IRMT
Information Relational Manifestation Theory
A research program in fundamental physics

Information Relational Manifestation Theory

What if space, time, and matter are not where physics begins — but what a deeper web of relations leaves behind?

Abdulaziz Abdi /Toronto /Working draft 0.9.33 /2026
Begin
I — The premise

Remove the stage, and see what is left.

For a hundred years, physics has staged the world inside a smooth continuum of space and time — a fixed arena on which fields ripple and particles move. The arena is assumed. Everything else is placed upon it.

IRMT asks a more unsettling question. What if the arena is not fundamental at all? What if space, distance, geometry — even the passage of time — are not the ground floor of reality, but patterns that emerge from something more primitive underneath?

The proposal is austere. At the bottom there are no coordinates, no distances, no particles. There is only a discrete web of events, related to one another by nothing more than order — which came before which — and the information carried along the links between them. From the statistics of that web, the theory contends, the familiar universe must be reassembled.

II — The primitive picture

Four things, and nothing more.

The substrate is built from a small vocabulary. Its discipline is that each piece is defined precisely, and none of it presumes the world it is meant to explain. The labels we attach to events are bookkeeping only; physics is whatever survives when the labels are scrambled.

𝒞
Events

A set of primitive happenings. Not points in space — just occurrences, without position or identity of their own.

Causal order

A relation of before-and-after. It never loops, it carries through, and between any two events lie only finitely many others. This is the seed of time.

𝓗
Fibers

Each event carries a small quantum state space — a finite bundle of complex information attached to it, the raw material of matter and charge.

U
Transports

Along each link, a rule carries information from one fiber to the next without loss. How that rule twists around a closed loop becomes force and geometry.

Trace the smallest closed loops in the web — the theory calls them causal diamonds — and compare the two ways information can travel around them. The mismatch is a single number that does not depend on how you labelled anything. Out of such mismatches, IRMT argues, the curvature of spacetime and the forces of nature are supposed to appear.

III — From relations, a universe

Five ways the world must be recovered.

If everything familiar is emergent, then every familiar structure has to be earned back — derived as a large-scale, statistical pattern of the network, not smuggled in by hand. IRMT divides that labour into five sectors. Each map below is generated from the audit ledger itself: a chain of what is assumed, what is proved, and where the argument still has to travel.

How to read the maps
Arrows — the kind of link between two steps
Green — derived. A step proved inside the theory.
Orange — foundational bridge. An assumption the route rests on.
Blue — construction. A definitional or structural link between objects.
Grey — imported theorem. A result borrowed from established mathematics.
Purple — open route. A link not yet secured; the work still ahead.
Red — empirical test. A prediction confronted with real data.
Boxes — the status of each step
Blue — substrate. The relational starting point.
Green — derived result. Established within the theory.
Teal — observable. A measurable quantity or target.
Cream — input or candidate. Supplied to the construction.
Purple — open problem. Not yet secured.
Red — empirical target. A prediction to be checked against data.
Grey — imported bridge. Carried over from external results.
01

The Quantum sector

Where quantum probability comes from — and why the correlations between distant measurements can be strong, but not arbitrarily strong. Alongside the ceiling itself, the Born rule now has a route of its own: rank-one weights extended to rank-general projectors, then to full effects and mixed states. What remains open is the last step down — deriving the update axioms from the substrate rather than assuming them.

