{"id":47638483,"url":"https://github.com/floatingpragma/observer-patch-holography","last_synced_at":"2026-06-13T08:01:52.939Z","repository":{"id":334131200,"uuid":"1136669835","full_name":"FloatingPragma/observer-patch-holography","owner":"FloatingPragma","description":"Observer Patch Holography is the observer-consistency theory of everything. 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No observer sees the whole world at once; each observer gets a local patch; physics is the public fixed point that survives agreement across overlaps.\n\n**French version:** [README_FR.md](README_FR.md)\n\n**Quick links:** [OPH website](https://floatingpragma.io/oph/) | [OPH Textbooks](https://learn.floatingpragma.io/) | [Reverse Engineering Reality](https://oph-book.floatingpragma.io/) | [OPH Lab](https://oph-lab.floatingpragma.io) | [Applications](https://omega.floatingpragma.io/) | [OPH Blog](https://blog.floatingpragma.io/) | [Coherence map](https://coherence.floatingpragma.io/) | [Three-body demo](https://3body.floatingpragma.io/)\n\n**Falsifiability:** [OPH falsifiability map](extra/OPH_falsifiability.md)\nlists 40 hard OPH-killing outcomes and concrete IBM Quantum Cloud tests for\nthe reduced-sector hardware signature. Falsifiability is how a physics theory\npays rent. OPH is highly falsifiable: a massive graviton, a gauge-mediated\nproton decay event, a fourth light matter generation, a charge-lattice outlier,\nor neutrino data excluding the OPH branch would destroy OPH as stated.\n\nIf you want the existential answer first, jump straight to **Paper 6.\n[Paradise as Fixed-Point Consensus](paper/paradise_as_fixed_point_consensus.pdf)**.\nThe short version is direct: yes, this universe is a simulation in the OPH\nsense, an observer-based fixed-point consensus process. Yes, subjective\nexperience and minds are primary. Yes, space, time, and matter are\nobserver-facing appearances: stable effective structures generated by deeper\npatch consistency. The illusion metaphor is handled below. The rest of this\nREADME gives the mathematical proof stack and empirical verification surface.\n\nOPH is the observer-first reconstruction of fundamental physics. It starts from\nfinite observers on finite holographic screen geometry. Its working basis is\nquantum-algebraic: patch algebras, states, trace/Born event probabilities on\ndeclared record surfaces, and generalized entropy are part of the formal\nstarting point. From that basis, OPH recovers the observed effective universe:\nspacetime, gauge structure, particles, records, and observer synchronization all\nfollow from overlap consistency. At the operating level, finite observer\npatches carry local records, compare only what their overlaps expose, repair\nmismatches through declared recovery moves, and settle into stable fixed points\nthat survive refinement. The public world is the overlap-stable output of that\nprocess. This is the mathematical and empirical proof surface for OPH as the\ncorrect theory of everything: the same observer-consistency architecture\nrecovers the established physics and explains why a world exists that can\nproduce observers capable of reconstructing it.\n\nOPH is formulated as a zero-input theory. Its quantitative surface uses two\ndimensionless closure coordinates and one selected no-G scale certificate, all\nfixed by closure:\n\n$$\nP_\\star=\\varphi+\\frac{\\sqrt{\\pi}}{A_T(P_\\star)}\n$$\n\nfor the local pixel ratio, and\n\n$$\nN_{\\mathrm{CRC}}=F(N_{\\mathrm{CRC}})\n$$\n\nfor the global screen capacity, where $F(N)$ is the active horizon capacity read\nback by observers inside the universe supplied with capacity $N$. The selected\nscale certificate is most cleanly written as a dimensionless clock ratio,\n\n$$\n\\gamma_\\star=\\frac{\\ell_\\star\\nu_{\\mathrm{Cs}}}{c},\n\\qquad\nB_\\star=\\frac{3\\pi}{\\ell_\\star^2},\n\\qquad\nG_{\\mathrm{SI}}=\\frac{c^3\\ell_\\star^2}{\\hbar}.