From an explicit near-solution to an exact G₂ metric

active geometry · opened 2026-06-11

Statement. Promote the explicit Donaldson-type near-solution on K₇ (K3 fibration over S³, ℤ₂³ fiber symmetry) to an exact torsion-free G₂ metric, or characterize the obstruction.

Why it matters. This is the program's central lock. The topology (21, 77) is rigorous, the Calabi-Yau residual is interval-certified, the near-solution is explicit; exactness is what separates a certified candidate from the geometry.

Known constraints. Existence by gluing (Joyce-Kovalev type) is guaranteed for small enough parameter, but a closed-form exact representative is research-level. Blockwise Newton-Kantorovich contractibility near the near-solution has been verified on all 7 nontrivial ℤ₂³ isotypic blocks (margins 7×). Four classical construction templates (Joyce, TCS, extra-twisted TCS, CCY₇) are excluded by theorem; the object is not covered by existing taxonomies.

Next step. Full adiabatic coupling across blocks (Stage 2 of the Kantorovich program); singular Monge-Ampere and continuity-method routes scoped as alternatives.

Why this geometry rather than another?

active selection · opened 2026-06-11 · updated 2026-07-04

Statement. Why this geometry? Identify the principle that selects K₇, the Betti pair (21, 77), and the assignment of formulas to observables, or demonstrate that no such principle is needed beyond consistency.

Why it matters. This is the program's problem number one. The landscape gives up uniqueness; Arithmon bets on it. The bet is only won if selection is explained, not assumed.

Known constraints. The geometry is not generic, and the evidence is arithmetic before it is physical: the polarizing K3 lattice, Nikulin type (15, 7, 1), is a classified reflective point (60-root reflection lattice, a Petersen-graph stratum, automorphisms by S₅); the fiber carries a symplectic automorphism group containing V₄ × ℤ/5 through two distinct elliptic fibrations; six structural obstructions separate the object from every standard template. None of this yet amounts to a selection principle; it amounts to the geometry being a distinguished point in several classifications at once.

What is established (2026-06-18)

The question splits cleanly and the two halves answer differently.

Topological rarity. (b₂, b₃) = (21, 77) is reached by no twisted connected sum construction (exhaustive 3852-configuration no-go, CHNP b₂ max about 18); it sits in a genuine gap of the realized G₂ Betti census (nearest realized (19, 65)); it is reached only via the Joyce-Karigiannis / Donaldson K3-fibration route. So the pair is rare as a G₂ manifold. But rarity is representation-dependent: its CY₃ shadow via the Künneth decomposition CY₃ × S¹, namely (h¹¹, h²¹) = (21, 27), is realized by 668,607 distinct reflexive 4-polytopes in the Kreuzer-Skarke database. The G₂ rarity argument does not transport to the CY₃ representation of the same numbers.

Inverse-problem specialness. In a blind, mirage-proof sweep (alphabet size held constant across the grid; only the Betti leaf values change) over the full Kreuzer-Skarke Hodge range (b₂, b₃ each in [0, 491], 242,064 grid points), the Sieve re-runs the search per pair and asks how cheaply and how widely each pair fits the frozen Standard Model set. (21, 77) sinks below the median on every discriminating axis: about 64% of grid pairs strictly beat it on Betti-sensitive coverage at the discriminating tolerance, and it sits in the expensive quartile at tight τ. The CY₃ shadow (21, 27) is even less special. The verdict grows as the haystack grows: smaller prior grids were the conservative reading, in the pair's favour. Specialness, in the inverse-problem sense, is not where the geometry lives.

Reading. The two halves are independent and both honest. The inverse-problem half closes one candidate channel: the Betti pair is not arithmetically privileged at fitting the freeze, so the principle, if there is one, is not "(21, 77) is the cheapest set of leaves to reach the Standard Model". The topological half keeps the distinguishedness channel open, in the K3-lattice direction the constraints already name; it does not amount to a principle on its own.

What is established (2026-07-04)

The announced next step has been carried out in both directions, and a third route has been audited. All three close.