Quantum sector dependency map QREV-2026-08-15-20 · Core WD 0.9.33 · Master Ledger 1.1.12 I · COHERENCE ROUTE II · OPERATIONAL PROBABILITY ROUTE III · BORN WEIGHTS AND UPDATE RULES definition foundational bridge state-space reduction maximum entropy circular moment negative control declared conditional derivation derive correlator finite coherence marginals cancel conditional target LQ-POVM + AX1J not yet extended conditional theorem WN-Q6 + AX1J purification UR1 + UR3 not derived premise Relational substrate FND-01 Relational Unity functional S_U FND-02 Unity-weighted history measure FND-03 · upstream open Circular orientation φ_coh QNT-01/02 Von Mises distribution QNT-03 [THM] Visibility η = I₁(κ)/I₀(κ) QNT-04 Damped-PR negative control QNT-20 · control Operational regions, settings and outcomes QNT-10 [DEF|EXT] Declared projective interface DEF-G0 QNT-11 Joint probability law P(a,b|x,y) QNT-05 · conditional Cosine correlator E = −cos θ QNT-06 CHSH approaching 2√2 QNT-09 Causal locality of marginals + free settings QNT-16 · open target No-signalling marginals QNT-07 Bipartite quantum boundary — Tsirelson QNT-08 [THM|EXT] Multipartite quantum boundary QNT-19 · open Frame covariance + RA1 / RA2 + normalization QNT-13 Rank-one Born weight QNT-14/17 Rank-general projective Born weights QNT-22 · conditional Full effect and mixed-state Born form QNT-23/24 · Naimark N7a projective update + N7b POVM classification QNT-26/27 [THM] N7c substrate derivation of update axioms QNT-28 · OPEN
FIG. 01 — Quantum-sector dependency map. Coherence route, operational probability route, and the Born-weight and update-rule stack.
02

The Gauge sector

The forces of nature as the twisting of transports around loops. A second route now runs beneath the first: from two austere axioms, a minimum five-dimensional carrier, a balanced 3|2 split, and from there a charge lattice, one anomaly-free family, and a unique Higgs representation. The observed group SU(3)×SU(2)×U(1) remains a target rather than a result, and chirality selection is still open.

Gauge sector dependency map QREV-2026-08-15-20 · Native finite/countable gauge structure — PASSED CONDITIONALLY I · TRANSPORT AND THE WILSON ACTION II · CARRIER SELECTION — THE NATIVE ROUTE III · CHIRAL MEASURE AND ANOMALY CONTROLS definition definition loop transport action definition continuum bridge effective source record cost balanced rank unity record exterior family executable filter rep. theorem five-carrier trace graded curvature unity-orientation chirality assumed not selected vacuum selector imported bridge SU(2)/SU(3) measure cancellation mod-two theorem not extended frozen only phase open Local Hilbert spaces H_i GAU-01 Local frame covariance GAU-02 Unitary link transports U_ij GAU-03 Path and loop holonomy GAU-04 Diamond–Wilson action S_W GAU-05 Continuum Yang–Mills action GAU-06 Connectivity-defect current GAU-10 AX-RNR-1 reciprocal differentiation + AX-PRC-1 record cost active axioms Minimum odd five-dimensional carrier m = 5 CAR-X6 · conditional Balanced 3|2 exterior form Δ_RDU minimized FORM-X6 S(U(3)×U(2)) and primitive charge lattice q = −2i + 3j G4 · Y = q/6 Complete exterior chiral family Q_L, u_R, d_R, L_L, e_R, ν^c [THM]+[CON] Exact anomaly cancellation GAU-11 · GG4 filter Unique Higgs representation (1,2), Y = 1/2 HIG-X6 · PASSED Internal gauge trace normalization g3 = g2 = g5, g_Y = √(3/5) g5 C1–C2 conditional gauge-Higgs tuple g5 = 0.9183221821… Finite mirror non-generation + one-family quotient MIR-01/02 · conditional GG3 chirality selection GAU-14 · OPEN Physical Standard Model gauge group GAU-07 · OPEN Fibered action-generated overlap kernel Q12-NODE-02 · conditional Coupled form-packet-Higgs vacuum orbit Q11-NODE-03 Finite overlap one-species / locality bridge Q11-NODE-04 · validated Finite non-Abelian overlap compatibility Q11-NODE-05 · PASSED Selected-family perturbative measure cancellation Q11-NODE-06 Ordinary Witten parity + 1 Q11-NODE-07 · four doublets Complete continuum Weyl / chiral-measure / QFT NOT PASSED Transverse non-Abelian gauge-current response OPEN · HIGH PRIORITY Arbitrary topology and determinant phase OPEN
FIG. 02 — Gauge-sector dependency map. Transport and the Wilson action, the native carrier route to a single chiral family, and the chiral-measure controls.
03

The Gravity sector

Gravity as geometry, and geometry as counting. This is now the most developed sector, not the least. An independent coframe, a Palatini elimination of the connection, and one jointly varied action yield exact finite Ward and Bianchi identities and a local recovery of Einstein–Cartan gravity. The whole structure closes on a single number — and that number is still measured, not derived.