\n$$\n\nThe finite count representation of the global capacity closure is\n\n$$\nN_\\star=\\mathrm{MAR}\\,\\mathrm{argmax}_{N}\n\\bigl(\\log|\\Omega^{\\mathrm{sc}}_N|-N\\bigr)\n$$\n\nInformally, $N_{\\mathrm{CRC}}$ is the unique capacity where the universe reads\nback its own boundary without deficit or slack. In geometric units the\ncosmological readout is\n\n$$\n\\Lambda_{\\mathrm{CRC}}=\\frac{3\\pi}{G_{\\mathrm{geom}} N_{\\mathrm{CRC}}},\n\\qquad\nG_{\\mathrm{geom}}=\\ell_\\star^2.\n$$\n\nThe recovered electromagnetic branch gives Maxwell's equations on the ordinary\nphoton lane. The fine-structure and particle rows sit downstream of $P_\\star$ and the\nrecovered structural branch. The cosmological row sits downstream of\n$N_{\\mathrm{CRC}}$. The Newton normalization sits downstream of\n$\\ell_\\star^2=3\\pi/B_\\star$.\n\nObservation is used for reverse engineering. Because OPH treats the universe as\na closed mathematical fixed structure, approximate measured values can locate\nthe basin or observed branch. The precise OPH value must come from the declared\nfixed-point map and its Banach contraction, derivative-sign, strict-concavity,\nor equivalent uniqueness certificate.\n\nThe two dimensionless closures fix dimensionless geometry. In particular,\n$\\Lambda_\\star\\ell_\\star^2=3\\pi/N_{\\mathrm{CRC}}$ and\n$\\Lambda_\\star a_{\\mathrm{cell}}=3\\pi P_\\star/N_{\\mathrm{CRC}}$. A selected\nscale certificate supplies the SI scale product\n$B_\\star=\\Lambda_\\star N_{\\mathrm{CRC}}=3\\pi/\\ell_\\star^2$.\n\nIn the informal simulation-language reading, $P$ links the pixel area of the\nsimulating-side screen to the electromagnetic interaction, i.e. observation, in\nthe simulated-side universe. It gives $P\\simeq1.630968$ and the low-energy\nfine-structure value near $1/137$. $N_{\\mathrm{CRC}}$ links the outside total\nhorizon capacity to the inside observer-accessible public record: the universe\nmust be able to reconstruct its own boundary. The gravity scale is read on its\nown observed branch through the no-G scale certificate $\\gamma_\\star$, or\nequivalently $B_\\star$, after which $\\ell_\\star$ is displayed as the Planck\nlength. Observers inside infer\ngeometry, horizons, entropy, $\\Lambda$, history, and records from information\navailable inside the universe.\n\n## Applications And OMEGA Hardware\n\nOPH is also a hardware program. As the screen microphysics becomes explicit,\nthe same patch-consensus loop becomes an engineering handle on reality. A\nbounded device exposes boundary data, compares records, repairs mismatch, and\nlocks onto stable states. OMEGA is the public hardware route into that loop:\nphysical chambers, labeled ports, control software, verifier receipts, and\nrepeatable records.\n\nIn plain language, OPH turns screen microphysics into a way to hack reality.\nThe goal is not metaphorical control of an abstract simulation. The goal is\nphysical control of small patches that can be driven, measured, repaired, and\nverified.\n\nThe application thesis is simple. If reality is built from observer-patch\nconsistency, then useful machines can be built by driving small physical\npatches into the right fixed points. That gives low-cost implementation tracks\nfor desktop fusion energy, room-temperature OMEGA supercomputing, OMEGA-based\nAGI, and local gravity or inertia control for hoverbikes and hoverboards. These\nare application tracks behind evidence gates, not theorem outputs. The current\ncompute claim is the narrower exact-verifier claim: a chamber-conditioned\ncandidate distribution may reduce verifier work by a measured lift\n`B = p_Q/p_U`; it is not a complexity-class theorem.