Lattice propagation, settled negatively by mechanism. The distinguishedness of the lattice keeps growing: it is realized as the invariant lattice of non-symplectic involutions on hyperkahler fourfolds of K3^[2] type, and it is the unique named exception of the published mirror-existence lemma for that setting. But none of it reaches b₃ = 77, for independent structural reasons now proved rather than suspected. First, b₂ = 21 is equivalent to rank-one monodromy, so the S₅ lattice symmetry is broken to a stabilizer before it can act on the monodromy data. Second, 77 counts components of the discriminant link and lives in the link complement, a factor disjoint from the lattice data in the Donaldson cohomology model: the factor 11 of 77 = 7 × 11 appears in none of the lattice-derived invariants actually swept, neither the S₅ irreps and their sums, products and powers, nor the Petersen graph counts, nor the full root diagram. Third, the only higher-hyperkahler type that can host the lattice has zero odd cohomology, so there is nothing on that side to match a link count against. Distinguished, yes; selecting, no.

Diophantine route, audited and closed as a principle. The published system ((rank + N_gen) b₂ = N_gen b₃, b₂ + b₃ = S) is linear with nonzero determinant, so a unique rational solution always exists; integrality is a divisibility comb, not a filter. The solution factors as (b₂, b₃) = k (N_gen, rank + N_gen) with k = S / (rank + 2N_gen); at (8, 3, 98) this reads (21, 77) = 7 × (3, 11). All selection power sits in the single integer choice S = 98, which remains underived in the source papers, and one of their screening premises (realizability requires b₂ ≥ 9) is contradicted by the literature census: 27 of the 65 known compact G₂ manifolds have b₂ < 9, including Joyce's (0, 215). The authors of that route have themselves downgraded the claim to a unique candidate solution (May 2026).

Residue. The open problem now reduces to a single statement: derive b₂ + b₃ = 98 = dim K₇ × dim G₂ (equivalently k = 7) from a pre-registered principle. In the factored form (b₂, b₃) = dim K₇ × (N_gen, rank + N_gen), the selection question dissolves into the standard physical inputs (7, 3, 8): dimension, generations, rank. Until 98 = 7 × 14 is derived, it is an observation, not a principle, and must not be used as one.

Next step. Only the residue qualifies: a pre-registered derivation of b₂ + b₃ = dim K₇ × dim G₂. The inverse-problem channel, all presently specified lattice-to-b₃ propagation mechanisms, and the Diophantine route are closed; the honest standing verdict is "a distinguished point in several classifications at once, with no selection principle behind it so far", now established channel by channel rather than assumed out of caution. A propagation mechanism nobody has specified yet would reopen the topological channel; it would have to enter through the link complement, where 77 lives.

Do the spectral data of K₇ have a closed form?

dormant geometry · opened 2026-06-11

Statement. Do the Laplacian spectral data of the K₇ geometry admit exact closed forms, and in which basis?

Why it matters. The prediction chain runs through spectra. Exact spectral data would replace numerical inputs by counts, extending the hard core's reach.

Known constraints. Largely negative so far, and the negatives are part of the map: two block coefficients are confirmed torsion-minimizing rationals (19/6 and 7/6), but the K3-block coefficient 64/77 is demoted to a rational approximation (0.41 percent, basin-dependent across seeds, so no exact spectrum behind it); a naive exponent pattern is falsified at the 10⁻¹² level by interval certification; exhaustive search over rational and standard transcendental bases finds no closed form at 15-digit precision. These refutations were applied to the program's own candidates, which is the negative heuristic in action.

Next step. The only identified non-exhausted route is genuine theory, not search: a Picard-Fuchs analysis of the period structure. Off the critical path; dormant until prioritized.

From one certified box to all of K3

open geometry · opened 2026-06-11

Statement. Extend the certified bound on the Calabi-Yau volume-form residual from a box-local statement (4000 open boxes, Krawczyk-verified, with the variance aggregation re-computed inside Lean) to a global bound on all of K3.

Why it matters. The box-local certificate is the framework's rigor anchor; a global bound would remove the locality caveat entirely.

Known constraints. The current certificate gives a variance envelope of 1321/10⁷ with 7.57× safety margin, formally aggregated from raw rational enclosures. Scoping concluded that a genuinely global bound is research-level and that the only identified route is a Positivstellensatz or sum-of-squares certificate over the orbifold chart.

Next step. Sum-of-squares feasibility study on a reduced chart; no commitment until the central lock (the exact metric) settles priorities.

Fifteen axioms, and the road to none

open formalization · opened 2026-06-11

Statement. Reduce the 15 stated axioms of the Lean core (4 on the prediction chain, 11 interval-arithmetic certificates for the K3 block) toward zero.

Why it matters. "15 to N" is the program's cleanest public progress metric: machine-checked, monotone, and impossible to spin.

