Document:

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                                                                 EXHIBIT 10.57

                                    REVOLVING
                                 NOTE AGREEMENT

$7,500,000                                           Dated as of January 3, 2001
                                                           At Syracuse, New York

         (1) Subject to the terms of this Revolving Note Agreement ("Note"),
commencing on January 20, 2001 and continuing through January 19, 2002, (the
"Advance Period"), FLEET NATIONAL BANK, its successors and assigns with banking
offices at One Clinton Square, Syracuse, New York 13202 ("Bank") agrees to loan
to APPLIEDTHEORY CORPORATION, a New York corporation with its offices at 1500
Broadway, New York, NY 10036 ("Borrower") on a revolving credit basis an amount
not to exceed Seven Million Five Hundred Thousand Dollars ($7,500,000) (the
"Loan") in the aggregate at any one time outstanding. So long as no Event of
Default has occurred and is then continuing, the Borrower may obtain term Loan
advances (an "Advance" or the "Advances") from the Bank during the Advance
Period in accordance with the provisions of this Note. Additionally, Bank agrees
to provide Letters of Credit (each a "Letter of Credit") as part of the Loan
facility hereunder upon the terms set forth herein. Borrower unconditionally
agrees that Loan amounts advanced by the Bank to the Borrower hereunder shall be
repaid by the Borrower as follows under the provisions of this Note.

         (2) Payment. Commencing on the first day of the first calendar month
following the date of the first Advance made by the Bank to the Borrower
hereunder and continuing on the first day of each succeeding calendar month
through and including January 1, 2002 (each a "Monthly Payment Date"), Borrower
shall pay to the order of the Bank interest on the then outstanding unpaid
balance of the amount of each Advance made under this Note at a rate of interest
equal to the "Applicable Interest Rate" (defined below), and on January 20, 2002
(the "Maturity Date"), Borrower shall pay to the Bank the then unpaid principal
balance of all amounts advanced under this Note, including, but not limited to,
any Letter of Credit plus all accrued and unpaid interest. Borrower shall have
the option of extending the Maturity Date for two (2) periods of one (1) year
each provided that (i) no Event of Default has occurred and is continuing and
(ii) Borrower gives Bank forty five (45) days prior written notice in form
reasonably acceptable to the Bank of its election to extend the Maturity Date
and provided further that there shall be no extension of the Maturity Date
without the prior written consent of NYSERNet.net, Inc. in each case.