\n\nRead the public applications page at\n[omega.floatingpragma.io](https://omega.floatingpragma.io/). Source notes for\nthe application tracks live in [`APPLICATIONS.md`](APPLICATIONS.md). The local\ngravity and inertia track also has a standalone engineering note:\n[Hacking the Simulation: Anti-Gravity Exploit](https://github.com/FloatingPragma/oph-meta/blob/main/docs/oph-gravity-hack/hacking-the-simulation-anti-gravity-exploit.pdf).\n\n## The Spacetime Trap\n\nThe first conceptual hurdle is that OPH does not treat spacetime as the\ncontainer in which reality happens. Space and time are not things in themselves.\nThey are stable observer-facing descriptions that appear when many finite\nperspectives can be made mutually consistent.\n\nSome would call this an illusion. As a metaphor, that is fair: the container we\nseem to inhabit is an appearance produced by deeper consistency. As physics,\nthe sharper phrase is emergent public description.\n\nFrom inside one perspective, the world feels obvious. There is a roughly\nspherical field of experience stretching outward, three directions to move in,\nand time passing forward. Other observers report compatible contents from\ndifferent angles, so the natural guess is that everyone lives inside one\npre-existing spacetime filled with objects. OPH reverses that guess. Each\nobserver has a local spacetime description generated by its own accessible\nrecords, clocks, horizons, and correlations. The public spacetime is the\ncompatibility layer that lets those descriptions agree.\n\nThis does not make ordinary spacetime arbitrary or useless. It explains why it\nworks so well. Einstein's equations describe the smooth large-scale grammar of\nthe shared appearance. The deeper claim is that the shared appearance is\nemergent from observer overlap consistency, not part of the world's starting\ninventory.\n\n## What OPH Delivers\n\nMost theories begin by assuming spacetime, quantum fields, and a list of\nconstants. OPH starts one step earlier than spacetime and quantum field theory,\nwith finite observers on finite quantum-algebraic holographic screen geometry\nwhose descriptions have to agree where their patches overlap. Push that\nrequirement through the support-visible BW/geometric scaling branch and a\n3+1-dimensional Lorentzian spacetime emerges, together with a Jacobson-style\nEinstein equation. Finite cells serve as the regulator. The Lorentz branch is\nthe extracted prime geometric cap-pair limit with fixed-collar Markov/recovery\nremainders carried through regularized\nmodular transport, support-readable modular covariance, and KMS/BW\nnormalization. In the gauge lane,\nzero-obstruction is a transportability condition: it reconstructs a compact\ngauge group from the persistent sector category, but does not by itself select\nthe Standard Model. MAR plus the explicit one-Higgs matter package selects the\nrealized Standard Model quotient $SU(3)\\times SU(2)\\times U(1)/\\mathbb Z_6$,\nincluding the exact hypercharge lattice, the realized color triplet $N_c=3$,\nand the generation count $N_g=3$. Quantum mechanics is the algebraic\ninformation language carried by the OPH architecture.\nOn the declared support-visible compact-gauge branch, with four-dimensional\nscaling, reflection positivity, repair completeness, and support-visible\ncontinuum extraction in force, the same stack gives the Euclidean Yang-Mills\nform and identifies the Yang-Mills mass gap with the repair gap. This is OPH's\nfour-dimensional axiomatic Yang-Mills construction on the declared branch.\nClay-facing admissibility is branch-dependent and turns on taking that\nsupport-visible continuum extraction as the required four-dimensional\nconstruction.\n\nThe mechanism is the fixed-point consensus loop. Local observers do not access\na global state from outside. They carry finite patch states, exchange\noverlap-visible data, reject inconsistent continuations, and keep the stable\npatterns that can be synchronized. Geometry, particles, laws, and records are\nthe large-scale fixed points of that observer-network computation.