The number of warrants or rights exercisable for cash or cashless basis.

No definition available.

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- Definition

The number of trading days prior to the date on which the written notice for exercise is received by the warrant agent considered for volume weighted average price of per share.

+ References

No definition available.

+ Details

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- Definition

Number of fractional warrants issued upon separation of units.

+ References

No definition available.

+ Details

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- Definition

Number of days of prior notice to be issued for redemption of warrants.

+ References

No definition available.

+ Details

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Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Redemption price per warrant.

+ References

No definition available.

+ Details

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Data Type:	dtr-types:perShareItemType
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Period Type:	duration

- Definition

Price of the entity's common stock which would be required to be attained for the redemption feature in the warrant to become effective.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Threshold period of specified consecutive trading days within which common stock price to redemption price of warrant must exceed threshold percentage for specified number of trading days to trigger redemption feature.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	xbrli:integerItemType
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- Definition

Threshold number of specified trading days that common stock price to redemption price of warrant must exceed threshold percentage within a specified consecutive trading period to trigger redemption feature.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	xbrli:integerItemType
Balance Type:	na
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- Definition

Period over which the warrants becomes exercisable post business combination expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The threshold number of business days for making the registration statement effective within number of days of initial business combination.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Threshold number of business days available for company to file the registration statement post initial business combination.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The period of time which must elapse after completion of a business combination before the Sponsor can transfer, assign or sell any Founder Shares unless other specified conditions are met.

+ References

No definition available.

+ Details

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Namespace Prefix:	biii_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of warrants or rights outstanding.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Period between issuance and expiration of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

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Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Details

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Namespace Prefix:
Data Type:	na
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Period Type:

- Details

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Data Type:	na
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- Details

Name:	srt_RangeAxis=srt_MinimumMember
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Data Type:	na
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- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=biii_PrivatePlacementWarrantsMember
Namespace Prefix:
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WARRANTS (Details)	6 Months Ended
WARRANTS (Details)	Jun. 30, 2026 D $ / shares shares	Jan. 07, 2026 shares	Dec. 31, 2025 shares
WARRANTS
Number of warrants outstanding	13,900,000		0
Number of fractional warrants issued upon separation of units	0
Exercisable term	30 days
Warrant term	5 years
Number of warrants or rights exercisable for cash	0
Threshold number of business days for filing of registration statement	20 days
Threshold business days for making the registration statement effective	60 days
Class A ordinary shares
WARRANTS
Warrant redemption, stock price trigger \| $ / shares	$ 18
Public warrants
WARRANTS
Number of warrants outstanding	5,750,000		0
Number of fractional warrants issued upon separation of units		0
Warrant term		5 years
Redemption price per warrant \| $ / shares	$ 0.01
Threshold trading days \| D	20
Threshold consecutive trading days \| D	30
Trading day prior to the date on which the notice of exercise is received \| D	10
Public warrants \| Minimum
WARRANTS
Number of days of prior notice of redemption to be issued \| D	30
Private placement warrants
WARRANTS
Number of warrants outstanding	8,150,000		0
Threshold period for not to transfer, assign or sell any of their shares or warrants after the completion of the initial business combination \| D	30