         (3) Advance Term and Interest Rates. At the time Borrower requests an
Advance, Borrower shall include in the Advance request the term of the requested
Advance and which of the following interest rate options Borrower elects with
respect to the Advance (the "Applicable Interest Rate"). Under no circumstances
may the requested Advance term extend beyond the Maturity Date. If no term or
interest rate option is specified by the Borrower, or if the amount of the
requested Advance is less than $100,000, the Advance involved shall bear
interest at the Bank's Prime Rate of interest minus two hundred (200) basis
points.
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                  (a)      LIBOR Advance. The Borrower may obtain Advances by
                           submitting an Advance request, in the form attached
                           hereto as Exhibit "A" two (2) Business Days prior to
                           the date on, which the Advance is to be made during
                           the Advance Period at the "LIBOR Rate" (defined
                           below) for the "Applicable Interest Period" (defined
                           below) plus forty (40) basis points. Each Advance
                           requested under this Section 3(a) shall be in the
                           minimum amount of $100,000. The term "LIBOR" or
                           "LIBOR Rate" shall mean, as applicable to any Advance
                           under this Section 3(a) (a "LIBOR Advance"), the rate
                           per annum as determined on the basis of the offered
                           rates for deposits in U.S. Dollars, for one (1)
                           month, two (2) months, three (3) months, four (4)
                           months, six (6) months or twelve (12) months as
                           specified by the Borrower (the "Interest Period")
                           which appears on the Telerate page 3750 as of 11:00
                           a.m. London time on the day that is two London
                           Banking Days preceding the first day of such LIBOR
                           Advance; provided, however, if the rate described
                           above does not appear on the Telerate System on any
                           applicable interest determination date, the LIBOR
                           rate shall be the rate (rounded upward, if necessary,
                           to the nearest one hundred-thousandth of a percentage
                           point), determined on the basis of the offered rates
                           for deposits in U.S. dollars for a period of time
                           comparable to such LIBOR Advance which are offered by
                           four major banks in the London interbank market at
                           approximately 11:00 a.m. London time, on the day that
                           is two (2) London Banking Days preceding the first
                           day of such LIBOR Advance as selected by Bank. The
                           principal London office of each of the four major
                           London banks will be requested to provide a quotation
                           of its U.S. Dollar deposit offered rate. If at least
                           two such quotations are provided, the rate for that
                           date will be the arithmetic mean of the quotations.
                           If fewer than two quotations are provided as
                           requested, the rate for that date will be determined
                           on the basis of the rates quoted for loans in U.S.
                           dollars to leading European banks for a period of
                           time comparable to such LIBOR Advance offered by
                           major banks in New York City at approximately 11:00
                           a.m. New York City time, on the day that is two
                           London Banking Days preceding the first day of such
                           LIBOR Advance. In the event that Bank is unable to
                           obtain any such quotation as provided above, it will
                           be deemed that LIBOR pursuant to a LIBOR Advance
                           cannot be determined. In the event that the Board of
                           Governors of the Federal Reserve System shall impose
                           a Reserve Percentage with respect to LIBOR deposits
                           of Bank, then for any period during which such
                           Reserve Percentage shall apply, LIBOR shall be equal
                           to the amount determined above divided by an amount
                           equal to 1 minus the Reserve Percentage. "Reserve
                           Percentage" shall mean the maximum aggregate reserve
                           requirement (including all basic, supplemental,
                           marginal and other reserves) which is imposed on
                           member banks of the Federal Reserve System against
                           "Euro-currency Liabilities" as defined in Regulation
                           D."

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                  (b)      Cost of Funds Advance. If the term of a requested
                           Advance is to be for more than one (1) year,
                           Borrower, by submitting an Advance request two (2)
                           Business Days prior to the date on which the Advance
                           is to be made, may obtain Advances during Advance
                           Period at a rate equal to the Bank's "Cost of Funds"
                           (defined below) for the term of the term of the
                           requested Advance (each Advance at the Cost of Funds
                           rate hereinafter called "Fixed Rate Loan"), plus
                           forty (40) basis points. Each Advance requested under
                           this Section 3(b) shall be in the minimum amount of
                           $100,000.

                           The term "Cost of Funds" means the per annum rate of
                           interest which the Bank is required to pay, or is
                           offering to pay, for wholesale liabilities of like
                           tenor, adjusted for reserve requirements and such
                           other requirements as may be imposed by federal,
                           state or local government and regulatory agencies, as
                           determined by the Bank.

                  (c)      Prime Rate Advance. The Borrower, by submitting an
                           Advance request, may obtain Advances at any time
                           during the Advance Period at the Bank's "Prime Rate"
                           of interest (defined below) minus 200 basis points.
                           Advances made by Bank to Borrower under the Target
                           Balance Service Agreement between Borrower and Bank
                           dated January 20, 1998 shall be deemed to be Advances
                           made under this Section 3(c). The term "Prime Rate"
                           means the variable per annum rate of interest so
                           designated from time to time by Fleet National Bank
                           as its prime rate. The prime rate is a reference rate
                           and does not necessarily represent the lowest or the
                           best rate being charged to any customer. Changes in
                           the rate of interest resulting from changes in the
                           Prime Rate shall take place immediately without any
                           notice or demand of any kind.