Gravity sector dependency map QREV-2026-08-15-20 · Gravity Gate — PASSED CONDITIONALLY (theoretical/structural) I · COFRAME, PALATINI AND EINSTEIN–CARTAN RECOVERY II · SOURCE, CLOCK AND NORMALIZATION coframe ontology connection elimination spin-2 kinetic universality theorem nonlinear transplant cube shelling irregular refinement joint source clock normalization causal orientation coupled evolution normalization empirical anchor not yet confronted no derivation of C external floor two active imports one-anchor posture Relational substrate FND-01 GR8 independent coframe ontology + Clifford replacement nondegeneracy assumed GR9 Palatini connection elimination H_eff = H_FP / 2 Two-dimensional TT quotient linearized finite class GR13–GR14 whole-action universality one common-coframe substitution GR14–GR15 nonlinear QREV-Cartan representative one jointly varied action GR15 finite Ward and holonomy-Bianchi identities PASSED · exact GR16–GR18 local 4D Einstein-Cartan recovery declared smooth class GR2 scalar incidence balance + GR3 spatial Ward balance joint variation · conditional Joint matter-geometry source no continuum stress-energy Q12-09 relational clock and derived inertia M_rel = 2 κ_H · p = 1 GR19 Lorentzian causal / real form common-clock unit gauge Dynamical matter backreaction on relational geometry GRA-09 · conditional GR20 one dimensionless coupling C unit invariance One measured G_N anchor C_G = 1/(16π G_N) Independent empirical gravity validation OPEN · freeze a surplus observable C3–C4 parameter-free coupling obstruction NOT PASSED Manifoldlikeness difficulty floor GRV-12 · external floor Scale-pair reduction target v_EW and ℓ_c GRV-13 · open target
FIG. 03 — Gravity-sector dependency map. Coframe and Palatini route to local Einstein–Cartan recovery, closing on a single measured normalization anchor.
04

The Matter sector

Why the electron, muon, and tau have the masses they do — and why the quarks are harder. The charged-lepton construction closes on its own declared domain, through the Koide relation and a stationary phase. The quark problem has since been moved: mass is no longer read off a pole but is the restricted Hessian of one common action, and the next gate is to build that operator in its retarded form. Nothing numerical is claimed here.

