Frequently Asked Questions

Our evaluation methodology is a multi-tiered deductive audit combining three rigorous frameworks: 1. **The 5-State Epistemic Scale:** Rather than a binary accept/reject, claims are evaluated into *Impossible*, *Unknowable*, *Undecidable*, *Possible*, or *Proveable*. 2. **Axiomatic & Barrier Triage:** Decomposes submitted theorems against standard AMS MSC2020 classifications and Timothy Gowers' *Tricki* known mathematical obstructions. 3. **Atomic Logic Ledgers ($L_1 dots L_n$):** The core argument is broken into atomic deductive gates. Each gate is tested for algebraic consistency, non-circular definitions, and valid inferences. 4. **Empirical & Computational Stress Tests:** Numerical sequences are evaluated against integer sequence fingerprint databases and continuous radix growth models. Supporting Lean4/Coq/Python code is independently inspected for mock routines or deceptive AST structures.

Every manuscript is evaluated against this strict canonical sequence: * **#1 UNKNOWABLE (Night Blue):** Based on what has been submitted, it's impossible to ever know if it is true or false. * **#2 UNDECIDABLE (Ocean Blue):** Based on what has been submitted, it's possible to know that it's one of true or false but don't know which one. * **#3 IMPOSSIBLE (Coral Red):** Based on what has been submitted, it's logically impossible or provably false. * **#4 POSSIBLE (Beetroot Purple):** Based on what has been submitted, it is possible that it is true. * **#5 PROVABLE (Spring Green):** Based on what has been submitted, it can be proved that it is true and we have the Lean4 code that does so.

The **Three-State Epistemic Minimum (TSEM)** is the foundational problem-solving framework that replaces traditional 2-state/binary (True/False, Accept/Reject) models. TSEM mandates that every problem space must be partitioned into three non-overlapping domains: 1. **Defensibly Possible (S_P):** Logically consistent with axioms and supported by constructive or empirical evidence. 2. **Provably Impossible (S_I):** Violates boundary constraints, conservation laws, or proven contradictions. 3. **Irreducibly Unknowable (S_U):** Undecidable from within the system or intrinsically inaccessible. **Why TSEM matters:** In binary systems, unprovable premises are routinely "overwritten" by aggressive arguers forcing a false choice. By keeping S_U in a **permanent, protected quarantine**, TSEM immunizes scientific evaluation against rhetorical bullying and allows the Dual-Engine Convergence loop to isolate verified truths.

Auditors evaluate submitted manuscripts against a strict, multi-tiered standard documented in our formal specification. Every review follows a mandatory compliance matrix: 1. **TSEM Partitioning & Provenance:** Partitions the claim into S_P, S_I, or S_U and verifies document SHA-256 digests. 2. **Atomic Logic Ledger Construction (L_1 to L_n):** Decomposes the core derivation into step-by-step logic gates tested for valid deductive inferences, unstated assumptions, non-circular definitions, and metric preservation. 3. **Computational & Proof-Code Verification:** Runs automated AST sweeps on Python/C++ scripts and mechanized Lean 4 kernel verification. 4. **Remediation Vector:** Provides the author with explicit, actionable mathematical guidance on how to repair identified gaps. For complete compliance details, section requirements, and review templates, see our [Review Specification](/guidelines) (**Penta-Ledger Review Specification v1.1**).

**Code Flagged** is an independent computational audit gate. When a paper presents plausible mathematical prose (clearing the *Possible* state), its supporting computer algebra scripts, Python simulators, or Lean4 mechanizations are tested. If the code contains hard-coded lookup tables, unproven circular mock axioms, or deceptive AI loops, a **`CODE_FLAGGED`** overlay is attached to transparently alert the research community.

Even the most established disciplines have internal blind spots and undeclared assumptions that may bias their results. We adopt a Gödelian approach by acknowledging that no coherent system can fully demonstrate its own foundational consistency or prove all its core truths from within - and 'triangulating' everything within a paper against as many independent disciplines as possible to detect implicit axiomatic assumptions, domain bias and uncover empirical contradictions or counter-examples. For problems that have remained unsolved for years, we assume that all the jigsaw pieces usually already exist, but that no single discipline holds all the pieces. To help us find the jigsaw pieces, we actively translate techniques, formalisms and heuristics from all areas of science including computer science, physics, astronomy, engineering, chemistry, biology, medicine, economics, financial markets, operational research, management science, neuroscience, behavioural science, experimental psychology and many more.

Many comprehensive papers contain multiple distinct theorems or conjectures. When a paper states multiple primary claims (e.g. Claim 1: Euclidean bound; Claim 2: Complex projective manifold extension), The Penta-Ledger evaluates each claim independently on the 5-state scale, and maps each atomic logic gate in the ledger to the specific claim it affects.

Each submitted manuscript is assigned a **Lead Auditor** that specialises in a diverse mix of computational analysis techniques and Formal Verification, to find the subtle inconsistencies, undeclared assumptions and encoded biases at the foundation of a claim. Taking an exhaustive interdisciplinary approach is vital because sometimes papers can be proven in one discipline yet disproved in another which can bring both disciplines into disrepute until the truth is discovered (if it can be) — the potential to disrupt one's own entire field highlights the importance of allowing senior researchers to make anonymous submissions. The Lead Auditor is supported by specialty co-auditors and automated code verification units. All audits are published under editorial board oversight.