                  (d)      With respect to any Advance made under Section 3(a)
                           or 3(b) above, Borrower must either repay such
                           Advance at the end of the Applicable Interest Period
                           or Cost of Funds Period, as the case may be or notify
                           the Bank two banking days prior to the expiration of
                           the period involved that Borrower intends to continue
                           such borrowing in which event Borrower must at such
                           time notify the Bank as to whether the borrowing will
                           be continued as an Advance under Section 3(a) or 3(b)
                           or 3(c) of this Note. If at the end of an Applicable
                           Interest Period or a Cost of Funds Period, the
                           Borrower has not given such two banking day notice
                           and does not repay the Advance in question, then, so
                           long as no Event of Default has occurred and is then
                           continuing, the Advance involved shall be repaid by
                           making an Advance under Section 3(c) for a period of
                           30 days.

                  (e)      The term "Business Day" shall have the meaning set
                           forth in Section 8 below.

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                  (f)      Letters of Credit provided hereunder shall bear
                           interest at the rate of forty (40) basis points per
                           annum.

         (4) Interest Computations. All computations of interest shall be made
by Bank on the basis of a 360-day year and the actual number of days elapsed.

         (5) Prepayment. In the event Borrower obtains an Advance under Section
3(a) or 3(b) above, the last day of the Advance term selected by the Borrower
shall be deemed to be and is referred to herein as the "Advance Maturity Date".
Borrower shall have the right at any time and from time to time to prepay in
whole or in part any Advance made under Section 3(c) above without penalty,
premium or yield maintenance fee. Borrower shall have the right to prepay a
LIBOR Advance in whole but not in part, provided that the Borrower shall pay any
applicable yield maintenance fee in an amount computed as follows. Borrower may
prepay a LIBOR Advance or advance only upon at least three (3) Business Days
prior written notice to Bank (which notice shall he irrevocable), and any such
prepayment shall occur only on the last day of the Interest Period for such
LIBOR Advance. Borrower shall pay to Bank, upon request of Bank, such amount or
amounts as shall be sufficient (in the reasonable opinion of Bank) to compensate
it for any loss, cost, or expense incurred as a result of: (i) any payment of a
LIBOR Advance on a date other than the last day of the Interest Period for such
LIBOR Advance; (ii) any failure by Borrower to borrow a LIBOR Advance on the
date specified by Borrower's Loan request; (iii) any failure by Borrower to pay
a LIBOR Advance on the date for prepayment specified in Borrower's written
notice. Without limiting the foregoing, Borrower shall pay to Bank a yield
maintenance fee in an amount computed as follows: The current rate for United
States Treasury securities (bills on a discounted basis shall be converted to a
bond equivalent) with a maturity date closest to the term chosen pursuant to the
Fixed Rate Election as to which the prepayment is made, shall be subtracted from
the LIBOR in effect at the time of prepayment. If the result is zero or a
negative number, there shall be no yield maintenance fee. If the result is a
positive number, then the resulting percentage shall be multiplied by the amount
of the principal balance being prepaid. The resulting amount shall be divided by
three hundred sixty (360) and multiplied by the number of days remaining in the
term chosen pursuant to the Fixed Rate Election as to which the prepayment is
made. Said amount shall be reduced to present value calculated by using the
above referenced United States Treasury securities rate and the number of days
remaining in the term chosen pursuant to the Fixed Rate Election as to which
prepayment is made. The resulting amount shall be the yield maintenance fee due
to Bank upon the prepayment of a LIBOR Advance. Each reference in this paragraph
to "Fixed Rate Election" shall mean an election for a rate of interest based
upon the LIBOR Interest Period.

                  If at any time, (i) the interest rate on an Advance Cost of
Funds rate and (ii) Bank in its sole discretion should determine that current
market conditions can accommodate a prepayment request, Borrower shall have the
right, at any time and from time to time, upon at least ten (10) Business Days
prior written notice to Bank, to prepay Fixed Rate Loan in whole (but not in
part), and Borrower shall pay to Bank a yield maintenance fee in an amount
computed as follows: the current rate for a United States Treasury securities
(bills on a discounted basis shall be converted to a bond equivalent) with a
maturity date closest to the maturity date of the