Matter and flavor dependency map QREV-2026-08-15-20 · charged leptons scoped PASS · numerical flavor NOT PASSED I · CHARGED-LEPTON CLOSURE — SCOPED PASS II · COMPLETE-RECORD HISTORY GEOMETRY (QREV-19/20) III · THE F210 GATE AND WHAT REMAINS projection singular values pair-symmetric manifold fixed point holonomy angle θ = q_K lowest invariant mass ratios agreement amplitude r = √2 not derived determinant current common scale scoped outputs ordered history soldering axiom tensor-product norm kinetic variation reaudit transport only C1 + F105 branch graded curvature history metric Gaussian order adiabatic subtraction degree-two record restricted Hessian static slice insufficient Schur/Feshbach add only after quotient required block no post-hoc swap downstream not derived downstream one common action Protected low-mode triplet Π_T PKT-01 · extraction open Projected operator M = Π_T Φ_sub Π_T PKT-03 Normalized packet p_a from (σ₁,σ₂,σ₃) PKT-04/05 Koide crossing R_K = (1+√2)/3 PKT-10 Koide coefficient q_K = 1/R_K PKT-17 Determinant phases Θ_a and D₃ invariant χ HOL-13/14 Stationary azimuth φ* = 2/9 HOL-15 Unified charged-lepton mass formula HOL-17 Observed charged-lepton agreement HOL-18 · numerically supported Cl(3) Pauli Frobenius norm √2 KOD-02 Koide identity K = 2/3 KOD-05 Physical Frobenius equipartition KOD-06 · OPEN Three-line flavor bundle F = L₁⊕L₂⊕L₃ HOL-03 · Λ²E_a Finite packet energy E_pkt MSC-12 · ξ₆, ξ₃ = ξ₆/2 Finite charged-lepton Matter Gate MAT-26 · PASSED scoped Exterior charge depth |Q| = n/3, A_u = 2/9, A_e = 1 F19-01 · PASSED EXACTLY Complete retained-record geometry G_comp F85/F89 · K < 0, complete F104 incidence-to-family projector soldering minimal cross-sector axiom F105 history inertia μ_hist = ζ_H q_K / 3 conditional · bosonic trace F112 auxiliary mechanical family connection [Y, D_sY] = 0 · modulo rephasing F112 locally pure frame A = −dU U† F_A = 0 on simple spectrum CP orientation lives in the retarded layer not local F112 curvature F159 graded-curvature Higgs/history completion V_HF = λ_H/3 Tr[(ρ²Y²−v²I)²] ω*² = 8 q_K F159 · conditional Full family-amplitude metric G_w = ρ²/6(‖w‖²I + ww^T) exact pullback · PASSED F126 mandatory quadratic overlap vertices action-derived sources F133/F134 moving sea, no double counting open-line typing · structural F61/F68/F105 coherence-record identity PASSED EXACTLY Section 22 / GR20 — mass is the restricted common-action Hessian m = κ / s* · CONTROLLING Clamped family operator K_X = Π_F ∇²S_mic Π_F Section-22 origin F210 constrained retarded compatibility Hessian OPEN · PRIMARY GATE K_phys(z) = K_clamp − J†D_B(z)⁻¹J Feshbach form Transverse non-Abelian gauge-current block OPEN · HIGH PRIORITY Positive intrinsically ordered quark spectra NOT PASSED Mass-ordered CKM and CP NOT PASSED Finite neutral BdG manifestation F19-06 · reopened Quantitative PMNS NOT PASSED Continuum flavor / QFT — measure, running, scattering NOT PASSED
FIG. 04 — Matter and flavor dependency map. Charged-lepton closure, complete-record history geometry, and the constrained compatibility-Hessian gate.
05

The Cosmology sector

The universe as a growing network, and a testable fingerprint. The background now follows from the same coframe action — Friedmann and Raychaudhuri equations, and exactly two tensor polarizations travelling at the speed of light. The large-angle suppression survives as one bounded signal from a calibrated kernel, not a derived prediction; the routes that promised more were closed by the program itself.

Cosmology and CMB dependency map QREV-2026-08-15-20 · Cosmology Gate — OPEN · the CMB result remains bounded phenomenology I · BACKGROUND AND PERTURBATIONS II · THE LOCKED CMB KERNEL III · DARK ENERGY AND THE REMAINING GATES common coframe homogeneous branch linear perturbations no extra modes coarse-grained separation ontology undecided origin open repaired determinant calibration input locked locked test bounded support not closed locked test bounded support origin not derived empirical replacement not derived awaiting data open Empirically normalized common-coframe gravity C16-04 · C_G from G_N Relational FLRW-Einstein-Cartan background COS1 · conditional Friedmann, Raychaudhuri, acceleration and continuity homogeneous branch Linear scalar-vector-tensor branch COS2 · conditional No scalar or vector graviton — exactly two tensor polarizations, c_T = 1 two-derivative order Causal-network growth and ordering dynamics COS-01 · OPEN Emergent scale factor a(t) COS-02 Block versus growth ontology fork COS-11 · typed open choice Operator-relative sea response Γ_rel[M|M₀] COS3 · local renormalization Relational substrate FND-01 C1 spectrum-level calibration α_CMB and L_H frozen Locked finite-coherence kernel F_ℓ COS-08 · constitutive C2 pseudo-C_ℓ map robustness COS-09 · numerically supported Bounded temperature-coherence target COS-11 · bounded phenomenology Cosmology Gate OPEN Microscopic derivation of the kernel amplitude and scale COS-08 · OPEN C3 direct real-space S₁/₂ test COS-10 · numerically supported WN-Q4 diffusion-to-CMB pointer research pointer COS6 phase-rate non-selection and gauge ambiguity CLOSED NEGATIVELY One universal empirical Λ ρ_Λ = 2 C_G Λ · REQUIRED/FROZEN Native primordial mechanism OPEN · no rolling source Independent empirical confrontation OPEN Core / ToE Gate NOT PASSED
FIG. 05 — Cosmology and CMB dependency map. Background and perturbations, the locked coherence kernel, and the gates that remain.
IV — An honest ledger

The rarest thing here is the bookkeeping.

