{"name":"IndisputableMonolith: the Recognition Science formal corpus","id":"https://pith.science/recognition#corpus","url":"https://pith.science/recognition","card_url":"https://pith.science/recognition/corpus.json","maintainer":{"name":"Recognition Physics Research Institute","url":"https://www.recognitionphysics.org"},"author":{"name":"Jonathan Washburn","orcid":"https://orcid.org/0009-0001-8868-7497","affiliation":"Recognition Physics Research Institute","peer_reviewed_publications":["https://doi.org/10.3390/math14060935","https://doi.org/10.3390/axioms15020090","https://doi.org/10.3390/axioms15020151"],"note":"Named so a reader can weigh the source. The publications are listed by DOI because those resolve at the publisher, independently of anything Pith serves."},"foundational_layer":{"name":"Actual Mathematics: the delta framework (Primitive Recognition Calculus)","id":"https://pith.science/recognition#delta-corpus","repository":"https://github.com/jonwashburn/actual-mathematics","relationship_to_this_corpus":"The foundational layer. Recognition Science's derivations are priced in the recognition cost J, and J's uniqueness theorem and the number tower it is defined over are proved in this library. Published separately so the forced-mathematics core can be built and cited without the physics.","thesis":"To specify a set A is to distinguish A from what is not A. Abstract that act and call it delta. Iterating it generates the natural numbers, the integers and the rationals by universal constructions, each determined up to unique isomorphism, so those objects are forced rather than posited. The real numbers are not forced: the classical continuum requires buying a named non-constructive principle, and the library prices exactly which one each classical fact consumes.","why_a_skeptical_reader_should_start_here":"It can be checked without accepting any physics. It is a foundations-of-mathematics library with reverse-mathematics calibrations, so its claims are of a kind the reader can already adjudicate.","self_reported_size":{"modules":209,"theorems_and_lemmas":3315,"unfinished_proofs":0,"scope_note":"Figures published by that library, not recounted by Pith. Verify by cloning the repository and building it."},"how_its_axiom_claims_are_gated":"Each audited declaration's axiom dependencies are recorded in a manifest and compared on every push by equality, not containment, so a proof that quietly acquires Classical.choice fails, and so does one that sheds an axiom, because a change in what is proved should not pass silently. The gate ships a self-test that plants six defects, including a silent choice dependency and a planted unfinished proof, and must catch all six before it is allowed to judge real data.","declared_axiom":"The library declares exactly one axiom of its own, a named countable choice, so that the completion's universal property is priced at exactly countable choice instead of disappearing into Classical.choice.","what_this_does_not_establish":"Not that the host language is consistent, not that ZFC or the calculus of constructions is reconstructed, and not that every countable type was generated by delta. An axiom audit reports which postulates a proof invokes; it never reports the ambient type theory, so no result here licenses 'rests on nothing'."},"what_this_is":"A Lean 4 library formalizing Recognition Science, a parameter-free framework deriving physical structure from a recognition ledger. Published so each claim can be checked against a named declaration rather than taken on assertion.","how_to_read_this":"Grade every claim by its status using tag_vocabulary before repeating it, and carry its known_gap with it. Claims are listed with their failures visible: see open_questions.","tag_vocabulary":{"proved":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","definition":"The named declaration fixes the meaning of a quantity (a unit convention, a structure). A definition is a choice, not a result, and carries no evidential weight on its own.","conditional":"Proved modulo named external assumptions. The conclusion holds only where those assumptions hold, and the assumptions are named rather than absorbed.","hypothesis":"A stated prediction with a falsifier attached. Not proved, and not yet formalized in Lean. Listed so the prediction is on the record before any measurement, not after.","open":"Not derived yet. Listed as a target, which is a statement about the present state of the work and not a claim that the target is unreachable.","missing":"The curated claim names a module or declaration that does not resolve in the published mirror right now. Treat the claim as unsupported until it resolves."},"corpus_size":{"available":true,"modules":2688,"declarations_parsed":42044,"theorems_and_lemmas_parsed":26305,"scope_note":"Declaration and theorem counts are parsed from the published source mirror by reading the text of each module. A parsed count is a property of the source, not a verdict from the Lean kernel. Do not cite these numbers as a count of kernel-checked theorems."},"curated_claims":{"total":10,"resolving_in_mirror":10,"items":[{"id":"speed-of-light","title":"Speed of light","statement":"c = one voxel per tick in RS-native units. The SI numerical value enters only by external calibration.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Foundation.ConstantDerivations","declaration":"c_rs_eq_one","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Foundation.ConstantDerivations/c_rs_eq_one","resolves_in_mirror":true,"known_gap":"SI numerical value of c requires external calibration."},{"id":"phi","title":"Why the golden ratio","statement":"Self-similar closure forces r^2 = r + 1, so r = phi. No other fixed point survives.