may be
applied to the Liabilities in whatever order or manner the Bank elects.

      12. NON RECOURSE. The obligations and liability of Grantor hereunder shall
be enforceable solely against the Collateral and Grantor shall not be personally
liable for payment or satisfaction of any of the Liabilities or any liability
under or arising out of this Agreement. Notwithstanding anything to the contrary
contained in this Agreement, the Bank waives any right of setoff, lien or
security interest, whether now existing or hereafter arising, upon and against
any and all deposits, balances or other property not constituting Collateral now
or hereafter in the possession, custody, safekeeping or control of the Bank or
any entity under the control of FleetBoston Financial Corporation, its
successors and assigns, or in transit to any of them.

      13. IRREVOCABLE PROXY. If the Collateral consists of or includes stock,
Grantor irrevocably constitutes and appoints Bank, whether or not the Collateral
has been transferred into the name of Bank or its nominee, as Grantor's proxy
with full power, in the same manner, to the same extent and with the same effect
as if Grantor were to do the same: (a) to attend all meetings of stockholders of
the issuer of any of the Collateral (the Company") held from the date hereof and
to vote the Collateral at such meeting in such manner as Bank shall at its sole
discretion deem appropriate, including without limitation, in favor of
liquidation of the Company; (b) to


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consent at the sole discretion of Bank to any and all action by or with respect
to the Company for which the consent of the stockholders to the Company is or
may be necessary or appropriate; and (c) without limitation to do all things
which Grantor can or could do as a stockholder of the Company, giving to Bank
full power of substitution or revocation; provided, however, that this proxy
shall not be exercisable by Bank, and Grantor alone shall have the foregoing
powers so long as no Event of Default has occurred; and further provided that
after the occurrence of an Event of Default, this proxy shall be effective only
if the Bank so elects. This proxy shall terminate when this Agreement is no
longer in force. Grantor hereby revokes any proxy heretofore given by Grantor to
any person with regard to any of the Collateral and agrees not to give any other
proxies in derogation hereof until this Agreement is no longer in force.

      14. CONTINUING AGREEMENT/TERMINATION. This is a continuing and irrevocable
Agreement, and no notice of the creation or existence of the Liabilities need be
given to Grantor. This security interest shall continue in effect
notwithstanding that from time to time no Liabilities may exist. This Agreement
may be terminated only (i) by a written agreement of the Bank, or (ii) upon
written request of Grantor at such time as the Liabilities have been satisfied
in full and the Bank has no remaining commitments to Debtor of any kind.

      15. NO WAIVER. Grantor agrees that no representation, promise, or
agreement made by the Bank or by any officer or employee of Bank, at, prior, or
subsequent in the execution and delivery of this Agreement shall modify, alter,
limit, or otherwise abridge the rights and remedies of the Bank hereunder unless
agreed by Bank in writing. None of the rights and remedies of Bank hereunder
shall be modified, altered, limited, or other otherwise abridged or waived by
any representation, promise, or agreement hereafter made or by any course of
conduct hereafter pursued by the Bank. No delay or omission on the part of the
Bank in exercising any right hereunder shall operate as a waiver of such right
or of any other right under this Agreement, and waiver of any right shall not be
deemed waiver of any right unless expressly agreed by the Bank in writing.

      16. JOINT AND SEVERAL LIABILITY. If there is more than one Grantor
hereunder, their representations, warranties, abilities, and obligations
hereunder shall be joint and several.

      17. LAWS/WAIVER OF JURY TRIAL. The validity, Construction, and performance
of this Agreement shall be governed by the laws of the State of New York,
GRANTOR AND BANK MUTUALLY HEREBY KNOWINGLY, VOLUNTARILY AND INTENTIONALLY WAIVE
THE RIGHT TO A TRIAL BY JURY IN RESPECT OF ANY CLAIM BASED HEREON, ARISING OUT
OF, UNDER OR IN CONNECTION WITH THE NOTE OR ANY OTHER LOAN DOCUMENTS
CONTEMPLATED TO BE EXECUTED IN CONNECTION HEREWITH OR ANY COURSE OF CONDUCT,
COURSE OF DEALINGS, STATEMENTS (WHETHER VERBAL OR WRITTEN) OR ACTIONS OF ANY
PARTY, THIS WAIVER CONSTITUTES A MATERIAL INDUCEMENT FOR BANK TO ACCEPT THE NOTE
AND TAKE THE LOAN.

      18. PARTIES IN INTEREST. All of the terms and provisions of this Agreement
shall inure to the benefit of and be binding upon and be enforceable by their
respective heirs, executors, legal representatives, successors, and assigns of
the parties hereto.

      19. SEVERABILITY. Any partial invalidity of tile provisions of this
Agreement shall not invalidate the remaining portions hereof or thereof.


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      20. MISCELLANEOUS. Grantor hereby expressly waives demand, presentment,
protest, or notice of dishonor on any and all of the Liabilities and with
respect to the Collateral.

Grantor:    NYSERNet.net,Inc.


By:         Anthony Jiga

            /s/ Anthony Jiga
            --------------------------------------------------
Title:      Treasurer

Dated as of January 3, 2001

      I/We acknowledge receipt of a copy of this Security Agreement and agree
with the terms thereof insofar as it is applicable to me/us.