What sets this program apart is not a bold claim but a refusal to make one loosely. Every statement in the specification wears a tag declaring exactly how much it is worth — whether it is a definition, a proven theorem, an imported result, a number from a computer, an educated guess, or an open problem. Failed approaches are not deleted; they are kept on the record so no one wanders down them twice.

The result is a document you can audit. For any conclusion, a reader can ask: what was assumed, what was proved, what was merely fitted — and what still has to be done.

[THM]Proved exactly, inside its declared construction.
[DEF]A definition or axiom — assumed, not shown.
[EXT]Imported from established mathematics or physics.
[NUM]A numerical result, tied to a specific computation.
[CONJ]A conjecture — expected, but not yet earned.
[OPEN]An open problem, stated as a precise gate to clear.
Working progress estimate, by sectorLedger 1.1.12
Specification, audit and governance80–85%

Mature control architecture; freeze work remains.

Gravity90–95%

Theoretical and structural gate passed conditionally; empirical validation and a parameter-free coupling remain open.

Primitive ontology and kinematics50–60%

Definitions coherent; physical selection and uniqueness open.

Matter and charged leptons45–50%

Strong effective construction; microscopic source and protection open.

Quantum sector35–40%

Conditional theorem stack; full effect, probability and preparation derivation open.

Generic gauge geometry30–35%

Transport and holonomy valid; observed gauge content not selected.

Cosmology15–20%

One bounded signal; kernel and dynamics not substrate-derived.

Complete microscopic dynamics10–15%

No unified microscopic action.

These are the working ranges recorded in the ledger, not measurements. The program deliberately declines to publish a single headline number: recent releases note that overall percentages are left unrecalibrated, because a sector can advance a long way without any gate actually closing. By the program’s own binary standard the number of completed sectors is still zero. That candor is the point.

What is claimed
  • A coherent kinematics: a single, precise language for the substrate.
  • Exact theorems inside their declared constructions.
  • A conditional route to quantum probability and its ceiling.
  • Negative controls that rule out several tempting shortcuts.
  • A register of falsifiable signatures to test against.
What is not
  • ×A derived gauge group of the Standard Model.
  • ×A completed theory of gravity or of cosmology.
  • ×Any dimensionful constant of nature, derived from first principles.
  • ×An unconditional, standalone prediction — yet.
  • ×A finished theory of anything. It is a program in progress.
V — The corpus

Sixteen papers, eight records, one frozen core.

The papers came one at a time, and each was a test — a result proposed, attacked, and, where it failed, revised or retired in the open. Read in order, Papers I through XVI are the trail of how the theory reached its present form. What they arrived at is gathered, corrected, and kept current in the Core Specification: the single authoritative statement of the theory. The papers show the road travelled; the specification is where it now stands.

  1. I

    Information Relational Manifestation Theory

  2. II

    Quantum Correlations & Gauge Structure from a Discrete Relational Substrate

  3. III

    The Relational Dirac Operator & the Problem of Generations

  4. IV

    The Emergence of Gravitation & the Einstein–Hilbert Action

  5. V

    Relational Cosmology

  6. VI

    The Measurement Problem as Relational Consistency

  7. VII

    Closing the Gravitational Sector

  8. VIII

    A First-Principles Derivation of the Koide Formula

  9. IX

    Closing the Program: Structural Architecture & Open Problems

  10. X

    From Spectral Universality Failure to Spectral Self-Organization

  11. XI

    The Koide Configuration in IRMT — Reachability

  12. XII

    Rank-One Collapse & the Emergence of Hierarchy

  13. XIII

    Koide Stabilization from Deficit-Gated Entropy

  14. XIV

    Finite Relational Coherence & the CMB Large-Angle Deficit

  15. XV

    Charged-Lepton Masses from Rank Collapse & Determinant-Line Holonomy

  16. XVI

    The Microscopic Origin of Determinant-Line Holonomy

Supporting the papers: Records 1–8 (the working ledgers), an archive of working notes, and a SHA-256 manifest so every claim can be traced to the exact file that carries it.