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term chosen pursuant to the Fixed Rate Election as to which the prepayment is
made, shall be subtracted from the "Cost of Funds" component of the fixed rate
in effect at the time of prepayment. If the result is zero or a negative number,
there shall be no yield maintenance fee. If the result is a positive number,
then the resulting percentage shall be multiplied by the amount of the principal
balance being prepaid. The resulting amount shall be divided by 360 and
multiplied by the number of days remaining in the term chosen pursuant to the
Fixed Rate Election as to which the prepayment is made. Said amount shall be
reduced to present value calculated using the above-referenced United States
Treasury securities rate and the number of days remaining in the term chosen
pursuant to the Fixed Rate Election as to which the prepayment is made. The
resulting amount shall be the yield maintenance fee due to Bank upon prepayment
of a Fixed Rate Loan. Each referenced in this paragraph to "Fixed Rate Election"
shall mean the election by Borrower pursuant to paragraph 3b of this Promissory
Note.

                  If by reason of an event of default Bank elects to declare the
Loan to be immediately due and payable, then any yield maintenance fee with
respect to the loan shall become due and payable in the same manner as though
Borrower had exercised such right of prepayment with respect to all then unpaid
Advances.

         (6) Payments. All payments shall be made by Borrower to Bank at One
Clinton Square, P.O. Box 4821, Syracuse, New York 13221-4821 or such other place
as Bank may from time to time specify in writing in lawful currency of the
United States of America in immediately available funds, without counterclaim or
setoff and free and clear of, and without any deduction or withholding or, any
taxes or other payments.

         (7) Application of Payments. All payments shall be applied first to the
payment of all fees, expenses and other amounts due to the Bank (excluding
principal and interest), then to accrued interest, and the balance on account of
outstanding principal; provided, however, that after an Event of Default,
payments will be applied to the obligations of Borrower to Bank as Bank
determines in its sole discretion.

         (8) Business Day: If this Note or any payment hereunder becomes due on
a day which is not a Business Day (as defined below), the due date of this Note
or payment shall be extended to the next succeeding Business Day, and such
extension of time shall be included in computing interest and fees in connection
with such payment. As used herein, "Business Day" shall mean any day other than
a Saturday, Sunday or day which shall be in the State of New York a legal
holiday or day on which banking institutions are required or authorized to close

         (9) Participations. Bank shall have the unrestricted right at any time
and from time to time, and without the consent of or notice to Borrower, to
grant to one or more banks or other financial institutions (each, a
"Participant") participating interests in Bank's obligation to lend hereunder
and/or any or all of the Loan. In the event of any such grant by Bank of a
participating interest to a Participant, whether or not upon notice to Borrower,
Bank shall remain responsible for the performance of its obligations hereunder
and Borrower shall continue to deal solely and directly with Bank in connection
with Bank's rights and obligations hereunder.

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                  Bank may furnish any information concerning Borrower in its
possession from time to time to prospective Participants, provided that Bank
shall require any such prospective Participant to agree in writing to maintain
the confidentiality of such information.

         (10) Right of Setoff. Borrower hereby grants to Bank, a continuing
lien, security interest and right of setoff as security for all liabilities and
obligations to Bank, whether now existing or hereafter arising, upon and against
its deposits, credits, collateral and property, now or hereafter in the
possession, custody, safekeeping or control of Bank or any entity under the
control of FleetBoston Financial Corporation, its successors and assigns or in
transit to any of them. At any time, without demand or notice (any such notice
being expressly waived by Borrower), Bank may set off the same or any part
thereof and apply the same to any liability or obligation of Borrower even
though unmatured and regardless of the adequacy of any other collateral securing
the Loans. ANY AND ALL RIGHTS TO REQUIRE BANK TO EXERCISE ITS RIGHTS OR REMEDIES
WITH RESPECT TO ANY OTHER COLLATERAL WHICH SECURES THE LINE LOANS, PRIOR TO
EXERCISING ITS RIGHT OF SETOFF WITH RESPECT TO ANY DEPOSITS, CREDITS OR OTHER
PROPERTY OF THE BORROWER ARE HEREBY KNOWINGLY, VOLUNTARILY AND IRREVOCABLY
WAIVED.

