Applied Identity Physics : The Sub-Lemma Process: A Step-by-Step Framework for Solving Hard Problems from Erd?s-Turán to the Collatz Conjecture
Language: English
Published by Amazon Digital Services LLC - Kdp Aug 2026, 2026
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
US$ 32.00
Quantity: 2 available
Add to basketItem description from seller
Neuware - The Evidence at Scale: 353 Erdos ProblemsPaul Erdos was the most prolific mathematician of the 20th century and spent decades cataloging open problems across mathematics, many with attached prizes. We applied the LDP to all 353 problems in the catalog.The result: Type Count Description Type 1 - Finite Escape 130Sub-lemma closes structurallyType 2 - Dual Axis 45P-axis and B-axis cannot both be smallType 3 - B-Balance 45Noble k-body balance decompositionType 4 - Torsion Gap 90Interior torsion forced to extremesType 2 - Computation Required 20PNBA gives bounds, exact value needs enumerationType 3 - Premise Invalid 3-5Question dissolved at inputAll 310 Type 1-4 problems are addressed structurally in Lean 4 files [9,9,5,1] through [9,9,5,13], with zero sorry across all files.For comparison: AlphaProof Nexus (DeepMind, May 2026) solved 9 of 353 problems using a state-of-the-art AI system at approximately $200-400 per problem. All 9 fall within the Type 1 category here. The LDP identifies the structure for 310+ problems simultaneously; the AI found proof paths for 9 specific ones through search.The approaches are complementary. AI search excels at finding exact values (the Computation Required category). The LDP excels at identifying structural type (the Narrative Trap categories). Neither replaces the other.4. Closing the Erdos-Turán ConjectureNow we apply all of the above to a single hard problem.The problem: Let A?N+ with ?a?A1/a=8. Must A contain arithmetic progressions of all lengths (Prize: $3,000. Open since 1936.)We will close this problem in three LDP runs. Each one feeds into the next.(ProofPress formatted for easy ai-mediated ingestion).…
Seller Inventory # 9798193966364
- Title
- Applied Identity Physics : The Sub-Lemma Process: A Step-by-Step Framework for Solving Hard Problems from Erd?s-Turán to the Collatz Conjecture
- Author
- Russell Vernon Trent
- Publisher
- Amazon Digital Services LLC - Kdp Aug 2026
- Publication year
- 2026
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 13
- 9798193966364
- Item weight
- 145 grams
- Dimensions
- 229x152x5 mm
The Evidence at Scale: 353 Erdős Problems
Paul Erdős was the most prolific mathematician of the 20th century and spent decades cataloging open problems across mathematics, many with attached prizes. We applied the LDP to all 353 problems in the catalog.
The result:
Type Count Description Type 1 — Finite Escape~130Sub-lemma closes structurallyType 2 — Dual Axis~45P-axis and B-axis cannot both be small
Type 3 — B-Balance~45Noble k-body balance decomposition
Type 4 — Torsion Gap~90Interior torsion forced to extremes
Type 2 — Computation Required~20PNBA gives bounds, exact value needs enumeration
Type 3 — Premise Invalid~3–5Question dissolved at input
All ~310 Type 1–4 problems are addressed structurally in Lean 4 files [9,9,5,1] through [9,9,5,13], with zero sorry across all files.
For comparison: AlphaProof Nexus (DeepMind, May 2026) solved 9 of 353 problems using a state-of-the-art AI system at approximately $200–400 per problem. All 9 fall within the Type 1 category here. The LDP identifies the structure for 310+ problems simultaneously; the AI found proof paths for 9 specific ones through search.
The approaches are complementary. AI search excels at finding exact values (the Computation Required category). The LDP excels at identifying structural type (the Narrative Trap categories). Neither replaces the other.
4. Closing the Erdős-Turán Conjecture
Now we apply all of the above to a single hard problem.
The problem: Let A⊆N+ with ∑a∈A1/a=∞. Must A contain arithmetic progressions of all lengths? (Prize: $3,000. Open since 1936.)
We will close this problem in three LDP runs. Each one feeds into the next.
(ProofPress formatted for easy ai-mediated ingestion)
"Synopsis" may belong to another edition of this title.