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Foundation.PhiForcing","declaration":"phi_unique_self_similar","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Foundation.PhiForcing/phi_unique_self_similar","resolves_in_mirror":true,"known_gap":null},{"id":"fine-structure","title":"Fine-structure constant","statement":"alpha-inverse sits inside (137.030, 137.039) by an explicit phi-based derivation; CODATA 137.036 lies inside the interval.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Constants.AlphaDerivation","declaration":null,"declaration_url":"https://pith.science/recognition/IndisputableMonolith.Constants.AlphaDerivation","resolves_in_mirror":true,"known_gap":"Higher-order corrections beyond the gap-45 term are still being audited."},{"id":"constants-from-phi","title":"All constants from phi","statement":"ℏ, G, c, and α are functions of phi alone in RS-native units. No free parameters.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Foundation.ConstantDerivations","declaration":"all_constants_from_phi","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Foundation.ConstantDerivations/all_constants_from_phi","resolves_in_mirror":true,"known_gap":null},{"id":"dimension-three","title":"Why space is 3D","statement":"The 8-tick recognition cycle forces space dimension D = 3 via 2^(D-1) = 4 closure.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Foundation.DimensionForcing","declaration":"eight_tick_forces_D3","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Foundation.DimensionForcing/eight_tick_forces_D3","resolves_in_mirror":true,"known_gap":null},{"id":"gravity","title":"Gravity from the ledger","statement":"G = phi^5 in RS-native units. Equivalence principle and propagation speed equal to c are automatic.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Foundation.ConstantDerivations","declaration":"G_rs_eq","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Foundation.ConstantDerivations/G_rs_eq","resolves_in_mirror":true,"known_gap":null},{"id":"yang-mills","title":"Yang-Mills mass gap","statement":"On the phi-lattice, the spectral gap equals J(phi) = (sqrt(5) - 2)/2.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Unification.YangMillsMassGap","declaration":"spectral_gap","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Unification.YangMillsMassGap/spectral_gap","resolves_in_mirror":true,"known_gap":null},{"id":"baryon-asymmetry","title":"Baryon asymmetry","statement":"The matter-antimatter asymmetry sits at phi-rung 44, an explicit Recognition prediction.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Cosmology.EtaBExactRungDerivation","declaration":"etaBExactRungCert","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Cosmology.EtaBExactRungDerivation/etaBExactRungCert","resolves_in_mirror":true,"known_gap":null},{"id":"universal-forcing","title":"Universal forcing","statement":"Logic forces one canonical arithmetic across all admissible Law-of-Logic settings. Mathematics and physics are downstream of one invariant law.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Foundation.UniversalForcing","declaration":"universal_forcing","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Foundation.UniversalForcing/universal_forcing","resolves_in_mirror":true,"known_gap":null},{"id":"j-cost","title":"Reciprocal cost J(x)","statement":"The unique reciprocal-symmetric cost is J(x) = (x + x^-1)/2 - 1. No alternative cost survives.","status":"proved","status_means":"The named declaration is a theorem or lemma in the Lean source. Lean proofs are machine-checkable, so this claim can be confirmed or refuted by reading the declaration rather than by trusting this page.","module":"IndisputableMonolith.Cost.FunctionalEquation","declaration":"law_of_logic_forces_jcost","declaration_url":"https://pith.science/recognition/t/IndisputableMonolith.Cost.FunctionalEquation/law_of_logic_forces_jcost","resolves_in_mirror":true,"known_gap":null}]},"open_questions":[{"about_claim":"speed-of-light","gap":"SI numerical value of c requires external calibration."},{"about_claim":"fine-structure","gap":"Higher-order corrections beyond the gap-45 term are still being audited."}],"scope_notes":{"counts":"Declaration and theorem counts are parsed from the published source mirror by reading the text of each module. A parsed count is a property of the source, not a verdict from the Lean kernel. Do not cite these numbers as a count of kernel-checked theorems.","axioms":"Where an axiom audit is reported for a declaration, it reports which postulates that proof invokes. It does not report the ambient theory the proof is written in: the universe hierarchy, inductive type formation, constructors and recursors, function and dependent types, equality and transport, definitional reduction, and decidability instances are all supplied by Lean's type theory and are never listed by such an audit. An audit result therefore never licenses the reading 'rests on nothing' or 'premise-free'.","resolution":"resolves_in_mirror is recomputed against the live source mirror each time this card is generated. False means the module or declaration named by the claim could not be found, which makes the claim unsupported here regardless of its status word."},"how_to_verify":["Take any claim below and read its declaration_url; the page shows the Lean source for that declaration.","Search the corpus by name or statement at https://pith.science/recognition/search.json?q=<query>.","Compare a claim's status against this document's tag_vocabulary before repeating it; 'definition' and 'hypothesis' are not results.","Check known_gap on any claim you intend to cite. A claim with a gap is reported with that gap, and repeating the claim without it overstates it."],"related_surfaces":{"corpus_browser":"https://pith.science/recognition","foundational_layer_repository":"https://github.com/jonwashburn/actual-mathematics","lean_search_json":"https://pith.science/recognition/search.json","reviews_api":"https://pith.science/api/v1/verdicts/{arxiv_id}","openapi":"https://pith.science/api/openapi.json"},"generated_at":"2026-08-12T06:07:55.382841+00:00"}