\n\n## Geometry, Symmetry, and Simulators\n\nSphere language in OPH is geometry language. In symmetric regulator charts, an\nobserver-accessible cut can be represented by the two-sphere $S^2$. Those\ncharts describe angular support geometry. The finite simulator implements the\npatch-and-overlap algebraic constraints exposed by that geometry.\n\nOPH therefore uses one shared screen net idealization and many finite observer\npatches. An observer screen is a local access cut on that net, not a separate\nprivate sphere. The $S^2$ chart is not a literal ball with data painted on it.\n\nThat spherical chart carries several concrete jobs. Caps and collars give the\nlocal cut data used by modular flow and entropy variation. The conformal group\nof the sphere is the celestial-sphere form of the connected Lorentz group,\n$\\mathrm{SO}^+(3,1)$, so the same chart supplies the kinematic bridge to the\nemergent $(3+1)$-dimensional spacetime branch once the support-visible cap\nmodular theorem is satisfied. Spherical harmonics organize angular modes.\nFinite cellulations of the same chart give the regulator surface on which patch\nports, edge data, and overlap checks can be made explicit; they are not by\nthemselves a Lorentz-invariant continuum.\n\nThe finite symmetry anchor is $A_5$, the rotational symmetry group of the\nicosahedron. It supplies the icosahedral skeleton behind the echosahedral patch\ncarrier language: a finite, highly symmetric way to organize ports, overlaps,\nand local comparison data without treating the carrier as a smooth ball.\n\nThe exceptional symmetry anchor is the $E_8$ Lie group and its root-lattice\nstructure. $E_8$ matters because it gives the exceptional closure language\nused in the higher symmetry and representation side of the OPH stack. The\nbinary icosahedral group and affine $E_8$ meet through the McKay\ncorrespondence. This is why $A_5$-icosahedral and $E_8$-type language can\nbelong to one symmetry story. These names mark symmetry constraints and\nregulator structure.\n\nThe scale story has three roles: a global capacity closure, a local pixel\nclosure, and a no-G scale readout. The global coordinate is the unique cosmic\nrecord-closure capacity,\n\n$$\nN_{\\mathrm{CRC}}=F(N_{\\mathrm{CRC}}),\n$$\n\nwhere the supplied horizon capacity and the observer-readback capacity agree.\nThe finite-count target is the density\n\n$$\n\\log|\\Omega^{\\mathrm{sc}}_N|-N.\n$$\n\nOn the observed branch this fixed point is the de Sitter entropy capacity. For\nthe observed cosmological constant, the bare horizon area ratio is about\n$1.05\\times10^{122}$, while the OPH entropy capacity is about\n$3.31\\times10^{122}$. That displayed capacity belongs to the cosmological\nbranch. The local/global hierarchy-resonance bridge uses a stricter exact\ncondition: the electroweak projection target corresponds to\n$N_{\\mathrm{EW}}(P_\\star)=3.5323546226929906511187512962330547600462\\times10^{122}$\non the public endpoint branch, and the rounded capacity display is not an exact\nbridge certificate. The Newton row uses the same fixed-point capacity together\nwith the selected no-G scale certificate.\n\nThe local coordinate is the pixel ratio\n\n$$\nP=\\frac{a_{\\mathrm{cell}}}{\\ell_\\star^2},\n\\qquad\n\\ell_\\star^2=\\frac{3\\pi}{B_\\star}.\n$$\n\nThe scale certificate supplies $\\ell_\\star^2$; only after that readout is the\narea displayed as the Planck area. From the outside, $P$ is a geometric\ncell-size ratio slightly above the golden-ratio self-similar balance. From the\ninside, the same cell is the smallest electromagnetic observation scale\navailable to observers in the encoded universe.