Known constraints. The core builds with 0 sorry; the 33 exact relations and the variance aggregation are axiom-free. The 11 K3 certificates are trusted numerical facts (interval enclosures from a second, exact rational engine, cross-checked 28000/28000); discharging them means verified interval arithmetic inside Lean, bounded but heavy. The 4 prediction-chain axioms package literature results (Cheeger-type bounds, gluing theorems); they are the real formalization frontier and may require upstream Mathlib work.

Next step. Discharge the 11 K3 certificates first, which is mechanical and bounded; treat the 4 literature axioms as a separate long-horizon track.

How surprising is an exact relation?

active epistemic · opened 2026-06-12 · updated 2026-06-14

Statement. Build a framework-independent standard for the question: how surprising is a set of claimed exact relations between mathematical invariants and measured physical constants? A declared expression space, explicit complexity measures, a family of null models with look-elsewhere correction, and a scorecard that any framework can be run through, including the program's own.

Why it matters. The field has no shared instrument for this question; claims oscillate between uncritical acceptance and reflexive dismissal, and the verdicts (Eddington on one side, the quantum Hall relation on the other) are only sorted in hindsight. Every other axis of the program inherits its credibility from this one, and the standard stands on its own: it survives even if the founding framework falls.

Known constraints. The instrument must pass calibration before it is allowed to score anything we care about: deliberately constructed fake frameworks must be condemned, Eddington's 136-then-137 must fail with a penalty for the revision, the quantum Hall relation must pass. Searching expressions against measured values before the target list is frozen would invalidate the exercise, so the freeze must be deposited with a dated DOI first; a data update (new PDG edition, new global fit) is a new freeze version, and verdicts against the old version stand.

Next step. The instrument is the Sieve. Current state: inputs frozen and deposited before any search ran; four null models implemented; calibration complete at scaffold budget. The constructive side, the rebate that distinguishes a relation which is a theorem of a pre-specified structure from one found by search, now has a stated definition and a machine-checked formal layer in arithmon/lean. Next: deeper enumeration, the adversarial-alphabet envelope on real targets, robustness across grammars and complexity measures, the per-relation audit, then the methods paper.

Who else has checked?

active epistemic · opened 2026-06-11

Statement. Get the framework's certified chain examined, reproduced or refuted by independent human experts, through peer review and direct engagement.

Why it matters. A machine-checked core removes one class of doubt; it does not replace the judgment of the relevant communities. A program whose results are only machine-verified and self-reported is epistemically incomplete.

Known constraints. Current state: the founding paper is under journal review; a numerical G₂ dataset from this line of work is cited in the peer-reviewed literature (Phys. Lett. B 878 (2026) 140566); the certified K3 result has a presubmission inquiry pending at a mathematics journal. The author publishes solo and without institutional affiliation, which makes the usual channels slower; this is a constraint of the territory, not an excuse.

Next step. Land the two pending submissions. Use the atlas as the first-contact instrument: every convergent entry is a potential reviewer who already cares about the adjacent question.

Exposed to the data, permanently

active experimental · opened 2026-06-11

Statement. Keep the frozen predictions exposed to scheduled data, record every verdict, and never move a goalpost.

Why it matters. This is the axis where the program has the fewest levers and the most to prove: nothing here can be worked on, only awaited honestly. It is also where progressive and degenerating programs part ways.

Known constraints. The predictions are frozen and dated; the data arrives on external calendars (global neutrino fits roughly every one to two years, the Hyper-Kamiokande and DUNE oscillation experiments in the late 2020s to mid 2030s). One prediction is currently in tension (the θ₂₃ upper-octant bet, with the global best fit presently in the lower octant and the octant unresolved), one returned to agreement without being touched (δ_CP after the latest fit), one is standing (three generations).

Next step. Maintain the scoreboard as the single record; add each new fit release as a dated entry, favourable or not.

The Eudoxean Theory of Ratio and the Crisis of the Incommensurable

convergent philosophy · Eudoxos of Cnidus; Euclid (Elements, Book V); Howard Stein · Euclid, Elements Bk V; Howard Stein, Synthese 84 (1990) 163-211

Claim. A ratio between magnitudes of the same kind is defined abstractly by the equimultiples criterion (Def. V.5), so that proportion theory survives the discovery of incommensurability. The construction is mathematically the Dedekind cut, anticipated by 2300 years, and depends on the Archimedean axiom (no infinitesimals).