Debtor:     AppliedTheory Corporation

By:         David A. Buckel

            /s/ David A. Buckel
            ------------------------------------------------
Title:      Chief Financial Officer

Dated as of January 3, 2001


WARNING: IT IS A CRIMINAL OFFENSE IN NEW YORK STATE FOR A DEBTOR TO KNOWINGLY
      SELL OR OTHERWISE DISPOSE OF COLLATERAL IN CONTRAVENTION OF THE TERMS OF A
      SECURITY AGREEMENT.


                     SCHEDULE A TO PLEDGE SECURITY AGREEMENT

I.    This Security Agreement applies to the following types of Collateral:

That Custody Account established by Grantor to the Bank under a Custody
Agreement dated January 7, 1998, such Custody Account being numbered 00014 32
1650 including all investments, certificated and uncertificated securities,
investment securities, equities, securities, instruments, stock, mutual funds,
unit trusts, notes, bonds, debentures and other property of every nature or
description and all dividends, interest and proceeds of every nature and
description at any time and from time to time credited to or forming a part of
such accounts.

II.   Additional Conditions:

The Required Value (the "Required Value") of the Collateral shall not be less
than the $7,500,000.00 maximum dollar amount of the Liabilities of the Debtor's
to the Bank under that certain Note Agreement dated as of January 3 , 2001
between AppliedTheory Corporation, as Borrower (the "Debtor") and the Bank as
such Note Agreement may from time to time be amended, modified or supplemented,
provided specifically however that in determining the dollar amount of the
Collateral, cash and cash equivalents shall be valued at one hundred percent
(100%), government securities shall be valued at ninety percent (90%), corporate
securities shall be valued at eighty percent (80%) and corporate equities with a
market value in excess of $10.00 per share shall be valued at seventy percent
(70%),

See Attached Schedule "B" for additional terms.


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                                  SCHEDULE "B"
                          TO PLEDGE SECURITY AGREEMENT
                      (INSTRUMENTS, STOCK, POSSESSED GOODS)



The following provisions are incorporated in to and form a part of the Pledge
Security Agreement (Instruments, Stock, Possessed Goods) between Fleet National
Bank ("Bank") and NYSERNet.net, Inc. ("Grantor") dated as of January 3, 2001.

      1. The term "Liabilities" means all indebtedness, liabilities, and
obligations of every kind or nature of AppliedTheory Corporation ("Debtor")
arising under or relating to that certain Note Agreement dated as of January 3,
2001 as in effect on the date hereof (the "Note Agreement"), such liabilities,
indebtedness and obligations of the Debtor to the Bank to specifically include,
but not be limited to principal, interest, fees and expenses of the Bank
required to be paid by the Debtor to the Bank under such Note Agreement. The
Note Agreement may not be amended, modified or supplemented without the prior
written consent of Grantor.

      2. Notwithstanding anything to the contrary contained in this Pledge
Security Agreement (Instruments, Stock, Possessed Goods), until the earlier of:

            a. one hundred fifty (150) days subsequent to the occurrence of an
Event of Default under the Note Agreement, or

            b. the filing by or against Debtor of a petition in bankruptcy or a
petition seeking reorganization or to effect a plan, composition or other
arrangement with creditors under any federal or state law relating to
bankruptcy, insolvency or relief of debtors, or

            c. the filing by or against Grantor of any petition in bankruptcy or
seeking reorganization or to effect a plan, composition or other arrangement
with creditors under any federal or state law relating to bankruptcy, insolvency
or relief of debtors,

the Bank agrees that the Bank will not exercise its remedies under Section 11 of
this Pledge Security Agreement (Instruments, Stock, Possessed Goods) or any
other remedies it may have against the Grantor or the Collateral, provided,
specifically however, that notwithstanding Section 3 below of this Schedule B,
during the period described in this Section 2, Grantor shall not be entitled to
make any withdrawals from the Collateral.

      3. The Bank agrees that subject to Section 2 immediately above, prior to
the occurrence of an Event of Default, Grantor shall have the right not more
frequently than monthly on a date specified by the Bank each month, to (a)
receive all cash income received as Collateral during the month preceding the
date of such withdrawal, and (b) to withdraw "Excess Collateral" (such quoted
term being defined as Collateral in excess of Collateral having the Required
Value specified by this Agreement, as determined by the Bank), provided that
Grantor shall not be entitled to any withdrawal from the Collateral if such
withdrawal would reduce the value of the
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Collateral remaining after such withdrawal below the Required Value, all as
calculated by the Bank.

      4. Prior to the occurrence of an Event of Default under the Note Agreement
or this Agreement (including the expiration of any applicable grace or cure
period), Grantor shall have the right to the extent and as provided for in the
Custody Agreements dated as of January 7, 1998 between the Grantor and the Bank,
to instruct the Bank with respect to the investment of Collateral, provided that
nothing in this sentence shall be deemed to alter the parties understanding that
the Bank shall hold the Collateral subject to the terms of this Pledge Security
Agreement.

      5. In the event of a conflict between the terms of this Pledge Security
Agreement and either or both of the Custody Agreements dated January 7, 1998
between the Grantor and the Bank, the terms of this Pledge Security Agreement
shall govern.



                                          FLEET NATIONAL BANK



                                          By: /s/ David A. Kavney
                                              --------------------------------
                                              David A. Kavney, Vice President


                                          NYSERNet.net, Inc.



                                          By: /s/ Anthony Jiga
                                              -------------------------------
                                              Anthony Jiga, Treasurer


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