         (11) Lost or Destroyed Documents. Upon receipt of an affidavit of an
officer of Bank as to the loss, theft, destruction or mutilation of the Note or
any other security or loan document which is not of public record, and, in the
case of any such loss, theft, destruction or mutilation, upon cancellation of
such Note or other security or loan document, Borrower will issue, in lieu
thereof, a replacement Note or other security or loan document in the same
principal amount thereof and otherwise of like tenor. The Bank agrees to
indemnify Borrower from liability in the event Borrower is required to make any
payment on account of any Note or other Loan Document replaced by the Borrower
at the Bank's request under this Section 9.

         (12) Bank Pledge. Bank may at any time pledge all or any portion of its
rights under the loan documents including any portion of this Note to any of the
twelve (12) Federal Reserve Banks organized under Section 4 of the Federal
Reserve Act, 12 U.S.C. Section 341. No such pledge or assignment or enforcement
thereof shall release Bank from its obligations under any of the loan documents.

         (13) Defaults. The occurrence of any of the following shall constitute
an "Event of Default" under this Note:

                  (a)      Failure by Borrower to make any payment within ten
                           (10) days of the date when due under this Note;

                  (b)      The occurrence and continuation beyond the applicable
                           space period, if any, of an event of default with
                           respect to any other indebtedness of Borrower to
                           Bank;

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                  (c)      Any representation or warranty contained in this
                           Note, any other loan document or in any certificate
                           delivered to Bank by Borrower shall have been
                           incorrect or false in any material respect as of the
                           date as to which the facts set forth were asserted;

                  (d)      If Borrower or NYSERNet shall file a voluntary
                           petition in bankruptcy or a voluntary 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;

                  (e)      If Borrower or NYSERNet shall have filed against
                           either of them an involuntary petition in bankruptcy
                           or an involuntary 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 and such petition is not dismissed within
                           thirty (30) days of the date of filing;

                  (f)      The entry of a judgment against Borrower not fully
                           covered by insurance less normal deductibles, and the
                           failure to either satisfy or stay the enforcement of
                           such judgment, within fifteen (15) days of the date
                           of such entry;

                  (g)      The acceleration before stated maturity of any
                           indebtedness for borrowed money owed by Borrower
                           where the amount involved exceeds $10,000;

                  (h)      Failure by NYSERNet to maintain the "Required Value"
                           of the "Collateral" [as those quoted terms are
                           defined in the Pledge Security Agreement between
                           NYSERNet and the Bank dated even date herewith (the
                           "Pledge Security Agreement")] as required by the
                           terms of such Pledge Security Agreement;

                  (i)      Failure by Borrower to perform any of Borrower's
                           other obligations under this Note or the documents
                           securing amounts due under this Note within fifteen
                           (15) days after notice from the Bank.

         (14) Acceleration. Upon the occurrence of an Event of Default the then
unpaid amount of this Note, together with all accrued and unpaid interest, shall
be and become due and payable.

         (15) Late Fee/Default Interest Rate. Further and not in lieu of any
other remedy, (a) if the entire amount of any required principal and/or interest
payment is not paid in full within ten (10) days of the date the same is due,
Borrower shall pay to Bank a late fee equal to five percent (5%) of the required
payment, and (b) upon the occurrence of an Event of Default or after maturity or
after judgment has been rendered on this Note (whether or not Bank has
accelerated payment on this Note), the amount due under this Note shall
thereafter at the option of the Bank

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bear interest at a rate equal to four percent (4%) per annum in excess of the
rate of interest that would otherwise be applicable prior to such Event of
Default, and Borrower agrees to pay interest at such rate until all amounts due
under this Note are paid in full.