Shipping rates from Germany to U.S.A.
| Item | 7 to 10 business days | 5 to 7 business days |
|---|---|---|
| First item | US$ 39.14 | US$ 50.32 |
Payment methods
- Bank Wire Transfer
- Check
- Paypal
Store description
Das Unternehmen AHA-BUCH GmbH: Seit der Gründung von AHA-BUCH im Juli 2005 ist unser Hauptziel, zufriedenen Kunden so schnell und so preisgünstig wie möglich ihren Bücherwunsch zu erfüllen. Unsere Firma beschäftigt 16 Mitarbeiter, die nur ein Ziel kennen: den Kunden und seine Wünsche! Auf über 3700 m2 Fläche haben wir über 100.000 Bücher, Modernes Antiquariat und Spiele auf Lager.
Specialty
Kinderbücher & Kinderhör Casetten, German Books, Software, Natur & Tiere, Ratgeber, Sachbücher, Englische Bücher, Medizin & Gesundheit, Universität & StudiumSeller's business information
AHA-BUCH GmbH
Garlebsen 48
Einbeck, Germany 37574
Terms of sale
General Terms and Conditions and Customer Information / Privacy Policy
I. General Terms and Conditions
§ 1 Basic provisions
(1) The following terms and conditions apply to all contracts that you conclude with us as a provider (AHA-BUCH GmbH) via the Internet platforms AbeBooks and/or ZVAB. Unless otherwise agreed, the inclusion of any of your own terms and conditions used by you will be objected to
(2) A consumer within the meaning of the following regulations is any natural person who concludes a legal transaction for purposes that can predominantly be attributed neither to their commercial nor their independent professional activity. An entrepreneur is any natural or legal person or a partnership with legal capacity who, when concluding a legal transaction, acts in the exercise of his independent professional or commercial activity.
§ 2 Conclusion of the contract
(1) The object of the contract is the sale of goods.
(2) If an article is listed by us at AbeBooks or ZVAB, the activation of the offer page at AbeBooks or ZVAB constitutes the binding offer to conclude a contract under the conditions contained in the article page.
(3) The contract is concluded via the online shopping cart system as follows:
The goods intended for purchase are stored in the "shopping cart". Via the corresponding button in the navigation bar you can call up the "shopping cart" and make changes there at any time.
After calling up the "Checkout" page and entering the personal data as well as the payment and shipping conditions, all order data will be displayed again on the order overview page.
Before sending the order, you have the option of checking all information again, changing it (also via the "back" function of the Internet browser) or cancelling the purchase.
By submitting the order via the "Buy now" button, you declare the acceptance of the offer in a legally binding manner, whereby the contract is concluded.
(4) The processing of the order and transmission of all information required in connection with the conclusion of the contract is partly automated by e-mail. You must therefore ensure that the e-mail address you have stored with us is correct, that the receipt of the e-mails is technically ensured and, in particular, that spam filters do not prevent it.
§ 3 Right of retention, retention of title
(1) You can only exercise a right of retention if it concerns claims from the same contractual relationship.
(2) The goods remain our property until full payment of the purchase price.
§ 4 Warranty
(1) The statutory warranty rights exist.
(2) In the case of used goods, the warranty period is one year from delivery of the item, deviating from the statutory regulation. The shortening of the deadline does not apply:
- culpably caused damages attributable to us from injury to life, limb or health and in the case of other damages caused intentionally or through gross negligence;
- insofar as we have fraudulently concealed the defect or have assumed a guarantee for the quality of the item.
(3) As a consumer, you are requested to check the item immediately upon delivery for completeness, obvious defects and transport damage and to inform us and the freight forwarder of any complaints as soon as possible. If you do not comply with this, this will have no effect on your statutory warranty claims.
§ 5 Choice of law, place of performance, place of jurisdiction
(1) German law shall apply. In the case of consumers, this choice of law shall only apply insofar as this does not withdraw the protection afforded by mandatory provisions of the law of the state of the consumer's habitual residence (principle of favourability).
(2) The place of performance for all services arising from the existing business relationships with us as well as the place of jurisdiction is our registered office, insofar as you are not a consumer, but a merchant, a legal entity under public law or a special fund under public law. The same applies if you do not have a general place of jurisdiction in Germany or the EU or if the domicile or habitual residence is not known at the time the action is brought. The right to appeal to the court at another statutory place of jurisdiction remains unaffected by this.
(3) The provisions of the UN Convention on Contracts for the International Sale of Goods shall expressly not apply.
II. Customer Information
- Identity of the Seller
AHA-BUCH GmbH
Garlebsen 48
D-37574 Einbeck
Germany
Telephone: 055639996039
E-mail: abebooks@aha-buch.de.
Alternative dispute resolution:
The European Commission provides a platform for out-of-court online dispute resolution (ODR platform), which can be accessed under https://ec.europa.eu/odr.