Enter the library →
VI — The invitation
“Not endorsement. Attack.”

The author is not asking to be believed. He is asking to be tested — for the sharpest readers to find the weakest joints in the argument and press on them. A theory that survives that is worth something. A theory that fears it is not.

Where to press hardest
  • The axioms beneath the quantum-probability route.
  • The gates that protect the construction from collapse.
  • The floors on manifold-likeness and chirality.
  • The CMB kernel, where theory meets real data.
Information Relational Manifestation Theory
Abdulaziz Abdi · Toronto, Canada
Core Specification v1.0 · Working draft 0.9.33 · Master Ledger 1.1.12
The Library

Every file, in the open.

The program is meant to be audited, not admired. What follows is the whole paper trail — the frozen specification, sixteen papers, eight working ledgers, and the note archive — each traceable through a SHA-256 manifest to the exact file that carries its claims.

The core document
IRMT Core Specification v1.0

Primitive structure, microscopic dynamics, observables, and evidentiary status — the single auditable statement of the theory as it presently stands. Working draft 0.9.33, release QREV-2026-08-15-20.

Read the specification ↓

The Papers

I – XVI

Best read in sequence. These are a progressive record: each paper tested the one before it, and the theory evolved through whatever survived. They document how the framework was built — not where it now stands. The current, authoritative statement is the Core Specification above; the papers are its evidence trail, not a substitute for it.

IInformation Relational Manifestation TheoryPDF ↓ IIQuantum Correlations & Gauge Structure from a Discrete Relational SubstratePDF ↓ IIIThe Relational Dirac Operator & the Problem of GenerationsPDF ↓ IVThe Emergence of Gravitation & the Einstein–Hilbert ActionPDF ↓ VRelational CosmologyPDF ↓ VIThe Measurement Problem as Relational ConsistencyPDF ↓ VIIClosing the Gravitational SectorPDF ↓ VIIIA First-Principles Derivation of the Koide FormulaPDF ↓ IXClosing the Program: Structural Architecture & Open ProblemsPDF ↓ XFrom Spectral Universality Failure to Spectral Self-OrganizationPDF ↓ XIThe Koide Configuration in IRMT — ReachabilityPDF ↓ XIIRank-One Collapse & the Emergence of HierarchyPDF ↓ XIIIKoide Stabilization from Deficit-Gated EntropyPDF ↓ XIVFinite Relational Coherence & the CMB Large-Angle DeficitPDF ↓ XVCharged-Lepton Masses from Rank Collapse & Determinant-Line HolonomyPDF ↓ XVIThe Microscopic Origin of Determinant-Line HolonomyPDF ↓

The Records

Working ledgers 1 – 8
Record 1
Claim Ledger
Record 2
Definition & Notation Ledger
Record 3
Action Ledger
Record 4
Coefficient Ledger
Record 5
Dependency Graph
Record 6
Retired & Superseded Claims
Record 7
Version & Revision Ledger
Record 8
Surplus & Falsifiability Register
Working-note archive

The full WN-series — the live edge of the program, where routes are proposed, tested, and often retired.

SHA-256 manifest

A cryptographic fingerprint of every file in the package, so any claim can be traced to the exact document it came from.

Complete package

Everything above in one archive — specification, papers, records, notes, and manifest. Consolidated working package.

Contact

Tell me where I'm wrong.

I'd genuinely like to hear from you — whether you're a physicist, a curious reader, or just someone who enjoys turning a big idea over in their hands. Questions are welcome, and so is agreement. But if a step in the reasoning looks shaky to you, tell me: a careful objection is the most useful gift you can send, and I read those first. No credentials required — only curiosity and honesty.

Author
Abdulaziz Abdi
Based in
Toronto, Canada
Say hello, or take a shot at it