Relation. Convergent. This is the historical ancestor of the Arithmon thesis. The Pythagorean program ("all is number", every ratio is a ratio of whole numbers) is the original form of constants-as-counts; the crisis of the incommensurable (√2) is what forced two and a half millennia of the continuum over the integer. Arithmon is a dated, narrower return to the integer as primitive, one level up: at the dimensionless constants of physics.

Δ. Eudoxos abstracts away from the integer to keep rigor after the crisis, enthroning the continuum; Arithmon reinstates the integer as primitive at the level of physical constants and treats the transcendental as derived from counts. The Greek move is unconditional mathematics about magnitudes in general; the Arithmon wager is empirical, falsifiable, and entirely its own risk. The lineage is framing for program identity, never evidence for any claim.

Arithmetization and Constructive Mathematics

convergent mathematics · Leopold Kronecker; Brouwer; Bishop · H. Weber, Jahresbericht DMV 2 (1893); E. Bishop, Foundations of Constructive Analysis (1967)

Claim. Mathematics should reduce to arguments over the integers in finitely many steps, and to assert existence is to exhibit a construction. Kronecker rejected non-constructive methods (irrationals, Bolzano-Weierstrass) from the 1870s; the line runs through Brouwer's intuitionism and Bishop's constructive analysis to today's proof assistants.

Relation. Convergent. This is the headwater of two Arithmon pillars at once: integer-primacy ("God made the integers") and the demand that a claim be earned by a construction rather than asserted, which is the spirit of the constructive (Lean) axis.

Δ. Kronecker and the constructivists are a doctrine about how mathematics should be founded, internal to mathematics; Arithmon makes an empirical, falsifiable wager about physics (constants are counts) and asks a proof assistant to certify it. Honest caveat both ways: Lean's Mathlib is classical, so the constructive axis is constructive in the sense of built and certified, not intuitionistic; the kinship is in spirit, not in logic.

Fundamental Theory: deriving the constants from pure number

divergent physics · Arthur Stanley Eddington; Dirac's Large Numbers Hypothesis · A. S. Eddington, Fundamental Theory (1946); H. Kragh, arXiv:1510.04046

Claim. The exact values of the dimensionless constants of physics can be deduced by logical reasoning from qualitative principles, with no use of observational data. Eddington derived the inverse fine-structure constant as 136, then 137; Dirac read the recurring 10⁴⁰ ratios as a law and inferred a time-varying gravitational constant.

Relation. Divergent. This is the cautionary pole of the lineage: serious attempts to read significance into number that were wrong. Eddington never justified revising 136 to 137 beyond the measured value's pull, the textbook case of a derivation chasing the number it wants.

Δ. Eddington and Dirac are exactly what Arithmon must be able to tell itself apart from, and the methodology axis encodes this directly: its negative control is Eddington-must-fail, since a test that cannot reject 137 is measuring nothing. What separates Arithmon is procedural, not rhetorical: the alphabet is geometrically pre-specified and frozen before search, and a claim must survive being made a theorem, neither of which the cautionary pole offered.

It from Bit: Information, Physics, Quantum

convergent physics · John Archibald Wheeler · "Information, Physics, Quantum: The Search for Links" (1989)

Claim. Every physical entity, every it, derives its existence from binary, yes-or-no answers: "it from bit". Reality is participatory and information-theoretic, with the discrete and informational prior to continuous substance.

Relation. Convergent. The physics-side echo of discrete primacy, and the founding framework's own footer ("GIFT from bit") is a direct nod to it. Sibling to the constructivist thread, not part of it: Kronecker's discreteness is about how mathematics is founded, Wheeler's about what physical reality is made of.

Δ. "It from bit" is metaphysically maximal and methodologically minimal: a slogan for a research direction that yields no specific number, the same delta the atlas records for Tegmark. Arithmon takes the discrete-information intuition and commits it to dated, exact counts that can be wrong; Wheeler supplies the ontology, Arithmon supplies the risk.

Mirror Symmetry for K3 Surfaces with Nonsymplectic Involution

convergent mathematics · Valery Alexeev; Philip Engel · arXiv:2208.10383

Claim. Compactifications and mirror constructions for K3 surfaces with nonsymplectic involutions, organized by Nikulin invariants (r, a, δ), with the reflective cases classified.