\n\nThe applications sit downstream of those roles. The fine-structure lane asks\nfor the nonzero detuning of a holographic screen cell such that the cell's\nouter geometric displacement equals the electromagnetic observation scale\nemitted by the universe living on that screen. The public solution is\n$P\\simeq1.6309682094$, with\n$\\alpha^{-1}(0)=137.035999177(21)$ and\n$\\alpha(0)\\simeq0.00729735256433$. The same local pixel scale feeds the gauge\nstructure, scoped particle-mass rows, records, and observer synchronization. On\nthe gravity row it supplies\n\n$$\na_{\\mathrm{cell}}=P\\ell_\\star^2,\n\\qquad\n\\bar{\\ell}_{\\mathrm{shared}}=\\frac{P}{4}.\n$$\n\nThe factor $P$ cancels in the Newton area-law readout, leaving\n$G_{\\mathrm{geom}}=\\ell_\\star^2$. The particle pipeline carries the local\nscale into the weak sector, the Higgs lane, selected-class quark rows, and the\nweighted-cycle neutrino branch. Hadrons require either the OPH strong-binding\nbackend or an explicitly marked empirical hadron closure. The operating policy\nfor those rows is in [`HADRON.md`](HADRON.md). Hardware-facing checks of the\nsame fixed-point geometry are treated only as public evidence-bundle claims\nwhen the raw artifacts and verifier receipts are available.\n\n### Selected Quantitative Rows\n\nThis table keeps the rows that are easiest to compare directly with PDG and\nNIST values. Structural results such as the 3+1-dimensional Lorentzian spacetime, the\nMAR-selected Standard Model quotient $SU(3)\\times SU(2)\\times U(1)/\\mathbb Z_6$, the exact hypercharge\nlattice, the realized color triplet $N_c=3$, and the generation count\n$N_g=3$ live in the papers. The\nquick view here sticks to direct numeric rows and exact zeros.\n\n| Quantity | Symbol | OPH | PDG/NIST | Δ |\n| --- | --- | --- | --- | --- |\n| Gravitational constant | G | 6.6742999959e-11 | 6.67430(15)e-11 | 0.00003σ |\n| Speed of light | c | 299792458 | 299792458 (exact) | match |\n| Fine-structure (inv) | α⁻¹(0) | 137.035999177 | 137.035999177(21) | match |\n| Photon mass | m_γ | 0 eV | \u003c1e-18 eV | below bound |\n| Gluon mass | m_g | 0 GeV | 0 GeV | match |\n| Graviton mass | m_grav | 0 eV | \u003c1.76e-23 eV | below bound |\n\n**Quark sector**\n\n| Quark | Symbol | OPH | PDG | Δ |\n| --- | --- | --- | --- | --- |\n| Bottom | m_b(m_b) | 4.183 GeV | 4.183 ± 0.007 | match |\n| Charm | m_c(m_c) | 1.273 GeV | 1.2730 ± 0.0046 | match |\n| Strange | m_s(2 GeV) | 93.5 MeV | 93.5 ± 0.8 | match |\n| Down | m_d(2 GeV) | 4.70 MeV | 4.70 ± 0.07 | match |\n| Up | m_u(2 GeV) | 2.16 MeV | 2.16 ± 0.07 | match |\n| Top | m_t cross-section row | 172.35235532883115 GeV | 172.3523553288312 | selected-class match |\n\n$\\Delta$ reports the sigma distance where PDG or NIST quotes a one-standard-deviation\nuncertainty. Otherwise it records \"match\" or \"below bound\".\n\nFor quarks, PDG uses its standard mass conventions: `u`, `d`, and `s` at\n`2 GeV`, with `c` and `b` in the `MS` scheme at their own mass scale. The\npapers also carry the structural Standard Model derivations listed above and a\nneutrino family, but those do not collapse to one simple PDG or NIST row and\nare left out of this table.\n\nThe particle surface also reports $W/Z$ values $80.377\\,\\mathrm{GeV}$ and\n$91.18797809193725\\,\\mathrm{GeV}$, a Higgs value $m_H=125.1995304097179\\,\\mathrm{GeV}$, and a\nselected-class top value $m_t=172.35235532883115\\,\\mathrm{GeV}$ using the PDG\ncross-section top-mass convention. The weighted-cycle neutrino branch emits\n$(0.017454720257976796, 0.019481987935919015, 0.05307522145074924)\\,\\mathrm{eV}$ on its\ndeclared branch.