- Information on the conclusion of the contract
The technical steps for the conclusion of the contract, the conclusion of the contract itself and the correction options are carried out in accordance with the provisions "Conclusion of the contract" of our General Terms and Conditions (Part I.).
- Contract language, contract text storage
3.1. The contract language is german.
3.2. The complete text of the contract will not be stored by us. Before sending the order, the contract data can be printed out or electronically saved via the print function of the browser. After receipt of the order by us, the order data, the legally prescribed information for distance contracts and the General Terms and Conditions will be sent to you again by e-mail.
- Essential characteristics of the goods or services
The essential characteristics of the goods and/or services can be found in the respective offer.
- Prices and terms of payment
5.1. The prices stated in the respective offers as well as the shipping costs represent total prices. They include all price components including all applicable taxes.
5.2. The shipping costs incurred are not included in the purchase price. They can be called up via a correspondingly designated button on our website or in the respective offer, are shown separately in the course of the ordering process and are to be borne by you in addition, unless free shipping has been promised.
5.3. If the delivery is made to countries outside the European Union, we may incur additional costs for which we are not responsible, such as.B customs duties, taxes or money transfer fees (transfer or exchange rate fees of the credit institutions), which are to be borne by you. Any costs incurred for the transfer of money shall also be borne by you in cases where the delivery is made to an EU member state, but the payment was initiated outside the European Union.
5.4. The payment methods available to you are indicated under a corresponding button on our website or in the respective offer.
5.5. Unless otherwise stated for the individual payment methods, the payment claims from the concluded contract are due for payment immediately.
- Terms of delivery
6.1. The terms of delivery, the delivery date and, if applicable, existing delivery restrictions can be found under a correspondingly designated button on our website or in the respective offer.
Insofar as no other deadline is specified in the respective offer or under the correspondingly designated button, the delivery of the goods will take place within 3-5 days after conclusion of the contract (in the case of agreed advance payment, however, only after the time of your payment instruction).
6.2. Insofar as you are a consumer, it is regulated by law that the risk of accidental loss and accidental deterioration of the sold item during dispatch shall only pass to you upon handover of the goods, regardless of whether the shipment is insured or uninsured. This does not apply if you have independently commissioned a transport company not named by the entrepreneur or a person otherwise designated to carry out the shipment.
- Statutory liability for defects
Liability for defects is governed by the "Warranty" provision in our General Terms and Conditions (Part I).
last update: 01/06/2022
Privacy policy
Unless otherwise stated below, the provision of your personal data is neither required by law or contract, nor is it necessary for the conclusion of a contract. You are not obliged to provide the data. Failure to provide this will have no consequences. This only applies if no other information is provided in the subsequent processing operations.
Collection, processing and disclosure of personal data when placing orders
When ordering, we collect and process your personal data only to the extent necessary to fulfil and process your order and to process your enquiries. The provision of the data is necessary for the conclusion of the contract. Failure to provide this provision means that no contract can be concluded. The processing takes place on the basis of Art. 6 para. 1 lit.b GDPR and is necessary for the performance of a contract with you.
Your data will be passed on, for example, to the shipping companies and dropshipping providers selected by you, payment service providers, service providers for order processing and IT service providers.
In all cases, we strictly observe the legal requirements. The scope of data transmission is limited to a minimum.
Duration of storage
After completion of the contract, the data will first be stored for the duration of the warranty period, then taking into account legal, in particular tax and commercial retention periods and then deleted after expiry of the period, unless you have consented to further processing and use.
Rights of the data subject
If the legal requirements are met, you have the following rights under Articles 15 to 20 GDPR: Right to information, to correction, to erasure, to restriction of processing, to data portability.
In addition, pursuant to Article 21 (1) GDPR, you have the right to object to processing based on Article 6 (1) f GDPR and to processing for direct marketing purposes.
Contact us on request. The contact details can be found in our imprint.
Right to lodge a complaint with the supervisory authority
In accordance with Article 77 GDPR, you have the right to complain to the supervisory authority if you believe that the processing of your personal data is not lawful.
Right to object
If the personal data processing listed here is based on our legitimate interest pursuant to Art. 6 para. 1 lit. f GDPR, you have the right to object to this processing at any time with effect for the future for reasons arising from your particular situation.
Shipping terms
We ship your order after we received them
for articles on hand latest 24 hours,
for articles with overnight supply latest 48 hours.
In case we need to order an article from our supplier our dispatch time depends on the reception date of the articles, but the articles will be shipped on the same day.
Our goal is to send the ordered articles in the fastest, but also most efficient and secure way to our customers.