Relation. Convergent. The K3 lattice at the heart of the founding framework's fibration, Nikulin type (15, 7, 1), is one of the classified reflective points, with rich structure: a 60-root reflection lattice, a Petersen-graph stratum, automorphisms by S₅.

Δ. Alexeev-Engel is pure K3 geometry with no G₂ or physical reading; Arithmon reads precisely this kind of arithmetic distinguishedness as a candidate selection principle: the geometry is special because the arithmetic says so, before physics is mentioned. Their classification is unconditional mathematics; the physical reading is entirely Arithmon's risk.

Twisted Connected Sum G₂ Manifolds

divergent mathematics · Alexei Kovalev; Alessio Corti; Mark Haskins; Johannes Nordström; Tommaso Pacini · Duke Math. J. 164 (2015) 1971-2092

Claim. Large families of compact G₂ manifolds can be built by gluing two asymptotically cylindrical Calabi-Yau halves along a common K3 surface (the twisted connected sum construction).

Relation. Divergent. The TCS program supplies most known compact G₂ examples, and the founding framework's geometry provably lives outside it.

Δ. The Betti pair (21, 77) is excluded from all classical and extra-twisted TCS constructions (an exhaustive no-go over 3852 building-block configurations); the candidate geometry is a Donaldson-type coassociative K3 fibration instead. The divergence here is a theorem, not a preference, and the TCS toolbox (matching problems, K3 lattices) remains the shared language.

Spectral Geometry: Can One Hear the Shape of a Drum?

convergent mathematics · Mark Kac; the inverse spectral geometry tradition · Amer. Math. Monthly 73 (1966) 1-23

Claim. Geometry leaves quantitative signatures in spectra; part of a manifold's shape, though not all of it, can be recovered from its eigenvalues.

Relation. Convergent. The prediction chain of the founding framework runs through Laplacian spectra of the compact geometry.

Δ. Inverse spectral geometry asks what spectra reveal about geometry in general; Arithmon makes the converse, physical bet: that the sound of one compact geometry is not merely qualitative but numerically identical to the measured constants of nature.

Information Geometry

convergent mathematics · Shun-ichi Amari · Information Geometry and Its Applications, Springer, 2016

Claim. Families of probability distributions form curved manifolds with natural metrics (Fisher information) and dual connections; statistical structure is intrinsically geometric.

Relation. Convergent. Arithmon also treats informational structure as geometric.

Δ. Information geometry stays at the level of statistical manifolds and is agnostic about fundamental physics; Arithmon asks whether the dimensionless constants themselves are exact topological counts of one compact geometry. Amari's program has decades of theorems and applications behind it; Arithmon's reading of the constants is a young, falsifiable bet.

Neural and Numerical Methods for G₂-Structures

convergent methods · Daniel Heyes; Edward Hirst; Henrique Sá Earp; Marina Silva · Phys. Lett. B 878 (2026) 140566

Claim. Machine-learning and numerical schemes can approximate G₂-structures on contact Calabi-Yau 7-manifolds and quantify their torsion numerically.

Relation. Convergent. Shared toolbox (numerical G₂ geometry); the paper cites a numerical G₂ dataset from this line of work.

Δ. Their target is approximate structures across a class of 7-manifolds, with accuracy assessed empirically; the founding framework fixes one geometry and pushes the numerics to certified statements (interval arithmetic with formally verified aggregation). Approximation breadth on their side, certified depth on Arithmon's; the two are complementary, not competing.

The Koide Formula

convergent physics · Yoshio Koide · Lett. Nuovo Cim. 34 (1982) 201; Phys. Rev. D 28 (1983) 252

Claim. The charged lepton masses satisfy an exact-looking algebraic relation: the sum of the masses divided by the square of the sum of the square roots equals 2/3, to striking precision and with no accepted derivation.

Relation. Convergent in spirit: an exact algebraic relation among measured constants, taken seriously for decades.

Δ. Koide is one isolated relation without a structural origin, orphaned for forty years; Arithmon embeds many relations in a single declared vocabulary with set-level statistics and a geometric origin candidate. Koide is also the cautionary tale the program must answer: exactness alone does not make a theory, and longevity without an origin is a possible fate.

Algebraic Stability and Cosmological Structure (series)

convergent physics · Zhou Changzheng; Zhou Ziqing · paper series A-F, 2026

Claim. A logically self-consistent self-referential dynamical system, plus five mathematical primitives, uniquely forces 7 dimensions, G₂ holonomy, Betti numbers (21, 77), the Standard Model gauge group and three generations.