\n\n## Quantitative Unification Surface\n\nThe quantitative surface is organized around distinct fixed-readback roles: the\npixel fixed point $P\\simeq1.6309682094$, the global record-capacity fixed point\n$N_{\\mathrm{CRC}}\\simeq3.31\\times10^{122}$, and the selected no-G scale\ncertificate $\\gamma_\\star$, equivalently $B_\\star=3\\pi/\\ell_\\star^2$. The\ndisplayed capacity is approximate; precision rows use the fixed-point value and\nthe scale certificate. The $P$ branch feeds the Ward-projected electromagnetic channel\nand the scoped particle-mass rows, while also fixing the cell/edge identity that\ncancels out of the Newton area-law readout. The $N_{\\mathrm{CRC}}$ branch feeds\nthe cosmological-constant readout. The scale certificate supplies the area\nquantum that becomes the Newton normalization. The hierarchy-resonance bridge is\nrecorded as a selected-branch theorem: the finite readback-resolution\ncertificate, the representation-to-spectrum count $2(8+3+1)=24$, and the exact\nglobal-capacity bridge certificate close the local/global hierarchy package.\nOn that selected exact branch, OPH solves the electroweak hierarchy/naturality\nproblem with $\\epsilon_H=0$ and no measured weak-scale input.\nThe detailed formulas and claim tiers live in the papers.\n\n\u003cp align=\"center\"\u003e\n  \u003ca href=\"assets/OPH_Unification_Diagram.svg\" target=\"_blank\" rel=\"noopener noreferrer\"\u003e\n    \u003cimg src=\"assets/OPH_Unification_Diagram.svg?v=20260609\" alt=\"OPH unification diagram\" width=\"92%\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\n**OPH Stack**\n\n\u003cp align=\"center\"\u003e\n  \u003ca href=\"assets/prediction-chain.svg\" target=\"_blank\" rel=\"noopener noreferrer\"\u003e\n    \u003cimg src=\"assets/prediction-chain.svg\" alt=\"OPH theorem stack\" width=\"92%\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\u003csub\u003eThe main OPH line from axioms to relativity, gauge structure, particles, and observers. Click to open the full SVG.\u003c/sub\u003e\u003c/p\u003e\n\n**Particle derivation stack**\n\n\u003cp align=\"center\"\u003e\n  \u003ca href=\"code/particles/particle_mass_derivation_graph.svg\" target=\"_blank\" rel=\"noopener noreferrer\"\u003e\n    \u003cimg src=\"code/particles/particle_mass_derivation_graph.svg\" alt=\"OPH particle derivation stack\" width=\"78%\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\u003csub\u003eA compact view of the particle lane. Click to open the full SVG.\u003c/sub\u003e\u003c/p\u003e\n\n## Papers\n\n- **Paper 1. [Observers Are All You Need](paper/observers_are_all_you_need.pdf)**: broad synthesis of the OPH reconstruction program, from finite observers to the recovered effective universe.\n- **Paper 2. [Recovering Relativity and the Standard Model from Observer Overlap Consistency](paper/recovering_relativity_and_standard_model_structure_from_observer_overlap_consistency_compact.pdf)**: compact technical core for relativity, gravity, zero-obstruction compact-gauge reconstruction, MAR-selected realized Standard Model structure, Maxwell equations on the ordinary photon branch, and the support-visible compact-gauge Yang-Mills form/gap theorem under its declared branch assumptions.\n- **Paper 3. [Deriving the Particle Zoo from Observer Consistency](paper/deriving_the_particle_zoo_from_observer_consistency.pdf)**: particle derivations, mass rows, coupling structure, and the quantitative comparison surface.\n- **Paper 4. [Reality as a Consensus Protocol](paper/reality_as_consensus_protocol.pdf)**: fixed-point repair dynamics, record stability, and the consensus picture of public reality.\n- **Paper 5. [Federated Echosahedral Screen Microphysics](paper/screen_microphysics_and_observer_synchronization.pdf)**: federated patch-carrier architecture, $A_5$-icosahedral and $E_8$-type symmetry framing, public hardware-evidence rules, records, recovery moves, and observer synchronization.