**Every audit is strictly human-led: the quality, validity, and epistemic classification of a review ultimately depends on the intellectual discernment and judgement of the Lead Auditor.** However, our human auditors make aggressive use of the leading edge of technology tooling, automation, and disruptive innovations. We use AI as a force multiplier to accelerate literature searches, adversarial hypothesis testing, brute-force parameter sweeps, edge-case probing, experiments, and writeups. Having built a world-leading understanding of how AI tackles complex mathematical and scientific problems, **we are neither naive to what AI can and cannot do, nor are we naive to what humans can and cannot do.** AI discovers counter-examples and explores edge-cases at machine scale; human Lead Auditors provide sovereign deductive discernment, domain context, and ultimate scientific accountability.

**You cannot contact a reviewer directly, at least not through us.** To guarantee complete impartiality, protect auditors from lobbying or academic pressure, and ensure fearless evaluation of contentious claims, reviewer identities and personal contact channels are strictly shielded.

We welcome applications from mathematicians, theoretical computer scientists, physicists, and mechanized formalization specialists (Lean 4 / Coq). Reviewers must demonstrate deductive rigor and a commitment to pedigree-blind evaluation. To apply, email your CV, areas of MSC specialization, cryptographic public key, and relevant verification experience to **admin@penta-ledger.org**.

For general inquiries, editorial questions, or partnership proposals, you can reach the core team directly by email at **admin@penta-ledger.org**.

Scientific truth depends entirely on the logical validity of the equations and deductions—not on institutional prestige, citation metrics, or academic rank. We allow anonymous and pseudonymous submissions for two vital reasons: 1. **Eliminate Pedigree Bias:** To give independent, early-career, and non-affiliated researchers a level playing field where mathematical deductions are evaluated purely on their technical merit. 2. **Safe Exploration for Risky & Disruptive Ideas:** To allow established researchers to receive feedback on their disruptive, highly-innovative or risky findings without compromising their reputation (or simply speculative findings that have a high chance of being wrong but are still worthy of publicly sharing just in case they are right). Every submission receives a 3rd-party verifiable timestamp block, SHA-256 document hash, and cryptographic receipt to establish scientific priority without requiring identity disclosure. This cryptographic receipt can be used by the author to reveal their identity in the future if they wish - but in the meantime, we have no way of knowing who they are.

* **Submit your paper (/submit):** For original manuscripts you have authored or co-authored. You must check a mandatory declaration confirming your authorship or authorization. * **Submit a public paper (/submit-public):** For nominating existing public domain preprints or papers (e.g. on arXiv, OpenReview, Zenodo, DOI, or university repositories). Submission is strictly URL-only, and that exact public URL is preserved and displayed as the canonical reference.

When nominating public domain research, The Penta-Ledger does not host duplicate uploads. Submitting the public URL ensures that the review links directly to the author's primary public distribution source, preserving canonical provenance.

* **If you are the Submitter:** Submitters can submit a formal **Constructive Disagreement** as part of the review workflow. You can submit clarifying derivations, fill identified logic gaps, or demonstrate why a flagged barrier does not apply for formal re-audit consideration. * **If you are a Community Member:** Every completed review auto-generates a companion **Editorial Blog Post**. You can read the Lead Auditor's narrative, post your counter-arguments, and engage in open mathematical discourse in the comment section.

The Penta-Ledger operates as an independent, non-profit scientific public good supported by research foundation grants and open-science benefactors. **We charge zero author fees, zero submission charges, and zero pay-to-publish fees.** All reviews, ledgers, and blog articles are 100% open-access.

When an author submits a manuscript, your browser uses native Web Crypto to generate an asymmetric RSA-2048 keypair. It then applies a subtle, non-occluding watermark strictly to the outer margins (top header and bottom footer) containing your UTC timestamp, SHA-256 document digest, OpenTimestamps (OTS) marker, and public key fingerprint. This provides mathematically irrefutable proof that your manuscript existed in that exact state at that exact moment in time.

**The Penta-Ledger never receives, transmits, or stores your private key.** Your RSA-2048 keypair is generated 100% locally inside your browser sandbox via the native Web Crypto API (`window.crypto.subtle`). When you submit, only the **Public Key** is sent in the form payload. Your private key stays on your device and is downloaded inside your receipt JSON. For complete source code and a 30-second Developer Tools audit guide, read our [Client-Side Cryptography & Key Sovereignty](/crypto-transparency) documentation.

Yes. Every published review and logic ledger can be downloaded as machine-readable **JSON**, publication-ready **LaTeX**, or **PDF**. You can cite audit ledgers in academic papers using the unique Review ID (e.g. `Review #MATH-202X-REF-001`) and permanent SHA-256 verification URL.

Yes! The entire Penta-Ledger platform is operating in **Public Beta (v0.9.4)**. During this beta phase, our epistemic auditing pipelines, automated code validation gates, and interactive logic ledgers are active for community and author submissions. We actively welcome researcher feedback, bug reports, and reviewer applications at **admin@penta-ledger.org**.