         (16) Financial Statements. Borrower shall maintain a system of
accounting in accordance with generally accepted accounting principles on a
basis consistently applied, permit representatives of the Bank to have access to
and to examine Borrower's properties, books and records at all reasonable times
on reasonable notice, and at no expense to the Bank, furnish to the Bank:

                  (a)      Within one hundred twenty (120) days of the end of
                           each of Borrower's fiscal years, Borrower's audited
                           financial statements for the then ended fiscal year,
                           and the annual operating budget for the next fiscal
                           year. Each such annual statement shall be accompanied
                           by an audit opinion by an independent certified
                           public accountant retained by Borrower and reasonably
                           satisfactory to the Bank and shall contain a balance
                           sheet and income statement together with comparative
                           figures for the prior year. Each such statement shall
                           fairly present the financial condition of Borrower
                           for the period covered.

                  (b)      Within one hundred twenty (120) days of Borrower's
                           fiscal year end, Borrower shall furnish to Bank a
                           copy of its annual 10K Report.

                  (c)      Such other financial information regarding Borrower
                           as the Bank may reasonably request.

                  Concurrent with delivery of each of the Borrower's financial
statements required above, Borrower shall provide to the Bank a copy of any
management letter delivered to the Borrower by the Borrower's independent
certified public accountants.

         (17) No Usury. All agreements between Borrower and Bank are hereby
expressly limited so that in no contingency or event whatsoever, whether by
reason of acceleration of maturity of the indebtedness evidenced hereby or
otherwise, shall the amount paid or agreed to be paid to Bank for the use or the
forbearance of the indebtedness evidenced hereby exceed the maximum permissible
under applicable law. As used herein, the term "applicable law" shall mean the
law in effect as of the date hereof provided, however, that in the event there
is a change in the law which results in a higher permissible rate of interest,
then this Note shall be governed by such new law as of its effective date. In
this regard, it is expressly agreed that it is the intent of Borrower and in the
execution, delivery and acceptance of this Note to contract in strict compliance
with the laws of the State of New York from time to time in effect. If, under or
from any circumstances whatsoever, fulfillment of any provision hereof or of any
of the loan documents at the time of performance of such provision shall be due,
shall involve transcending the limit of such validity prescribed by applicable
law, then the obligation to be fulfilled shall automatically be reduced to the
limits of such validity, and if under or from circumstances whatsoever Bank
should ever receive as interest an amount which would exceed the highest lawful
rate, such amount which would be excessive interest shall be applied to the
reduction of

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the principal balance evidenced hereby and not to the payment of interest. This
provision shall control every other provision of all agreements between Borrower
and Bank.

         (18) Certain Waivers. Borrower expressly waives any presentment,
demand, protest or notice in connection with this Note, now or hereafter
required by applicable law.

         (19) Payment of Fees and Expense. Borrower shall pay on demand all
expenses of Bank in connection with the preparation, administration, default,
collection, waiver or amendment of loan terms, or in connection with Bank's
exercise, preservation or enforcement of any of its rights, remedies or options
hereunder, including, without limitation, fees of outside legal counsel or the
allocated costs of in-house legal counsel, accounting, consulting, brokerage or
other similar professional fees or expenses, and any fees or expenses associated
with travel or other costs relating to any appraisals or examinations conducted
in connection with the loan or any collateral therefor, and the amount of all
such expenses shall, until paid, bear interest at the rate applicable to
principal hereunder (including any default rate) and be an obligation secured by
any collateral.

         (20) New York Law. This Note and the rights and obligations of the
parties hereto shall be construed and interpreted in accordance with the laws of
the State of New York, exclusive of New York's conflicts of laws rules and
public policies.

         (21) Right to Sell a Portion of Loan to Prospective Participant. The
Bank shall have the unrestricted right at any time and from time to time and
without the consent of or notice to the Borrower to grant to one or more banks
or other financial institutions (each. a "Participant") participating interests
in any Loan evidenced by this Note. In the event of any such grant by the Bank
of a participating interest to a Participant, whether or not upon notice to the
Borrower, the Bank shall remain responsible for the performance of its
obligations hereunder and the Borrower shall continue to deal solely and
directly with the Bank in connection with the Bank's rights and obligations
hereunder. The Bank may furnish any information concerning the Borrower in its
possession from time to time to prospective participants, provided that the Bank
shall require any such prospective participant to agree in writing to maintain
the confidentiality of such information.