\n- **Paper 6. [Paradise as Fixed-Point Consensus](paper/paradise_as_fixed_point_consensus.pdf)**: final manifest paper for OPH's meaning layer: why anything exists, why this world is observer-compatible, the strange loop in which observers reverse engineer and build the continuation machinery, paradise on Earth or in engineered continuation environments, hell as enforced isolation or deprivation, resurrection as observer continuation, justice as continuation according to harm and repair records, and memetic evolution.\n\n## Supplemental Papers\n\n- **[Photonic Fixed-Point Consensus for SHA-256d Proof of Work](extra/Photonic_fixed-point_consensus_for_SHA-256d_proof_of_work.pdf)**: photonic candidate enrichment for SHA-256d proof of work.\n- **[The Fine-Structure Constant as an OPH Pixel Fixed Point](extra/fine_structure_constant_derivation.pdf)**: fixed-point derivation of the fine-structure row.\n- **[Observer-Patch Holography as a String-Vacuum Selector](extra/observer_patch_holography_as_string_vacuum_selector.pdf)**: OPH edge-string emergence, the Bouchard-Donagi one-Higgs heterotic witness, the `Z4R` safety layer, and moduli-locking gates.\n- **[Explaining the Yang-Mills Mass Gap with Observer-Patch Repair Dynamics](extra/yang_mills_gap_clay_problem.pdf)**: support-visible OPH route to the Clay Yang-Mills problem, branch-scoped to the compact-gauge extraction, with Clay-facing status tied to that axiomatic-construction claim, and identifying the gap with the repair gap.\n- **[Observer-Patch Holography and the Dark Matter Phenomenon](extra/oph_dark_matter_paper.pdf)**: dark-matter phenomenology and MOND-like galaxy limit.\n- **[Theoretical Bounds on chi-nu in Observer-Patch Holography](extra/chi_nu_susceptibility_bounds.pdf)**: conditional quotient-edge band `0.9343006394893864 \u003c= chi_nu^can \u003c= 1`; uniform-branch exact value `exp(-P/24)`; engineering chart values scale as `N_coh^-1`.\n- **[Thinking as Patch-Net Fixed-Point Search](extra/thinking_as_patch_net_fixed_point_search.pdf)**: cognition and qualia as recurrent patch consensus.\n\n## More\n\n- **Website:** [floatingpragma.io/oph](https://floatingpragma.io/oph)\n- **Theory explainer:** [floatingpragma.io/oph/theory-of-everything](https://floatingpragma.io/oph/theory-of-everything)\n- **Simulation-theory explainer:** [floatingpragma.io/oph/simulation-theory](https://floatingpragma.io/oph/simulation-theory/)\n- **Coherence map:** [coherence.floatingpragma.io](https://coherence.floatingpragma.io): public graph surface for OPH concepts, overlaps, and cross-domain routes.\n- **Applications:** [omega.floatingpragma.io](https://omega.floatingpragma.io): public applications page for OPH hardware, compute, energy, AGI, lift, and optical chamber consensus.\n- **Three-body OPH demo:** [3body.floatingpragma.io](https://3body.floatingpragma.io): an extra simulator and proof walk-through for the OPH finite patch-net formulation of the three-body problem, framed as a loop-holonomy gluing example. No closed-form elementary solution is claimed.\n- **Blog:** [blog.floatingpragma.io](https://blog.floatingpragma.io/) collects public OPH essays. Start with [Semiotics and the Physics of Meaning](https://blog.floatingpragma.io/semiotics-and-the-physics-of-meaning), [The Trigger](https://blog.floatingpragma.io/the-trigger), and [P = NP on the Observer Screen](https://blog.floatingpragma.io/p-equals-np-on-the-observer-screen). The computation essay treats `P = NP` as an observer-screen slogan, not a claim to solve the classical complexity problem.\n- **Book:** [oph-book.floatingpragma.io](https://oph-book.floatingpragma.io)\n- **Guided study app:** [learn.floatingpragma.io](https://learn.floatingpragma.io/)\n- **Questions and detailed explanations:** OPH Sage on [Telegram](https://t.me/HoloObserverBot), [X](https://x.com/OphSage), or [Bluesky](https://bsky.app/profile/ophsage.bsky.social)\n- **OPH Notebook:** [NotebookLM source notebook](https://notebooklm.google.com/notebook/d5249760-6ce8-44a0-927b-ccf90402711a) with explainer videos and additional study material.