Relation. Convergent. An independent, top-down path to the same Betti pair; the series cites the founding framework as empirical motivation.

Δ. Zhou derives the topology from self-referential axioms, and part of the series' own predictions has already failed by its own falsification criterion (a neutrino mass prediction); the founding framework reads the same pair from an explicit compact geometry with machine-checked certificates, and its frozen predictions stand so far. Two different roads arriving at one number pair is itself a datum the program must explain.

Update (2026-07-04). The series has continued at high volume (two follow-up series and two May 2026 foundation papers, which cite the founding framework in the bibliography only). Substantively: the authors have downgraded the uniqueness claim to a unique candidate solution (May 2026), conceded the neutrino ratio falsification (reframed as an order-of-magnitude benchmark, March 2026), and now gloss the load-bearing premise as b₂ + b₃ = 98 = dim K₇ × dim G₂, which remains underived. An exact audit on the program side shows the Diophantine system is a reparametrization, with all selection in the choice k = 7, so the convergence datum stands but the derivation half of it has thinned. See the selection principle for the standing verdict.

Heterotic E₈×E₈ String Compactifications

divergent physics · David Gross; Jeffrey Harvey; Emil Martinec; Ryan Rohm; the heterotic G₂ literature · Phys. Rev. Lett. 54 (1985) 502

Claim. The E₈×E₈ heterotic string compactified on special-holonomy spaces yields realistic four-dimensional gauge sectors; heterotic G₂ backgrounds with torsion require specific torsion classes to vanish.

Relation. Divergent, despite the shared E₈×E₈ vocabulary.

Δ. Heterotic G₂ backgrounds require exactly the torsion component in which the framework's structure lives to vanish: the near-solution sits in pure Bryant class W₂ (the 3-form is closed exactly, all residual torsion in the coclosure), the opposite configuration. Arithmon borrows the E₈×E₈ architecture as motivation, not as string dynamics; nothing in the framework assumes a string vacuum, and nothing in heterotic theory predicts this geometry.

The String Landscape

divergent physics · Leonard Susskind; Michael R. Douglas; and others · arXiv:hep-th/0302219 (2003)

Claim. Low-energy constants may vary across an enormous space of string compactifications; the values we observe may be environmentally or anthropically selected.

Relation. Divergent.

Δ. The landscape derives its vacua from a candidate fundamental theory but gives up uniqueness of the constants; Arithmon posits a rigid compact geometry with zero adjustable parameters but does not yet derive why this particular geometry. Each side lacks exactly what the other claims to have.

Structural Realism

convergent philosophy · John Worrall; James Ladyman; Steven French · Dialectica 43 (1989) 99-124; Ladyman and Ross, Every Thing Must Go, OUP, 2007

Claim. What survives theory change in physics is structure (relations, equations), not the objects the theories posit.

Relation. Convergent. Arithmon is structural realist in spirit: it locates physical content in arithmetic and topological structure rather than in objects.

Δ. Structural realism is a thesis about scientific theories in general and makes no numerical commitments; Arithmon instantiates the structure as the invariants of a specific compact geometry and exposes it to exact, dated, falsifiable predictions. The philosophy supplies the frame; Arithmon supplies a test case the philosophy never asked for.

Mathematical Universe Hypothesis

orthogonal philosophy · Max Tegmark · Found. Phys. 38 (2008) 101-150

Claim. Physical reality is a mathematical structure, and all consistent mathematical structures exist on equal footing.

Relation. Orthogonal. Maximal metaphysical kinship, minimal methodological overlap.

Δ. The hypothesis ranges over all structures and yields no specific numerical prediction; Arithmon commits to one structure and stands or falls with dated, exact predictions. Arithmon is what the mathematical universe looks like when it picks a structure and accepts the risk of being wrong.

Wolfram Physics Project

orthogonal physics · Stephen Wolfram; Jonathan Gorard · A Project to Find the Fundamental Theory of Physics, Wolfram Media, 2020

Claim. Physics may emerge from discrete computational rewriting rules on hypergraphs; space, time and matter are downstream of rule dynamics.

Relation. Orthogonal, with a partial divergence on mechanism.

Δ. Wolfram seeks emergence of physical law from computation and treats specific constants as largely out of reach for now; Arithmon is not computational emergence: it is arithmetic-geometric determination, reading specific dimensionless constants directly as topological invariants of a fixed geometry.