         (22) Business Purpose. Borrower represents that the proceeds of this
Note will be used for business or commercial purposes.

         (23) Interpretation. This Note is intended by the parties as the final,
complete and exclusive statement of the transactions evidenced by this Note. All
prior or contemporaneous promises, agreements and understandings, whether oral
or written, are deemed to be superceded by this Note, and no party is relying on
any promise, agreement or understanding not set forth in this Note. This Note
may not be amended or modified except by a written instrument describing such
amendment or modification executed by Borrower and Bank.

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         (24) Jury Waiver. BORROWER AND BANK (BY ACCEPTANCE OF THIS NOTE)
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 THIS 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, INCLUDING,
WITHOUT LIMITATION, ANY COURSE OF CONDUCT, COURSE OF DEALINGS, STATEMENTS OR
ACTIONS OF BANK RELATING TO THE ADMINISTRATION OF THE LOAN OR ENFORCEMENT OF THE
LOAN DOCUMENTS, AND AGREE THAT NEITHER PARTY WILL SEEK TO CONSOLIDATE ANY SUCH
ACTION WITH ANY OTHER ACTION IN WHICH A JURY TRIAL CANNOT BE OR HAS NOT BEEN
WAIVED. EXCEPT AS PROHIBITED BY LAW, BORROWER HEREBY WAIVES ANY RIGHT IT MAY
HAVE TO CLAIM OR RECOVER IN ANY LITIGATION ANY SPECIAL, EXEMPLARY, PUNITIVE OR
CONSEQUENTIAL DAMAGES OR ANY DAMAGES OTHER THAN, OR IN ADDITION TO, ACTUAL
DAMAGES. BORROWER CERTIFIES THAT NO REPRESENTATIVE, AGENT OR ATTORNEY OF BANK
HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT BANK WOULD NOT, IN THE EVENT OF
LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER. THIS WAIVER CONSTITUTES A
MATERIAL INDUCEMENT FOR BANK TO ACCEPT THIS NOTE AND MAKE THE LOAN.

         (25) Use of Proceeds. No portion of the proceeds of the Loan shall be
used, in whole or in part, for the purpose of purchasing or carrying any "margin
stock" as such term is defined in Regulation U of the Board of Governors of the
Federal Reserve System.

         (26) Amendments or Modifications. This Revolving Note Agreement may not
be amended, modified or supplemented without the express written consent of
NYSERNet.net, Inc.

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                                   APPLIEDTHEORY CORPORATION

                                   By: /s/ David A. Buckel
                                       -----------------------------------------
                                           DAVID A. BUCKEL
                                           Chief Financial Officer

                                   FLEET NATIONAL BANK

                                   By: /s/ David A. Kavney
                                       -----------------------------------------
                                           DAVID A. KAVNEY
                                           Vice President

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                      Exhibit A To Revolving Note Agreement

                                  DRAW REQUEST

TO:   FLEET NATIONAL BANK

Attn: ________________________________________________

         The Borrower, AppliedTheory Corporation, hereby requests a draw from
Fleet National Bank under the Revolving Note Agreement dated as of January 3,
2001.

         We wish to draw $____________at the following interest rate specified
in the Revolving Note Agreement:

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

         Kindly confirm by fax to our fax number (   ) ________________________.

Dated: _______________________

                                   APPLIEDTHEORY CORPORATION

                                   By: _________________________________________
                                       David A. Buckel
                                       Chief Financial Officer<PAGE>   1
                                                                   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
<PAGE>   2
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

2
<PAGE>   3
      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

3
<PAGE>   4
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.

4
<PAGE>   5
      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.

5
<PAGE>   6
                                  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
<PAGE>   7
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

                                       2

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