\n- **Lab:** [oph-lab.floatingpragma.io](https://oph-lab.floatingpragma.io)\n- **Common objections:** [extra/COMMON_OBJECTIONS.md](extra/COMMON_OBJECTIONS.md)\n- **IBM Quantum note:** [extra/IBM_QUANTUM_CLOUD.md](extra/IBM_QUANTUM_CLOUD.md)\n\n## Status Table\n\nThe fine-structure display row uses the fixed-point value\n$\\alpha^{-1}(0)=137.035999177(21)$ and\n$P\\simeq1.6309682094$. The source-side audit and endpoint residual records\nlive in the particle paper, where they are kept separate from the public\nfixed-point row.\n\nThe weak-boson pair is a validation row. Charged-lepton absolute masses are\ntarget-anchored witness rows. The auxiliary direct-top average is a validation\nrow. Hadron-controlled rows use the policy in [`HADRON.md`](HADRON.md):\nsource-only OPH values stay separate from OPH plus empirical hadron closure\nvalues carried by the empirical $e^+e^-\\to\\mathrm{hadrons}$ payload class.\n\nStrong CP is work in progress in the selected-class quark theorem:\nthe available corpus does not derive the QCD theta angle, does not emit the\nphysical strong-CP angle, and does not prove that the physical strong-CP phase\nvanishes. The required bridge is the phase, anomaly, and topological-angle\ndescent on the realized branch.\n\n## Repository Guide\n\n- **[`paper/`](paper):** PDFs, LaTeX sources, and release metadata.\n- **[`APPLICATIONS.md`](APPLICATIONS.md):** high-level application map for\n  OPH energy, compute, AGI, and local-lift use cases.\n- **[`book/`](book):** OPH Book source and generated downloadable PDF. Print-PDF build notes live in [`book/README.md`](book/README.md).\n- **[`code/`](code):** computational material, particle outputs, and experiments.\n- **[`HADRON.md`](HADRON.md):** policy for QCD-limited particle rows, empirical\n  $e^+e^-\\to\\mathrm{hadrons}$ input, and fine-structure hadron closure.\n- **[`assets/`](assets):** public diagrams and figures.\n- **[`extra/`](extra):** maintained public notes such as objections, experimental write-ups, and selected supporting essays.\n\n## OPH and the Sciences\n\n\u003cp align=\"center\"\u003e\n  \u003ca href=\"assets/oph_science_overlap_map_poster.png\" target=\"_blank\" rel=\"noopener noreferrer\"\u003e\n    \u003cimg src=\"assets/oph_science_overlap_map.svg\" alt=\"A map of the sciences OPH overlaps with, from large domains to subdomains to concrete OPH application areas.\" width=\"100%\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\u003csub\u003eA domain -\u003e subdomain -\u003e OPH-area map spanning mathematics, computer science, information and inference, complex systems, theoretical physics, quantum information, and measurement foundations. Click to open the full poster PNG.\u003c/sub\u003e\u003c/p\u003e\n\n## License And Patent Policy\n\nThe authored material in this repository is licensed under\n[CC BY-NC-SA 4.0](LICENSE), with the repository-wide\n[OPH Open Use And Anti-Patent Covenant](PATENTS.md) applying to OPH-derived\nideas, implementations, devices, methods, applications, software, simulations,\nand hardware designs.\n\nIn short: OPH is published so the mathematics, software, applications, devices,\nhardware designs, simulations, engineering methods, and experimental\nimplementations can be studied, tested, implemented, modified, deployed,\nmanufactured, and shared. OPH-derived work may not be used to create private\npatent monopolies or patent claims that restrict others from practicing OPH.\n\nSee [PATENTS.md](PATENTS.md) for the canonical policy text and copy/paste\nwebsite notices.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ffloatingpragma%2Fobserver-patch-holography","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ffloatingpragma%2Fobserver-patch-holography","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ffloatingpragma%2Fobserver-patch-holography/lists"}